化学反应工程原理课件 3-1

3StirredTankReactorsReactions

homogeneousheterogeneousModeofoperation

continuoussemi-batchbatch(CSTR)(BSTR)Assumption:Thecompositionandtemperatureareuniformeverywhereinthereactor,butmaychangewithtime.idealreactorTheeffectoftransportphenomena?no.Forhomogeneousreactions,3.1MaterialBalance

ForasystemwithMreactions,thenumberofkeycomponentsK

M.

Theregionforapplyingthebalances

(controlvolume)isthewholereactionvolumeV,Q0,ci0Q,ciVciinwhichthereactionrateisconstant.ThematerialbalanceforcomponentiisItisageneralequation.

Notethedifferencein

reactionvolumeVreactorvolumeVRQ0,ci0Q,ciVci

i=1,2,...K

(3.1)where(3.2)3.2IsothermalBSTR(singlereactions)3.2.1Reactiontimeandreactionvolume

1.Calculationforreactiontime

Thematerialbalancebecomes(3.5)WithnA=nA0(1

XA),(3.6)ThereactiontimeiswhichisapplicabletoanyBSTR,suchashomogeneousorheterogeneous,isothermalornon-isothermal.Abatchreactionistheonewithconstant-volume,nA0/V=cA0,sothat(3.7)(3.8)Foranorderirreversiblereaction,Thereactiontimeis(3.10)(3.11)(

1)For=1,(3.12)

2.Calculationforreactionvolume

Thereactionvolumeis

V=Q0(t+t0)

(3.13)whereQ0isthevolumetricflowrate,andt0isthetimefornonproductiveoperation,suchascharging,discharging,washing,andsoon.Theactualreactorvolumeis

VR＝V/f(3.14)wheref=0.40.8,loadingcoefficient.Example3.1

EsterifyingreactionwithaceticacidandalcoholinBSTR:

(A)

(B)

(R)

(S)production:12000kg/dayaceticether;massratiooffeed:A:B:S＝1:2:1.35;rateequation:

rA=k1(cAcB

cRcS/K)

wherek1=4.7610-4l/molmin,K=2.92;other:,

t0=1h,f=0.75,XA=0.35;Determine:

V,VR

CH3COOH+C2H5OH

CH3COOC2H5+H2OSolution:

ForaBSTR,V=Q0(t+t0).(1)calculatevolumetricflowrateQ0

FA=12000/(880.3524)=16.23kmol/h

Q0=16.23604.35/1020=4.155m3/h(2)concentrations

cA0=FA/Q0=16.23/4.155=3.908mol/l

cB0=3.908602/46=10.20mol/l

cS0=3.908601.35/18=17.59mol/l(3)calculatereactiontimet

t=7130s=1.98h(A)(B)(4)reactionvolumeV=Q0(t+t0)=4.155(1.98+1)=12.38m3(5)reactorvolume

VR=V/f=12.38/0.75=16.51m3Example3.1aInthesamereactor,ifXA=0.4,doestheoutputofR/dayincreaseordecrease?

ForXA=0.4,t=2.56h.feed:

Q0=V/(t+t0)m3/h

molesofAconverted:

Q0cA0XA=VcA0XA/(t+t0)kmol/houtputofR/day:

24VcA0XAMR/(t+t0)=11481kgExercises:Chap.3:1,2

3.2.2Optimumreactiontime

ForareactionAR,theobjectivefunctionistheoutputperunitoperatingtime,

FR=

VcR/(t+t0)

(kmol/h)(3.15)Takingthederivativewithrespecttot,(3.16)=0TheoptimumtimeshouldsatisfythefollowingconditionTheequationmaybesolvedbynumericalorgraphicalmethod.or(3.17)t0toptcopttcRtangent(XA)(XA)(Xopt)cROptimizationforothers:Fortheminimumoperatingcost,

theobjectivefunctionforoptimizationistheoperatingcost.Fortheminimumamountofrawmaterialperunitmassproduct,thelongerthereactiontime,thelessitis.Example3.1b

FindtheoptimumreactiontimeforthemaximumproductionofRperunitreactiontimeandtheconversion.ThereactiontimefromExample3.1isSolvedbytrialanderrormethod:TherateofformationofRis

VcA0XA/(t+t0)kmol/hXA

t/h

XA/(t+t0)

0000.10.3820.07240.20.8680.10710.31.530.11860.42.560.11240.311.610.11880.321.700.11853.3IsothermalBSTR(multiplereactions)3.3.1Parallelreactions

AP,

rP=k1cA

(desired)AQ,

rQ=k2cA

k1k2Materialbalances:A:(3.24)P:(3.25)Q:(3.26)

Fort=0,cA

=cA0

,

cP

=0,

cQ

=0,

determinethereactiontime.IntegrationofEq.(3.24)yields

(3.27)or(3.28)

cQ

=cA0

cA

cP

(3.29)(3.30)cPcQcA0cA0tProductdistribution:Forabovesimplecondition,

cP

/cO=k1/k2andwith(3.27)k1andk2canbedeterminedexperimentally.Example3.2

Forliquidreactions:A+BP,

rp=2cAkmol/m3h(desired)

2AQ,

rQ=0.5cA2

kmol/m3hI.C.:att=0,cA0=cB0=2kmol/m3.DetermineXAandYPatt=3h.Solution:TherateofconversionofAisRA=

rP

2rQ=2cA

cA2(A)Thematerialbalance

ofAisAtt=3h,

cA=2.482103

kmol/m3,

XA=0.9988.(C)Reactiontime:(D)Integration:ThematerialbalanceforPis=1.3838kmol/m3i.e.,

YP=1.3838/2=0.6919(E)(F)Eliminating

dtwithEqs.(C)and(E),wehave3.3.2Seriesreactions

APQMaterialbalances:k1k2A:(3.33)P:(3.34)I.C.:att=0,cA=cA0,cP=0,cQ=0.Reactiontime:ThematerialbalanceofPbecomes(3.36)i.e.,(3.35)(3.37)Fortheordinarydifferentialequation(ODE)Thegeneralsolutionis

y=eP(x)dx[Q(x)eP(x)dxdx+C]Productdistribution:

IfPisthedesiredproduct,thereisanoptimumreactiontime

topt.(k1

k2)(3.38)(k1

k2)(3.39)0tcA0cAcPcQ

DeterminationoftoptforintermediateproductP:

LettingdcP

/dt=0,weobtain

(k1

k2)(3.40)TheyieldofPis(3.64)APQk2>>k1

k2<<k1

k1k2(k1

k2)(3.38)Example3.3

NH3+CH3OHCH3NH2+H2OAmmoniaMethanolmo