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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Information needed to predict what a reactor can do,Reactor,Input,Output,Performance equation,Relates input to output,Contacting 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 not so fast, then the rate of chemical reaction, and maybe heat and mass transfer too, will determine what will happen,.,Fluidized Bed Reactor,Case 1,Case 2,Case 3,RTDs of gas and solids,Gas RTDs,Solids RTDs,Bi-modal RTD,Mixing in disc impeller systems,Tilted configuration,Structure in an eccentric stirred tank,Concentric orbits in a 3-disc system,sol.rutgers.edu/shinbrot/Group_Index.html,高粘体系的液体,混合现象,Chapter 9 Distributions of Residence Times for Chemical Reactors,Overview,Nonideal reactors,Part-1:,characterize (non)ideal reactors,Residence Time Distribution (,RTD,),E,(,t,),Mean residence time,t,m,Variance,2,Cumulative distribution function,F,(,t,),Part-2:,predict conversion and exit,concentrations,based on RTD,RTD,not unique,models,Part 1 Characterization and Diagnostics,9.1 General characteristics,Two major uses of the RTD to characterize nonideal reactors,1. 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 reactor,Examples:,Channeling,Tank reactor,Dead,zone,Bypassing,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,9.1.1 RTD function,Residence time,: the time the atoms spent in the reactor,Plug-flow reactor, batch reactor,All the atoms in the reactors have the same residence time,CSTR,Feeds mixed immediately, but withdrawn continuously,“RTD”:,some molecules leave quickly, others overstay their welcome.,RTD,: a characteristic of the mixing that occurs in a chemical reactor,9.2 Measurement of the RTD,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 fluid,no adsorption on the walls or surfaces, etc.,Pulse input and Step input,阶跃注入,脉冲注入,9.2.1 Pulse input experiment,Reactor,Feed,Injection,Detection,Effluent,C,C,t,C,C,t,t,t,Pulse injection,Step injection,Step response,Pulse response,C,C,t,t,Pulse injection,Pulse response,Only flow carries tracer,(No diffusion),E(t): resident time distribution function,how much time different fluid elements have spent in the reactor,C(t),t,Pulse response,E(t),t,Fraction of material leaving the reactor that has resided in the reactor for times between,t,1,and,t,2,t,1,t,2,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,Convolution integral,（卷积）,Pulse,Imperfect pulse,Step,A general description:,Output concentration Input concentration,Input,Equivalent form,9.2.2 Step tracer experiment,C,C,t,t,Step injection,Step response,Step injection,Advantage of F(t): easier experiments,Drawbacks:,differentiation,error,large amount of tracer,9.3 Characteristics of the RTD,E(t): exit-age distribution function,age distribution of the effluent stream,i.e.,the lengths of time various atoms spend,at reaction conditions,9.3.1 Integral relationships,The cumulative RTD function,F,(,t,),9.3.2 Mean residence time,The first moment,gives the 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, =,t,m,9.3.3 Other moments of the RTD,The,second moment,about,the mean is the,variance,The,third moment,skewness,The two parameters most commonly used to characterize the RTD are, and ,2,.,9.3.4 Normalized RTD function,E,(,),: 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 performance inside reactors of different sizes can be compared directly.,Example: all perfectly mixed CSTR:,9.3.5 Internal-age distribution,I,(,),: represents the age of a molecule inside the reactor,I(,),: the fraction of material,inside the reactor,that has been inside the reactor for a period time between and + ,CSTR:,P633,推导过程,9.4 RTD in ideal reactors,9.4.1 RTDs in batch and plug-flow reactors,Plug flow reactor:,Properties of Dirac delta function,For plug flow,E(t),t,Out,F(t),t,1.0,9.4.2 Single-CSTR RTD,In Out = Accumulation,From tracer experiment:,E(,),F(,),1.0,1.0,9.4.3 Laminar flow reactor,U,The minimum time the fluid may spend in the reactor:,0.5,E(,),0.5,F(,),1,PFR,CSTR,LFR,Normalized RTD function for a laminar flow reactor,9.5 Diagnostics and troubleshooting,9.5.1 General comments,9.5.2 Simple diagnostics and troubleshooting using the RTD for ideal reactors,A. The CSTR,Perfect operation,(P),(b) Bypassing (BP),(c) Dead volume (DV),Summary,B. Tubular reactor,(a) Perfect operation of PFR (P),(b) PFR with channeling (Bypassing, BP),(c) PFR with dead volume (DV),Summary,9.5.3 PFR/CSTR series RTD,CSTR + PFR,PFR + CSTR,RTD is not unique to a particular reactor sequence.,CSTR,PFR,PFR,CSTR,E(t),t,PFR,1/,CSTR,Example: comparing second-order reaction systems,CSTR + PFR,PFR + CSTR,CSTR,PFR,PFR,CSTR,(1),(2),Part 2Predicting Conversion and Exit Concentration,9.6 Reactor modeling using the RTD,RTD + Model + Kinetic data,Exit conversion and,Exit concentration,Models for predicting conversion from RTD data,Zero adjustable parametersa. Segregation modelb. Maximum mixedness model,2. One adjustable parameter a. Tanks-in-series model b. Dispersion model,3. Two adjustable parameters Real reactors modeled as combinations of ideal reactors,RTD: tells 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,),Mixing of reacting species:,one of the major factors controlling the behavior of chemical reactors,.,For,first-order,reactions,Conversion is independent of concentration,Once 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,Macromixing:,Produces a distribution of residence times,without, 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,:,Complete segregation,:,All molecules of the same age group remain together as they travel through the reactor 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.,9.7 Zero-parameter models,9.7.1 Segregation model,Mixing of the globules of different ages 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. (X,1,X,2,X,3,.),RTD + Model + Kinetic data,Exit conversion and,Exit concentration,Mean conversion of those globules spending between time,t,and,t,+,dt,in the reactor,=,Conversion achieved in a globule after spending a time,t,in the reactor,X,Fraction of globules that spend between t and,t+dt,in the reactor,Segregation model,Summary,: if we have the RTD, the reaction rate expression, then for a segregated flow situation (i.e., model), we have sufficient information to calculate the conversion.,Consider a first-order reaction:,For a batch reactor:,For constant volume and with,N,A,=,N,A0,(1-,X,),solution,Mean conversion for a first-order reaction,Example: Applications of the segregation model for an ideal PFR, a CSTR, and a laminar flow reactor (first-order reaction),(1) PFR:,Chapter 4,(2) CSTR:,Chapter 4,(3) Laminar flow reactor,Hilder, M.H.,Trans. Ichem,E,59,p143(1979),9.7.2 Maximum mixedness model,Segregation model: mixing occurs at the,latest,possible point.,Maximum mixedness model,: mixing occurs at the,earliest,possible point.,Segregation model,Maximum mixedness model,The volume of fluid with a life expectancy between, and +,The rate of generation of the substance A in this volume:,Maximum mixedness gives the lower bound on conversion (X),when n1,.,Mole balance,9.7.3 Segregation vs. maximum mixedness predictions,If,then,O. Levenspiel, P358,(a),(b),(c, d, e),9.8 Using software packages,Read CD.,9.9 RTD and multiple reactions,For multiple reactions use an ODE solver to couple the mole balance equations, dC,i,/dt=r,i,(where r,i,is the net rate of reaction).,Segregation model,Maximum mixedness model,Summary,1.,E,(,t,),dt,: fraction of material exiting the reactor that has spent between time,t,and,t+dt,in the reactor.,2. The,mean residence time,3. The,variance,about the mean residence time is,is equal to the space time, for constant volumetric flow, = ,0,4. The cumulative distribution function,F,(,t,),gives the fraction of effluent material that has been in the reactor a time,t,or less:,5. The RTD functions for an ideal reactor are,Plug flow,CSTR,Laminar flow,6. The dimensionless residence time is,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,8. Segregation model,For multiple reactions,9. Maximum mixedness:,For multiple reactions,谢谢！,
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