化学反应工程英文课件Chapter

1、化化 学学 反反 应应 工工 程程Basics of Non-Ideal Flow So far we have treated two flow patterns, plug flow and mixed flow. These can give very different behavior (size of reactor, distribution of products). We like these flow patterns and in most cases we try to design equipment to approach one or the other beca

2、use lone or the other often is optimum no matter what we are designing for.lthese two patterns are simple to treat.化化 学学 反反 应应 工工 程程But real equipment always deviates from these ideals. How to account for this? That is what this and following chapters are about. Overall three somewhat interrelated f

3、actors make up the contacting or flow pattern: 1. the RTD or residence time distribution of material which is flowing through the vessel;2. the state of aggregation of the flowing material, its tendency to clump and for a group of molecules to move about together;3. the earliness and lateness of mix

4、ing of material in the vessel.化化 学学 反反 应应 工工 程程Let us discuss these three factors in a qualitative way at first. Then, this and the next few chapters treat these factors and show how they affect reactor behavior. The Residence Time Distribution, RTD Deviation from the two ideal flow patterns can be

5、caused by channeling of fluid, by recycling of fluid, or by creation of stagnant regions in the vessel. Figure 11.1 shows this behavior. In all types of process equipment, such as heat exchangers, packed columns, and reactors, this type of flow should be avoided since it always lowers the performanc

6、e of the unit. 化化 学学 反反 应应 工工 程程化化 学学 反反 应应 工工 程程Setting aside this goal of complete knowledge about the flow, let us be less ambitious and see what it is that we actually need to know. In many cases we really do not need to know very much, simply how long the individual molecules stay in the vessel

7、, or more precisely, the distribution of residence times of the flowing fluid. This information can be determined easily and directly by a widely used method of inquiry, the stimulus-response experiment.This chapter deals in large part with the residence time distribution (or RTD) approach to nonide

8、al flow. We show when it may legitimately(合理地) be used, how to use it, and when it is not applicable what alternatives to turn to. 化化 学学 反反 应应 工工 程程In developing the “language” for this treatment of nonideal flow (see Danckwerts, 1953), we will only consider the steady-state flow, without reaction a

9、nd without density change, of a single fluid through a vessel. State of Aggregation of the Flowing Stream Flowing materials is in some particular state of aggregation, depending on its nature. In the extremes these states can be called microfluids and macrofluids, as sketched in Figure. 11.2. 化化 学学

10、反反 应应 工工 程程Figure 11.2 Two extremes of aggregation of fluidMicrofluidMacrofluid化化 学学 反反 应应 工工 程程Two-Phase Systems. A stream of solids always behaves as a macrofluid, but for gas reacting with liquid, either phase can be a macro-or microfluid depending on the contacting scheme being used. The sketche

11、s of Figure. 11.3 show completely opposite behavior. Single-Phase Systems. These lie somewhere between the extremes of macro- and microfluids. 化化 学学 反反 应应 工工 程程Figure 11.3 Examples of macro- and microfluid behavior. 化化 学学 反反 应应 工工 程程Earliness of MixingThe fluid elements of a single flowing stream ca

12、n mix with each other either early or late in their flow through the vessel. For example, see Fig. 11.4.Usually this factor has little effect on overall behavior for a single flowing fluid. However, for a system with two entering reactant streams it can be very important. For example, see Fig. 11.5.

13、 化化 学学 反反 应应 工工 程程Figure 11.4 Examples of early and of late mixing of fluid. 化化 学学 反反 应应 工工 程程Figure 11.5 Early or late mixing affects reactor behavior.化化 学学 反反 应应 工工 程程Role of RTD, State of Aggregation, and Earliness of Mixing in Determining Reactor Behavior In some situations one of these factors

14、can be ignored; in others it can become crucial. Often, much depends on the time for reaction, the time for mixing , and the time for stay in the vessel . In many cases has a meaning somewhat like but somewhat broader(更广的).rectmixtstaytstaytmixt化化 学学 反反 应应 工工 程程11.1 E, THE AGE DISTRIBUTION OF FLUID,

15、 THE RTDIt is evident that elements of fluid taking different routes through the reactor may take different lengths of time to pass through the vessel. The distribution of these times for the stream of fluid leaving the vessel is called the exit age distribution E, or the residence time distribution

16、 RTD of fluid. E has the units of time-1.化化 学学 反反 应应 工工 程程停留时间分布密度函数停留时间分布密度函数 E(t) 函数函数对于同时进入反应器入口的对于同时进入反应器入口的 N 个流体粒子个流体粒子，若在出口处，若在出口处进行检测，则其中进行检测，则其中停留时间介于停留时间介于 t t + dt 之间之间的流体粒的流体粒子个数子个数 dN 所占的分率为所占的分率为 E(t) dt dN / N 我们定义我们定义 E(t) 为为停留时间分布密度函数停留时间分布密度函数。 如：在某时刻进入反应器入口的如：在某时刻进入反应器入口的 100 个流体粒

17、子，到达出个流体粒子，到达出口时停留时间为口时停留时间为 5 6 min 的粒子有的粒子有 8 个，若取个，若取 t = 5 min，dt = t 1 min，则此时则此时 E(t) dt = dN / N = N / N = 8 /100 = 0.08； E(t) = dN / (dt*N) = N / ( t *N) = 0.08 min-1当 dt 0，则，则 E(t) dt 是一个瞬时是一个瞬时( 如如t = 5 min 时时 )的分率的分率化化 学学 反反 应应 工工 程程停留时间分布函数停留时间分布函数 F(t) 函数函数对于同时进入反应器入口的对于同时进入反应器入口的 N 个流体

18、粒子个流体粒子，若在出口，若在出口处进行检测，则其中处进行检测，则其中停留时间介于停留时间介于 0 t 之间之间的流体粒的流体粒子所占的分率为子所占的分率为 F(t) 我们定义我们定义 F(t) 为为停留时间分停留时间分布函数布函数。 如：在某时刻进入反应器入口的如：在某时刻进入反应器入口的 100 个流体粒子，到个流体粒子，到达出口时停留时间为达出口时停留时间为 0 5 min 的粒子有的粒子有 20 个，若取个，若取 t = 5 min，则此时，则此时 F(t) = 20 /100 = 0.2。F(t) 是一个累积（如是一个累积（如 t = 05 min ）的分率。）的分率。 化化 学学

19、反反 应应 工工 程程停留时间分布停留时间分布停留时间分布的定量描述停留时间分布的定量描述停留时间分布密度函数停留时间分布密度函数 E (t)E(t) = 0, t 0 red fluid and only red fluid in the exit stream is younger than age t. Thus we have streamexit in the fluid red offraction t agean younger th streamexit offraction = But the first term is simply the F value, while t

20、he second is given by Eq. 1. So we have, at time t, 0FE tdt(7) 化化 学学 反反 应应 工工 程程and on differentiatingFEddt(8) In graphical form this relationship is shown in Fig. 11.13.These relationships show how stimulus-response experiments, using either step or pulse inputs can conveniently give the RTD and me

21、an flow rate of fluid in the vessel. We should remember that these relationship only hold for closed vessels. When this boundary condition is not met, then the Cpluse and E curves differ. 化化 学学 反反 应应 工工 程程Figure 11.13 Relationship between the E and F curves. 输入曲线输入曲线响应（输出）曲线响应（输出）曲线c0(t)脉冲法测定反应器的脉冲法

22、测定反应器的 E 分布曲线分布曲线 M E tdt = C tdt( )( )C tE t =M0M= C(t)dt0)()()(dttctctEM 为示踪剂为示踪剂的加入量的加入量( )( )( )000t E t dtt = =t E t dtE t dt停留时间分布的统计特征值停留时间分布的统计特征值022022)( )()(tdttEtdttEttt1. 平均停留时间平均停留时间 (mean residence time)2. 方差方差 (variance)对闭式容器对闭式容器(closed vessel) ,若采用无因次停留时间若采用无因次停留时间 :2,()( )()( )2202

23、2t0t = = 1t = Edt1 = -1t E tdt = ttt 1. 活塞流模型活塞流模型(t)()E=t -t)( , 1)( , 0)(tttttF理想反应器的停留时间分布理想反应器的停留时间分布)(tt t = 0tE(t)tt )(t0)(tF1.0tt010(1)d|1 01|1) 1(102022d1. Plug Flow2. Mixed Flow1( )-t/tE t =et( ) 1-t/tF t = -e理想反应器的停留时间分布理想反应器的停留时间分布1- 0=e d= 02211de化化 学学 反反 应应 工工 程程化化 学学 反反 应应 工工 程程Figure

24、11.14 Properties of the E and F curves for various flows. Curves are drawn in term of ordinary and dimensionless time units. Relationship between curve is given by Eqs. 7 and 8. 存在滞流区存在滞流区非理想反应器的停留时间分布非理想反应器的停留时间分布使使 t t 减小减小存在沟流存在沟流存在沟流存在沟流非理想反应器的停留时间分布非理想反应器的停留时间分布存在短路存在短路非理想反应器的停留时间分布非理想反应器的停留时间分

25、布存在短路存在短路层流反应器层流反应器E( )0,0.521E( ),0.52非理想反应器的停留时间分布非理想反应器的停留时间分布化化 学学 反反 应应 工工 程程For closed vessel, at any time these curves are related as follows : E,MpulsevCF,mstepvCFE,ddtV,tv1,EEt,EFall dimensionless, E = 1 -time,tt化化 学学 反反 应应 工工 程程EXAMPLE 11.1 FINDING THE RTD BY EXPERIMENTThe concentration re

26、ading in Table E11.1 represent a continuous response to a pulse input into a closed vessel which is to be used as a chemical reactor.Calculate the mean residence time of fluid in the vessel and tabulate and plot the exit age distribution E.化化 学学 反反 应应 工工 程程Table E11.1Time t, (min) Tracer Output Conc

27、entration, Cpulse(gm/ liter fluid)0 05 310 515 520 425 230 135 0化化 学学 反反 应应 工工 程程SOLUTIONThe mean residence time, from Eq.4, is iiiiiiiiCCtttCtCttconstantmin1512455313022542051551035The area under the concentration-time curve. Area = iiiCt= ( 3+5+5+4+2+1 ) 5 = 100 gmmin / liter化化 学学 反反 应应 工工 程程gives

28、 the total amount of tracer introduced. To find E, the area under this curve must be unity; hence, the concentration readings must each be divided by the total area, giving areaCEThus we have 0 5 10 15 20 25 30 0 0.03 0.05 0.05 0.04 0.02 0.01 , min-1 t, min areaCE化化 学学 反反 应应 工工 程程Figure E11.1 Plot o

29、f Et distribution of Example 11.1.化化 学学 反反 应应 工工 程程11.2 CONVERSION IN NON-IDEAL FLOW REACTORS To evaluate reactor behavior in general we have to know four factors: 1. the kinetics of the reaction2. the RTD of fluid in the reactor3. the earliness or lateness of fluid mixing in the reactor4. whether t

30、he fluid is a micro or macro fluid For microfluids in plug or mixed flow we have developed the equation in the earlier chapters. For intermediate flow we will develop appropriate models in , , and . 化化 学学 反反 应应 工工 程程To consider the early and late mixing of a microfluid, consider the two flow pattern

31、s shown in Fig.11.17 for a reactor processing a second-order reaction: In (a) the reactant starts at high concentration and reacts away rapidly because n 1; In (b) the fluid drops immediately to a low concentration. Since the rate of reaction drops more rapidly than does the concentration you will e

32、nd up with a lower conversion. Thus, for microfluids:Late mixing favors reactions where n 1;Early mixing favors reactions where n 1;However, the earliness of mixing has no effect on the reaction where n = 1.(12)化化 学学 反反 应应 工工 程程Figure 11.17 This shows the latest and the earliest mixing we can have f

33、or a given RTD. 化化 学学 反反 应应 工工 程程For macrofluids, imagine little clumps of fluid staying for different lengths of time in the reactor (given by the E function). Each clump reacts away as a little batch reactor, thus fluid elements will have different compositions. So the mean composition in the exit

34、 stream will have to account for these two factors, the kinetics and the RTD. In words, thenttdtall elementsof exit streamconcentration offractmean concentration reactant remaining of reactant in an element of in exit stream age between and ttdtion of exitstream which is of age between and 化化 学学 反反

35、应应 工工 程程In symbols this becomes0for an element or little00at exitbatch of fluid of age element0or in terms of conversions ()or in a form suitable for numerical iAAAAtAACCdtCCXXdtEEAall age00intervalselementntegrationC AAACtCCE(13)化化 学学 反反 应应 工工 程程From on batch reactor we have AA0elementAA00element1A

36、0A0elementC for first-order reactions (14)CC1 for second-order reactions (15)C1C for an nth-order reaction 1 (1)CktAnAekC tnCkt1/1 n(16)These are terms to be introduced the performance equation, Eq.13.化化 学学 反反 应应 工工 程程Note: For first-order reactions, the reaction result of macrofluid is identical to

37、 that of microfluid . On the other hand, when a reaction with any kinetics occurs in a plug flow reactor, it can always get the same result no matter the reacting fluid is macro or micro.化化 学学 反反 应应 工工 程程The Dirac Delta Functions, . One E curve which may puzzle(使迷惑 ) us is the one which represents p

38、lug flow. We call this the Dirac function, and in symbols we show it as ) )t t( (t t0 0000,()0,tttttt=(17) which says that the pulse occurs at t = t0 , as seen in Fig.11.18. 化化 学学 反反 应应 工工 程程Figure 11.18 The E function for pulg flowE, s-1t0Infinitely high zero width, but with area = 1, ( t - t0 )化化

39、学学 反反 应应 工工 程程The two properties of this function which we need to know are 0000Area under the curve:()1 Any integrationwith a function:() ( )( ) ttdtttf t dtf t0 (18)(19)Once we understand what this means we will see that it is easier to integrate with a function than with any other. For example,66

40、00360(5)5 (just replace by 5)(5)0tt dtttt dt化化 学学 反反 应应 工工 程程EXAMPLE 11.4 CONVERSION IN REACTORS HAVING NON-IDEAL FLOW The vessel of Example 11.1 is to be used as a reactor for a liquid decomposing with rate -1, 0.307 minAArkCkFind the fraction of reactant unconverted in the real reactor and compare

41、 this with the fraction unconverted in a plug flow reactor of the same size. 化化 学学 反反 应应 工工 程程SOLUTIONFor the plug flow reactor with negligible density change we have AAAAXAAACCkCdCkrdXCA000ln11and with from Example 11.1 (0.307)(15)4.600.01kAACeeeCThus the fraction of reactant unconverted in a plug flow reactor equals 1.0%. 化化 学学 反反 应应 工工 程程For the real reactor the fraction unconverted, given by Eq.13 for macrofluids, is found in Table E11.4. Hence the fraction of reactant unconverted in the real reacto