反应工程基础(程易)cha

回顾 1 基本概念 解题思路 解题思路 基本环节 设计方程 CSTR PFR Batch 1级和2级反应 恒容变容 熟记 熟知 熟查 2 膨胀因子 膨胀率 3 理想反应器 极端行为 CSTR PFR 实际反应器 4 教学与学习 A 科学概念 知识库 B 技能 解决问题的能力 思路 细节 实验解析数值 工具 i C 相关的数学 0维 CSTR代数方程 组 1维 PFR常微分方程 组 2维 2D PFR偏微分方程 组 直接求解迭代 试差 直接解析数值解 如Matlab 直接解析 如拉氏变换 数值解 如COMSOL D 收获 知识 方法论 信心 物理 建模 求解 应用 Chapter8Steady StateNonisothermalReactorDesign Overview HeateffectsinchemicalreactorsMolebalancesRatelawsStoichiometryEnergybalance Objectives DescribethealgorithmforCSTRs PFRs andPBRsthatarenotoperatedisothermally SizeadiabaticandnonadiabaticCSTRs PFRs andPBRs Usereactorstagingtoobtainhighconversionsforhighlyexothermicreversiblereactions CarryoutananalysistodeterminetheMultipleSteadyStates MSS inaCSTRalongwiththeignitionandextinctiontemperatures AnalyzemultiplereactionscarriedoutinCSTRs PFRs andPBRswhicharenotoperatedisothermallyinordertodeterminetheconcentrationsandtemperatureasafunctionofposition PFR PBR andoperatingvariables UseCOMSOLtosolveforbothaxialandradialtemperatureandconcentrationprofiles 8 1Rationale infonecessarytodesignnonisothermalreactors Example highlyexothermicreaction adiabatic plug flowreactor Tocalculatethereactorvolumenecessaryfor70 conversion A B 1 Molebalance designequation 2 Ratelaw Arrheniusequation 3 Stoichiometry liquidphase 4 Combining Tvariesalongthelengthofthereactor kwillalsovary Tosolvethis weneedanotherrelationshipbetweenXandT orTandV 5 Energybalance T0 enteringtemperature HRx heatofthereaction CPA heatcapacity 8 2Theenergybalance 8 2 1Firstlawofthermodynamics Foraclosedsystem nomasscrossesthesystemboundaries Totalenergyofthesystem Heatflowtothesystem Workdonebythesystemonthesurroundings notexactdifferentialsofastatefunction Opensystem acontinuous flowreactor Energybalanceonanopensystem Rateofaccumulationofenergywithinthesystem Rateofflowofheattothesystemfromthesurroundings Rateofworkdonebythesystemonthesurroundings Rateofenergyaddedtothesystembymassflowintothesystem Rateofenergyleavingthesystembymassflowoutofthesystem Unit Joule s Energybalanceonawell mixedopensystem schematic Thestartingpoint Howtoexpresstheseterms 8 2 2Evaluatingtheworkterm FlowworkandShaftwork P pressure Pa Flowworkunit Flowwork combinedwiththosetermsintheenergybalancethatrepresenttheenergyexchangebymassflowacrossthesystemboundaries Inalmostallchemicalreactorsituations thekinetic potential and other energytermsarenegligibleincomparisonwiththeenthalpy heattransfer andworkterms andhence Enthalpy J mol Enthalpy 0 inletconditions 8 2 4Dissectingthesteady statemolarflowratestoobtaintheheatofreaction Steady stateenergybalance In Out Expressingmolarflowratesintermsofconversion Reaction HeatofreactionattemperatureT Steady stateenergybalance 8 2 5Dissectingtheenthalpies Calculateenthalpywhenphasechangesareinvolved EnthalpyofspeciesiinthegasatT EnthalpyofformationofspeciesiinthesolidphaseatTR HQinheatingsolidfromTRtoTm HeatofmeltingatTm HQinheatinggasfromTbtoT HeatofvaporationatTb HQinheatingliquidfromTmtoTb Example Ifnophasechange Meanheatcapacity Phasechangeconsidered Whenreactingfluidisheatedwithoutphasechangefromentrancetemperature Ti0 toatemperatureT Assumption CPi const ormean Thenext Alreadyknown 8 2 6Relating HRx T H Rx TR and CP HeatofreactionattemperatureT Energybalanceintermsofmeanorconstantheatcapacities Lastpage Seeexample P338 339 i e 8 3Adiabaticoperation 8 3 1Adiabaticenergybalance Assume T XEB CSTRPFRPBRBatch X T Linearrelationship XEB conversionfromEnergyBalance small Example Effectofinerts Thefollowingconversiontemperaturerelationshipisforanadiabaticreaction A B containing50 inerts SketchXvs Tforwhentheinertsareincreasedto75 whentheinertsaredecreasedto25 Solution Thefollowingconversiontemperaturerelationshipisalsoforanadiabaticreaction A B containing50 inerts Example cont d Solution Note TheinertsNEVERenterintothesecalculationsof or SketchXvs Tforwhentheinertsareincreasedto75 whentheinertsaredecreasedto25 Asyouincreaseinerts thereismoresensibleheattosupplythereactionandthetemperaturedoesnotdropasmuchwhentheinertsareincreased 8 3 2Adiabatictubularreactor EnergybalanceforadiabaticoperationofPFR Differentialmolebalance AdiabaticPFR PBRalgorithm Theelementaryreversiblegas phasereaction PressuredropneglectedPureAenters Molebalance Ratelaw With Stoichiometry Gas Combine Energybalance IfpureAentersandiff CP 0 then Example p353 357 VCSTRvs VPFR AlgorithmAdiabaticReactions 1 ChooseX CalculateT Calculatek CalculateT To CalculateCA CalculateCB CalculateKC Calculate rA 2 IncrementXandthenrepeatcalculations 3 Whenfinished plot vs XorusenumericaltechniquetofindV LevenspielPlotforanexothermic adiabaticreaction Consider PFR Shadedareaisthevolume Foranexitconversionof40 Foranexitconversionof70 CSTR Foranexitconversionof40 Foranexitconversionof70 CSTR PFR Foranintermediateconversionof40 andexitconversionof70 ThebestarrangementisaCSTRwitha40 conversionfollowedbyaPFRupto70 conversion 8 4Steady statetubularreactorwithheatexchange V FA0T0 FAeTe T 8 4 1DerivingtheenergybalanceforaPFR Expanding where PFRenergybalance PBRenergybalance A B C Coupleddifferentialequations Ifcoolanttemperaturevariesdownthereactor Thenext 8 4 2Balanceonthecoolantheattransferfluid FA0 T0 Tao Ta Tao HeattransferfluidR2 ReactantsR1 CaseA Co currentflow RateofenergyinatV RateofenergyoutatV V RateofheataddedbyconductionthroughTheinnerwall 0 VariationofcoolanttemperatureTadownthelengthofreactor exothermic endothermic V Ta Ta V and CaseB Countercurrentflow Solutiontothiscountercurrentflowproblemtofindtheexitconversionandtemperaturerequiresatrial and errorprocedure 1 Ta0 300K 2 Ta2 340K 3 T a0 310K 4 Ta2 330K 5 Ta0 300K TrialandErrorprocedureforcountercurrentflowproblems 4 NowguessacoolanttemperatureatV 0andX 0of330K WeseethattheexitcoolanttemperatureofTa2 330KwillgiveacoolanttemperatureatV V1of300K 1 ConsideranexothermicreactionwherethecoolantstreamentersattheendofthereactoratatemperatureTa0 say300K 2 Assumeacoolanttemperatureattheentrance X 0 V 0 tothereactorTa2 340K 3 CalculateX T andTaasafunctionofV Wecanseethatourguessof340KforTa2atthefeedentrance X 0 givesacoolanttemperatureof310K whichdoesnotmatchtheactualenteringcoolanttemperatureof300K ExampleP360 365 8 5Equilibriumconversion Forreversiblereactions theequilibriumconversion Xe isusuallycalculatedfirst Forendothermicreactions XeincreaseswithincreasingtemperatureForexothermicreactions Xedecreaseswithincreasingtemperature Example Ratelaw Concentrationequilibriumconstant Van tHoffEquation Forthespecialcaseof IntegratingtheVan tHoffEquationgives 8 5 1Adiabatictemperatureandequilibriumconversion Exothermicreactions T0 T01 Xe Energybalance Adiabatictemp Equilibrium T01 T0 For1st orderreaction MakeXe Tcurve Reactorstagingwithinterstagecoolingorheating Higherconversionscanbeachievedforadiabaticoperationbyconnectingreactorsinserieswithinterstagingcooling T Equilibrium X Endothermicreactions Interstageheating X T 8 5 2Optimumfeedtemperature Whyisthereamaximumintherateofreactionwithrespecttoconversion hencewithrespecttotemperatureandreactorvolume foranadiabaticreactor Exothermic ReversibleReaction RateLaw T Equilibrium X T03 T02 T01 Xe3 Xe2 Xe1 Fixedreactorsizeorcatalystweight Exothermic ReversibleReaction X V X3 T03 X2 T02 X1 T01 T0 rA Reactorexit T01 T02 T03 X T CurveA Reactionrateslow conversiondictatedbyrateofreactionandreactorvolume Astemperatureincreasesrateincreasesandthereforeconversionincreases CurveB Reactionrateveryrapid Virtualequilibriumreachedinreactionconversiondictatedbyequilibriumconversion OptimumInletTemperature FixedVolumeExothermicReactor 8 6CSTRwithheateffects CSTRmolebalance Note CSTR wellmixedwithuniformtemperature butreactioncanbecarriedoutnon isothermally Isothermaloperation feedtemperature temperatureinCSTR termintheCSTR 8 6 1Heataddedtothereactor Forexothermicreactions Forendothermicreactions X T Ta1 Ta2 T0 FA0 T X Heatexchanger Rateofenergyinbyflow Rateofenergyoutbyflow Rateofheattransferfromexchangertoreactor 0 HeattransfertoaCSTR Ataquasi steadystate Forlargevaluesofthecoolantflowrate where Forlargecoolantflowrate Designequation 8 6CSTRwithheateffects 8 7Multiplesteadystates X T Ta1 Ta2 T0 FA0 T X Forlargecoolantflowrate CSTR FormsoftheenergybalanceforaCSTRwithheatexchange Example AdiabaticLiquidPhaseinaCSTR SecondOrderReactionCarriedOutAdiabaticallyinaCSTR Theacid catalyzedirreversibleliquid phasereaction ThereactionissecondorderinA Thefeed whichisequimolarinasolvent whichcontainsthecatalyst andA entersthereactoratatotalvolumetricflowrateof10dm3 minwiththeconcentrationofAbeing4M Theenteringtemperatureis300K a WhatCSTRreactorvolumeisnecessarytoachieve80 conversion b Whatconversioncanbeachievedina1000dm3CSTR Whatisthenewexittemperature c Howwouldyouranswerstopart b change iftheenteringtemperatureofthefeedwere280K AdditionalInformation Solution 1 CSTRDesignEquation 2 RateLaw 3 Stoichiometry liquidphase 4 Combine 5 DetermineT 380K a WhatCSTRreactorvolumeisnecessarytoachieve80 conversion 6 SolvefortheRateConstant k atT 380K 7 CalculatetheCSTRReactorVolume V Solution b Whatconversioncanbeachievedina1000dm3CSTR Whatisthenewexittemperature 1 CSTRDesignEquation 2 RateLaw 3 Stoichiometry liquidphase 4 Combine NOTE Wewillfinditmoreconvenienttoworkwiththisequationintermsofspacetime ratherthanvolume Givenreactorvolume V youmustsolvetheenergybalanceandthemolebalancesimultaneouslyforconversion X sinceitisafunctionoftemperature T Analysis 5 SolvetheEnergyBalanceforXEBasafunctionofT Fromtheadiabaticenergybalance asappliedtoCSTRs 6 SolvetheMoleBalanceforXMBasafunctionofT 7 PlotXEBandXMB PlotXEBandXMBonthesamegraph asfunctionsofT toseewheretheyintersect Thiswilltellyouwhereyoursteady statepointis X 0 87andT 387K c Howwouldyouranswerstopart b change iftheenteringtemperatureofthefeedwere280K Solution 1 CSTRDesignEquation 2 RateLaw 3 Stoichiometry liquidphase 4 Combine Givenreactorvolume V youmustsolvetheenergybalanceandthemolebalancesimultaneouslyforconversion X sinceitisafunctionoftemperature T 5 SolvetheEnergyBalanceforXEBasafunctionofT 6 SolvetheMoleBalanceforXMBasafunctionofT 7 PlotXEBandXMB X 0 062atT 286K stable X 0 38atT 318K unstable X 0 75atT 355K stable X 0 062atT 286K stable X 0 38atT 318K unstable X 0 75atT 355K stable 1 SolvetheEnergyBalanceforXEBasafunctionofT 2 SolvetheMoleBalanceforXMBasafunctionofT Start upofaCSTRwheretherearethreesteadystatesolutions 8 7Multiplesteadystates SteadystateoperationofaCSTRinwhichafirst orderreactionistakingplace then where If Molebalance Heatgeneratedterm Heatremovedterm Varyenteringtemperature R T T IncreaseT0 8 7 1Heatremovedterm R T Varynon adiabaticparameter R T T Increase T0 Ta 0 8 7 2Heatofgeneration G T For1st orderliquidphasereaction Lowtemperature Hightemperature LowT HighT G T T T LowE HighE G T Increase Heatgeneratedcurves G T For2nd orderliquidphasereaction 8 7 3Ignition extinctioncurve IntersectionofR T andG T thetemperatureatwhichthereactorcanoperateatsteadystate R T G T TC1 TC2 TS2 TS3 R T G T Ignition extinctioncurve TS1 Ts T0 1 2 3 4 5 6 7 8 9 10 11 12 Uppersteadystate Lowersteadystate Unstablesteadystates R T G T R G G R R G G R Ignition extinctioncurve T01 T02 T03 T04 T05 T06 Ignitiontemp Extinctiontemp 8 7 4RunawayreactionsinaCSTR R T G T R T G T Runaway Slope TC T T AtT where DifferencebetweenthereactortemperatureandTC If isexceeded transitiontothe uppersteadystatewilloccur Formanyindustrialreactions E RTistypicallybetween16and24 andthereactiontemperaturesmaybebetween300to500K Consequently thiscriticaltemperaturedifferencewillbesomewherearound15to30 C Stabilitydiagram Toshowregionsofstableoperationandunstableoperation 2 1 3 4 5 G T 6 1st orderreaction Tc S S CP0 1 Runaway Unstable Stable Tc1 Tc2 Runawaywilloccur Norunaway won tmovetouppersteadystates PleaserefertoCD ProfessionalReferenceShelf 8 8Nonisothermalmultiplechemicalreactions Tietogetherallthepreviouschapterstoanalyzemultiplereactionsthatdonottakeplaceisothermally 8 8 1Energybalanceformultiplereactionsinplug flowreactors ForasinglereactioninaPFR ForqmultiplereactionsinthePFR Reaction1 Reaction2 PFRenergybalance qindependentreactions 8 8 2EnergybalanceformultiplereactionsinCSTR Forqreactionsandmspecies Tworeactions 8 9Radialandaxialvariationsinatubularreactor Overviewofenergybalances 1 Adiabatic CSTR PFR BatchorPBR Therelationshipbetweenconversionandtemperaturefor Foranexothermicreaction T XEB T0 2 CSTRwithheatexchanger 3 PFR PBRwithheatexchange andlargecoolantflowrate T Ta FA0T0 coolant PBR Ta PFR Ta 3A PBRintermsofconversion 3B PFRintermsofconversion 3C PBRintermsofmolarflowrates 3D PFRintermsofmo