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1、10.37ChemicalandBiologicalReactionEngineering,Spring2007Prof.WilliamH.GreenLecture1:Preliminaries&RemembranceofThingsPastThislecturecovers:reactionstoichiometry,lumpedstoichiometriesincomplexsystemssuchasbioconversionsandcellgrowth(yields),extentofreaction,independen
2、ceofreactions,measuresofconcentrations,singlereactionsandreactionnetworks,andbioreactionpathways.FoFAFigure1.AschematicofacontrolvolumewithinflowofFoandoutflowofspeciesA,FA.F=totalmolarflowrate(moles/sec)Fo=totalmolarflowrateenteringcontrolvolumeFA=molarflowrateofspe
3、ciesAFAo=molarflowrateofspeciesAenteringcontrolvolumeNA=MolesofspeciesAMassbalance:(changein“A”insidecontrolvolume)=(amountof“A”thatentered)-(amountof“A”thatexited)+(amountof“A”createdinsidethecontrolvolume)–(amountof“A”destroyedinsidethecontrolvolume)dNA=−FF+GAoAAdt
4、molesGA[]=secIfhomogeneous,Gr=VAAelse,Gr=dVAA∫whereVisvolumeandrAistherateofAcreatedordestroyed(moles/sec/volume).Themassbalancecanalsobewrittenas:convmection*(diffusion+(,dρA2=∇vDρρ+∇+rAAAdtwherevisvelocity,Disthediffusioncoefficient,andρAisthemolardensityofA(moles/
5、volume).Example:Citeas:WilliamGreen,Jr.,coursematerialsfor10.37ChemicalandBiologicalReactionEngineering,Spring2007.MITOpenCourseWare(http://ocw.mit.edu),MassachusettsInstituteofTechnology.Downloadedon[DDMonthYYYY].A+B→C+DmoleArAC=−kABr[][],,=+kAB[][][][]A=literwherek
6、isameasurablerateconstantthatchangeswithrespecttoTandPbutremainsconstantwithrespecttochangingconcentrations.IfrkAB=[][],then1m=−1rr=νAA,11whereνisthestoichiometriccoefficientforspeciesAinreaction1.Likewise,A,1m=+1rr=νCC,11Iftherearenreactionsinvolvingspecies“A”thennr
7、rAA=∑ν,iii=1Gt()=rxyzt(,,,)dxdydzAA∫∫∫%(&('Vol.-((,,,))(,,,)(,,,)kTxyztAxyztBxyzt[][]NVmAdA[]=−kAB[][]→*onlytrueiftherearenoflows!dtdNA=≈rdVrV,assumeristruethroughoutvolume∫AAAdtIfthesystemishomogeneousandtherearenoflows:dNA=rVAdtTherefore:d⎛⎞NA⎜⎟=riffhomogeneous,nof
8、low,constantVAdt⎝⎠VExtentofReactionξ[=]moles,extentofrxn.molesξ"[]=,rateofextentofrxn.secABCD+→+10.37ChemicalandBiologicalReactionE
