[學(xué)習(xí)]反應(yīng)工程基礎(chǔ)程易chapter9-rtd

1、Information needed to predict what a reactor can do,,Reactor,,,Input,Output,Performance equationRelates input to output,,,Contacting pattern or how materials flow through and contact each other in the reactor,Kinetics o

2、r 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.,,,Flu

3、idized 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-d

4、isc system,http://sol.rutgers.edu/~shinbrot/Group_Index.html,,高粘體系的液體混合現(xiàn)象,Chapter 9 Distributions of Residence Times for Chemical Reactors,Overview,Nonideal reactorsPart-1: characterize (non)ideal reactorsResidence T

5、ime 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,Part 1 Characterization

6、and Diagnostics,9.1 General 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/avai

7、lable reactors when a new reaction is used in the reactor,Examples:,Channeling,Tank reactor,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Dead zone,,,Bypassing,Th

8、e three concepts,RTDMixingModel- 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 s

9、pent in the reactorPlug-flow reactor, batch reactorAll the atoms in the reactors have the same residence timeCSTRFeeds mixed immediately, but withdrawn continuously“RTD”: some molecules leave quickly, others overst

10、ay 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, in

11、to the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of timeTracer: nonreactive, easily detectable, similar physical properties to the fluid, no adsorpt

12、ion on the walls or surfaces, etc.Pulse input and Step input,階躍注入,脈沖注入,9.2.1 Pulse input experiment,,,,,,,,Reactor,,,Feed,Injection,Detection,Effluent,,,,,,,,C,C,t,,C,,,,,C,t,t,t,,,,Pulse injection,Step injection,Step r

13、esponse,Pulse response,?,?,,,,,,C,C,t,,t,,Pulse injection,Pulse response,,Only flow carries tracer(No diffusion),,,,,E(t): resident time distribution functionhow much time different fluid elements have spent in the rea

14、ctor,,,,,,C(t),t,Pulse response,,,,,,,E(t),t,Fraction of material leaving the reactor that has resided in the reactor for times between t1 and t2,,,,t1,t2,,,,,,,,,,Problems using Pulse input:,“Pulse”: can be hard to obta

15、in a reasonable pulse at the injection pointLong tails of the measured C(t) curve,Convolution integral,（卷積）,,Pulse Imperfect pulseStep,A general description:Output concentration ~ Input concentration,,Input,Equivale

16、nt form,,9.2.2 Step tracer experiment,,,C,,,,,C,t,t,,,Step injection,Step response,,,,,,Step injection,Advantage of F(t): easier experimentsDrawbacks: differentiation?error large amount of tracer,,,,,9.3 Chara

17、cteristics 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 relation

18、ships,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 dis

19、persion, for constant volumetric flow, ? = ?0,? = tm,,,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 th

20、e 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

21、 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

22、 fraction of material inside the reactor that has been inside the reactor for a period time between ? and ?+ ??,,,CSTR:,P633推導(dǎo)過程,,,,,,9.4 RTD in ideal reactors,9.4.1 RTDs in batch and plug-flow reactors,,Plug flow reacto

23、r:,,,,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 fl

24、ow 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 troubl

25、eshooting,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,(

26、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,PF

27、R,,,,,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 modelin

28、g 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 adjusta

29、ble 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 th

30、e 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

31、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 mix

32、ing 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

33、 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

34、 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

35、 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 differen

36、t conversion. (X1,X2,X3...),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 s

37、pending 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

38、., model), we have sufficient information to calculate the conversion.,Consider a first-order reaction:,,,For a batch reactor:,For constant volume and with NA = NA0(1-X),,,solution,Mean conversion for a first-order react

39、ion,,,,,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

40、.H. Trans. IchemE 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,Ma

41、ximum 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 n>1.,M

42、ole 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

43、 to couple the mole balance equations, dCi/dt=ri (where ri 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 betwee

44、n 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

45、) 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 inte

46、rnal-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 r