1、Information needed to predict what a reactor can doReactorInputOutputPerformance equationRelates input to outputContacting pattern or how materials flow through and contact each other in the reactor Kinetics or how fast things happen.If very fast,then equilibrium tells what will leave the reactor.If
2、 not so fast,then the rate of chemical reaction,and maybe heat and mass transfer too,will determine what will happen.output=input,kinetics,contactingf第1页，共72页。Fluidized Bed Reactor第2页，共72页。Case 1Case 2Case 3第3页，共72页。RTDs of gas and solidsGas RTDsSolids RTDsBi-modal RTD第4页，共72页。Mixing in disc impelle
3、r systems Tilted configuration Structure in an eccentric stirred tank Concentric orbits in a 3-disc systemhttp:/sol.rutgers.edu/shinbrot/Group_Index.html第5页，共72页。高粘体系的液体高粘体系的液体混合现象混合现象第6页，共72页。第7页，共72页。Chapter 9 Distributions of Residence Times for Chemical Reactors第8页，共72页。Overview Nonideal reactor
4、s Part-1:characterize(non)ideal reactorsResidence Time Distribution(RTD),E(t)Mean residence time,tmVariance,2 Cumulative distribution function,F(t)Part-2:predict conversion and exit concentrations based on RTDRTD not unique models第9页，共72页。Part 1 Characterization and Diagnostics第10页，共72页。9.1 General
5、characteristics Two major uses of the RTD to characterize nonideal reactors1.To diagnose problems of reactors in operation2.To predict conversion or effluent concentration in existing/available reactors when a new reaction is used in the reactorExamples:Channeling Tank reactorDead zoneBypassing第11页，
6、共72页。第12页，共72页。第13页，共72页。第14页，共72页。第15页，共72页。The three concepts RTD Mixing Model-To describe the deviations from the mixing patterns assumed in ideal reactors-To characterize the mixing in nonideal reactors第16页，共72页。9.1.1 RTD functionResidence time:the time the atoms spent in the reactorPlug-flow re
7、actor,batch reactorAll the atoms in the reactors have the same residence timeCSTRFeeds mixed immediately,but withdrawn continuously“RTD”:some molecules leave quickly,others overstay their welcome.RTD:a characteristic of the mixing that occurs in a chemical reactor 第17页，共72页。9.2 Measurement of the RT
8、D RTD is determined experimentally by injecting an inert chemical,molecule,or atom,called a tracer,into the reactor at some time t=0 and then measuring the tracer concentration,C,in the effluent stream as a function of time Tracer:nonreactive,easily detectable,similar physical properties to the flui
9、d,no adsorption on the walls or surfaces,etc.Pulse input and Step input阶跃注入脉冲注入第18页，共72页。9.2.1 Pulse input experimentReactorFeedInjectionDetectionEffluentCCtCCtttPulse injectionStep injectionStep responsePulse response第19页，共72页。CCttPulse injectionPulse response()NC ttOnly flow carries tracer(No diff
10、usion)00()NC ttNN0()()C tE tN0()NE ttNE(t):resident time distribution functionhow much time different fluid elements have spent in the reactor第20页，共72页。()dNC t dtC(t)tPulse response00()NC t dt0()1E t dt0()()()C tE tC t dtE(t)tFraction of material leaving the reactor that has resided in the reactor f
11、or times between t1 and t221()ttE t dtt1t2第21页，共72页。Problems using Pulse input:“Pulse”:can be hard to obtain a reasonable pulse at the injection point Long tails of the measured C(t)curve第22页，共72页。0()()()toutinCtCtt E t dtConvolution integral（卷积）Pulse Imperfect pulseStepA general description:Output
12、concentration Input concentrationInput0()()()toutinCtCt E tt dtEquivalent form第23页，共72页。9.2.2 Step tracer experimentCCttStep injectionStep response00step0step()()()toutoutCE t dtF tCCF tC0()()stepdC tE tdtC00()()toutCtCE t dtStep injectionAdvantage of F(t):easier experimentsDrawbacks:differentiation
13、error large amount of tracer 第24页，共72页。第25页，共72页。第26页，共72页。0()()()toutinCtCtt E t dt第27页，共72页。第28页，共72页。9.3 Characteristics of the RTDE(t):exit-age distribution function,age distribution of the effluent stream i.e.,the lengths of time various atoms spend at reaction conditions第29页，共72页。9.3.1 Integra
14、l relationshipsThe cumulative RTD function F(t)0 Fraction of effluent()that has been in reactor()for less than time tE t dtF tt Fraction of effluent()that has been in reactor1()for longer than time tE t dtF tt 第30页，共72页。9.3.2 Mean residence time000()()()mtE t dtttE t dtE t dtThe first moment gives t
15、he average time the effluent molecules spent in the reactor.Space time or average residence time,=V/In the absence to dispersion,for constant volumetric flow,=0=tm第31页，共72页。9.3.3 Other moments of the RTD220()()mttE t dtThe second moment about the mean is the variance333/201()()msttE t dtThe third mo
16、ment,skewnessThe two parameters most commonly used to characterize the RTD are and 2.第32页，共72页。9.3.4 Normalized RTD function,E()t()()EE t:represents the number of reactor volumes of fluid based on entrance conditions that have flowed through the reactor in time t.Why we use a normalized RTD?The flow
17、 performance inside reactors of different sizes can be compared directly.Example:all perfectly mixed CSTR:0()1Ed/1()tE te()()EE te 第33页，共72页。9.3.5 Internal-age distribution,I():represents the age of a molecule inside the reactorI():the fraction of material inside the reactor that has been inside the
18、 reactor for a period time between and+()(1()/IF()()dEId/1()Ie CSTR:P633推导过程推导过程第34页，共72页。0()()tF tE t dt第35页，共72页。9.4 RTD in ideal reactors9.4.1 RTDs in batch and plug-flow reactors()()E ttPlug flow reactor:0 when 0()when 0 xxx()1x dx()()()g xxdxgProperties of Dirac delta function0()()mttE t dtttdt
19、220()()0ttdtFor plug flow第36页，共72页。E(t)tOutF(t)t1.0第37页，共72页。9.4.2 Single-CSTR RTD0dCCVdt/0()tC tC eIn Out=Accumulation/0/000()()()tttC eC teE tC t dtC edt/()()teE tEe/00()tmtttE t dtedt22/22200()(1)txtedtxe dxFrom tracer experiment:第38页，共72页。E()F()1.01.0第39页，共72页。第40页，共72页。9.4.3 Laminar flow reacto
20、r2220maxavg221211rrrUUURRRRU22201()()21(/)21(/)LR Lt rU rr Rr R00()2()dU rrdr0()dE t dt222224/24.1/tdtrdrrdrRRr R第41页，共72页。22320/2/2()()0()124tttF tE t dtE t dtdttt 222300022()42dLrdrLRE t dtdtdttttt23()2E tt22maxavg0222LLRVtUUR230 2()22tE ttt222/2/2/21()22mdtttE t dtttThe minimum time the fluid may
21、 spend in the reactor:第42页，共72页。30 0.5()1 0.52E 20 0.5()11 0.54F 0.5E()0.5F()1PFRCSTRLFRNormalized RTD function for a laminar flow reactor第43页，共72页。9.5 Diagnostics and troubleshooting9.5.1 General comments第44页，共72页。9.5.2 Simple diagnostics and troubleshooting using the RTD for ideal reactorsA.The CS
22、TR(a)Perfect operation (P)(b)Bypassing(BP)第45页，共72页。(c)Dead volume(DV)Summary第46页，共72页。B.Tubular reactor(a)Perfect operation of PFR(P)(b)PFR with channeling(Bypassing,BP)第47页，共72页。(c)PFR with dead volume(DV)Summary第48页，共72页。9.5.3 PFR/CSTR series RTD-()/0 ()psPtPstE tetCSTR+PFRPFR+CSTRRTD is not uniq
23、ue to a particular reactor sequence.CSTRPFRPFRCSTRE(t)tPFR1/CSTR第49页，共72页。Example:comparing second-order reaction systemsCSTR+PFRPFR+CSTRCSTRPFRPFRCSTR(1)(2)第50页，共72页。Part 2Predicting Conversion and Exit Concentration第51页，共72页。9.6 Reactor modeling using the RTDRTD+Model+Kinetic data Exit conversion
24、and Exit concentrationModels for predicting conversion from RTD data1.Zero adjustable parametersa.Segregation modelb.Maximum mixedness model2.One adjustable parameter a.Tanks-in-series model b.Dispersion model3.Two adjustable parameters Real reactors modeled as combinations of ideal reactorsRTD:tell
25、s how long the various fluid elements have been in the reactor,but does not tell anything about the exchange of matter between the fluid elements(i.e.,the mixing)第52页，共72页。(1)dXkXdtMixing of reacting species:one of the major factors controlling the behavior of chemical reactors.For first-order react
26、ions,Conversion is independent of concentrationOnce the RTD is determined,the conversion can be predicted.For reactions other than first order,RTD is not sufficient.Model:to account for the mixing of molecules inside the reactor第53页，共72页。Macromixing:Produces a distribution of residence times without
27、,however,specifying how molecules of different ages encounter one another in the reactor.Micromixing:Describes how molecules of different ages encounter one another in the reactor.Two extremes:(1)Complete segregation:All molecules of the same age group remain together as they travel through the reac
28、tor and are not mixed with any other age until they exit the reactor(2)Complete micromixing:Molecules of different age groups are completely mixed at the molecular level as soon as they enter the reactor.第54页，共72页。9.7 Zero-parameter models9.7.1 Segregation modelMixing of the globules of different ag
29、es occurs here.Mixing occurs at the latest possible moment.Each little batch reactor(globule)exiting the real reactor at different times will have a different conversion.(X1,X2,X3.)第55页，共72页。RTD+Model+Kinetic data Exit conversion and Exit concentrationMean conversion of those globules spending betwe
30、en time t and t+dt in the reactor=Conversion achieved in a globule after spending a time t in the reactorXFraction of globules that spend between t and t+dt in the reactor()()d XX t E tdt()()d XX tE t dt0()()XX t E t dtSegregation model第56页，共72页。第57页，共72页。Summary:if we have the RTD,the reaction rate
31、 expression,then for a segregated flow situation(i.e.,model),we have sufficient information to calculate the conversion.Consider a first-order reaction:(1)dXkXdtAproductsk For a batch reactor:AAdNr Vdt For constant volume and with NA=NA0(1-X)A0AAAA01dXNr VkC VkNkNXdt 1ktX te solutionMean conversion
32、for a first-order reaction0000()()(1)()()()ktktXX t E t dteE t dtE t dteE t dt01()ktXeE t dt 第58页，共72页。Example:Applications of the segregation model for an ideal PFR,a CSTR,and a laminar flow reactor(first-order reaction)()()E tt(1)PFR:00()()1()ktXX t E t dteE t dt 01()ktXetdt 11kDaXee 11kDaXee Chap
33、ter 4(2)CSTR:/1()tE te0(1/)0(1/)01()11111/ktk tktXeE t dteXdtXek 11kDaXkDa1kXkChapter 4第59页，共72页。(3)Laminar flow reactor230 for(/2)()for(/2)2tE ttt30 for(0.5)()1 for(0.5)2E 001()1()ktkXeE t dteEd 30.512keXd 0.520.51(1 0.5)(0.5)kkeXk ekd Hilder,M.H.Trans.IchemE 59 p143(1979)第60页，共72页。第61页，共72页。9.7.2
34、Maximum mixedness modelSegregation model:mixing occurs at the latest possible point.Maximum mixedness model:mixing occurs at the earliest possible point.Segregation modelMaximum mixedness model第62页，共72页。0()dEd 00()1()EdF01()VF01()AArVrFThe volume of fluid with a life expectancy between and+The rate
35、of generation of the substance A in this volume:第63页，共72页。000001()|()1()|1()0AAAAFCC EFCrF0()()1()AAAAdCErCCdF 00()1()AAAdXECrCXdF 0()()1()AArdXEXdCFMaximum mixedness gives the lower bound on conversion(X)when n1.Mole balance第64页，共72页。9.7.3 Segregation vs.maximum mixedness predictions2A2A0rCsegmmXXI
36、fthen2A2A0rCmmsegXX2A2A0rCmmsegXXAAnrkCA1AAnrnkCC 2A2A2A1nrn nkCC1n 2A2A0rCsegmmXX0n 2A2A0rCsegmmXX01n2A2A0rCmmsegXX第65页，共72页。O.Levenspiel,P358(a)(b)(c,d,e)第66页，共72页。9.8 Using software packagesRead CD.第67页，共72页。9.9 RTD and multiple reactionsFor multiple reactions use an ODE solver to couple the mole
37、 balance equations,dCi/dt=ri(where ri is the net rate of reaction).Segregation model0()()AACCt E t dt0()()BBCCt E t dt1i qAAiAidCrrdt1i qBBiBidCrrdt()()AAdCCt E tdt()()BBdCCt E tdt第68页，共72页。Maximum mixedness model0()()1()AiAAAdCErCCdF 0()()1()BiBBBdCErCCdF 第69页，共72页。Summary1.E(t)dt:fraction of mater
38、ial exiting the reactor that has spent between time t and t+dt in the reactor.2.The mean residence time0()mttE t dt3.The variance about the mean residence time isis equal to the space time for constant volumetric flow,=0 220()()mttE t dt4.The cumulative distribution function F(t)gives the fraction o
39、f effluent material that has been in the reactor a time t or less:1()fraction effluent material that has been in the reactor a time or longerF tt 0()tF tE t dt第70页，共72页。5.The RTD functions for an ideal reactor are()()E ttPlug flowCSTR/()teE tLaminar flow ()02E tt2 3()22E ttt6.The dimensionless resid
40、ence time ist()()EE t 7.The internal-age distribution,I(),gives the fraction of material inside the reactor that has been inside between a time and a time+d第71页，共72页。8.Segregation model0()()XX t E t dtFor multiple reactionsAA0()()CCt E t dt9.Maximum mixedness:0()()1()AAdXrEXdCFFor multiple reactionsA0()()1()netAAAdCErCCdF 0()()1()netBBBBdCErCCdF 第72页，共72页。
