[學(xué)習(xí)]反應(yīng)工程基礎(chǔ)程易chapter10-modelnonidealrea

1、,,,,Nonideal Flow Characterized by Residence Time Distribution (RTD),Pulse input of tracer,,F(t),,,RTD-方差的加和性,一次矩的加和性,二次矩的加和性,[s],[s2],假設(shè)界面處無返混 ( 小)有,對矮胖反應(yīng)器：端部的返混貢獻(xiàn)很大對細(xì)長反應(yīng)器：端部返混貢獻(xiàn)可忽略,,卷積（E(t): 傳遞函數(shù)的概念）,Chap9 - Summ

2、ary,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

3、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 f

4、low,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?,（自學(xué)，P

5、633－634）,***Simple diagnostics and troubleshooting using the RTD for ideal reactors***,8. Segregation model,,For multiple reactions,9. Maximum mixedness:,,For multiple reactions,,,***遲混與早混（見網(wǎng)絡(luò)學(xué)堂補充材料）***,,,,,O. Levenspiel

6、, P358,(a),(b),(c, d, e),Chapter 10Models for Nonideal Reactors,Overview,Use the RTD to evaluate parametersModel of reactor flow patternsTanks-in-series modelDispersion model,10.1 Some guidelines,RTD data + Kinetics

7、+ Model = Prediction,Guidelines to develop models for nonideal reactors,1. The model must be mathematically tractable.,2. The model must realistically describe the characteristics of the nonideal reactors. The phenomena

8、occurring in the nonideal reactor must be reasonably described physically, chemically, and mathematically.,3. The model must not have more than two adjustable parameters.,,,,10.1.1 One-parameter models,Nonideal CSTRs inc

9、lude a reactor dead volume VD, no reaction takes place,Nonideal CSTRs with a fraction of fluid bypassing the reactor, exiting unreacted,Tanks-in-series model,Dispersion model,,* This parameter is most always evaluated by

10、 analyzing the RTD determined from a tracer test.,Examples:,10.1.2 Two-parameter models,,,,C(t),t,,,,,,,,,Vs,VD,?0,?b,?s,?0,,,10.2 Tanks-in-series (T-I-S) model,1,2,3,,,,,Pulse,,,,,,V1 = V2 = Vi,? = ? 0,?1 = ? 2 = ? i

11、,,First reactor:,Second reactor:,,,,,ODE:,Solution:,,Same to third reactor ...,,,n CSTRs:,,,(C2 = 0 at t = 0),RTD for equal-size tanks in series:,?: Vtotal/?,,,,,,,n: calculated from RTD,Levenspiel book (3rd),First order

12、 reaction:,,,,E(?),,,?,,,n = 10,n = 4,n = 2,n: non-integer, or integer,First order reaction:,,1,,n =?,,If n = 2.53, you might calculate the conversions for n = 2 and n = 3 to bound the value.,,,,,Graphical method of eval

13、uating the performance of N tanks in series for any kinetics,Levenspiel, p329,,,-rA,CA,,CA0,CA1,CA2,CA3,,,,,,,,,CA4,Parallel lines for same size tanks,,,,,Slope:,For microfluid:,一級等溫反應(yīng),二級等溫反應(yīng),Chemical conversion of Macro

14、fluids,10.3 Dispersion model,,Molar flow rate of tracer (FT) by both convection and dispersion,Da: effective dispersion coefficient, m2/s,,Pulse tracer balancedispersion,10.4 Flow, reaction, and dispersion,10.4.1 Balanc

15、e equations,,,Second-order ODE,,,,,Similar to A:,,1st-order reaction,Dimensionless,,Damköhler numberfor first-order reaction,,,Damköhler numberfor first-order reaction,,Peclet number,l: characteristic length

16、term,Per: reactor Peclet number, it uses reactor length, L,Pef: fluid Peclet number, it uses characteristic length that determines the fluid’s mechanical behavior,Empty tube:,Packed bed:,?: bed porosity,,: pipe diameter,

17、10.4.2 Boundary conditions,Boundary conditions for closed vessels and open vessels.,Closed-closed vessels: assume that there is no dispersion or radial variation in concentration either upstream (closed) or downstream (

18、closed) of the reaction section,Open-open vessels: dispersion occurs both upstream (open) and downstream (open) of the reaction section,,,,,,,,,Da=0,Da>0,Da=0,,,z = 0,z = L,dispersion,,,,,,,,Da>0,Da>0,Da>0,,

19、,z = 0,z = L,dispersion,Closed-closed vessel,Open-open vessel,,10.4.2A Closed-closed vessel boundary condition,Entrance boundary condition,z = 0,,z = L,Exit condition,,Danckwerts boundary conditions,,,,,,,z = 0,0-,0+,,FA

20、,Entrance:,,,CA0,,,CA(0+),,z,0-,0+,z=0,Example: CSTR, CA0 ? CA,exit,Exit:,,,CA(L-),L-,L+,CA(L+),,,10.4.2B Open-open system,,,Open-openBoundary condition,,z = 0,z = L,10.4.2C Back to the solution for a closed-closed syst

21、em,,,,,Analytical solution,,Outside the limited case of a first-order reaction, a numerical solution of the equation is required.,Three ways to find Da, and the Peclet number,1. Laminar flow with radial and axial molecu

22、lar diffusion theory,2. Correlations from the literature for pipes and packed beds,3. Experimental tracer data,,10.4.4 Dispersion in a tubular reactor with laminar flow,,,The molecules on the center streamline (r = 0) ex

23、ited the reactor at a time t = ?/2;The molecules traveling on the streamline at r = 3R/4 exited the reactor at time:,Radial diffusion in laminar flow,Convective-diffusion equation for tracer transport in both the axial

24、and radial direction,,,,,,,,Laminar flow,Aris-Taylor dispersion coefficient,Average axial concentration,,10.4.5 Correlations for Da,Please refer to the book, p674-676.,10.4.6 Experimental determination of Da,,Unsteady-s

25、tate tracer balance,,,Mass of tracer injected, M,,,,,,,Calculating Per using tm and ?2 determined from RTD data for a closed-closed system,,Open-Open vessel boundary conditions,,At the entrance:,,At the exit:,,,Per >

26、100,,Calculate ?:,,,,Calculate ?:,Calculate Per:,,Case 1. The space time ? is known.,Case 2. The space time ? is unknown. This situation arises when there are dead or stagnant pockets that exist in the reactor along with

27、 the dispersion effects. To analyze this situation we first calculate tm and ?2 from the data as in case 1. Then,,,... ? finding the effective reactor volume,RTD ? tm, ?2 ? Per,10.4.7 Sloppy tracer inputs,,Open-Open syst

28、em,,10.5 Tanks-in-series vs. dispersion model,,,Equivalency between models of tanks-in-series and dispersion,or,where,10.6 Numerical solutions to flows with dispersion and reaction,,Steady state:,Analytical solutions to

29、dispersion with reaction can only be obtained for iso-thermal zero- and first-order reactions.,Case A. Aris-Taylor analysis for laminar flow,,,,,,,Closed-closedBoundary cond.,Open-openBoundary cond.,,,,Case B: Full num

30、erical solution,,,,10.7 Two-parameter models – modeling real reactors with combinations of ideal reactors,10.7.1 Real CSTR modeled using bypassing and dead space,,,,Dead zone,bypassing,,Vs,,,CA0, ?0,,?b,CA0,,CAS,Vd,,1,2

31、,CA,?0 = ?b +?s,Balance at junction ?:,,,,,Modeling,,For first-order reaction, a mole balance on CSTR (Vs),,,,,RTD,,,,10.7.1B Using a tracer to determine the model parameters in CSTR-with-dead-space-and-bypass model,,,,,

32、CT0, ?0,,?b,CT0,,CTS,Vd=(1-?)V,,1,2,CT,?0 = ?b +?s,Tracer balance for step input,Modelsystem,Vs=(1-?)?0,Vs=?V,,Junction ? balance:,,,,Evaluating model parameters,,,,10.7.2 Real CSTR modeled as two CSTRs with interchange

33、,,,,,?0,V1,V2, CA2,,?0,CA1,,,?1,?1,,,Using a tracer to determine the model parameters in a CSTR with an exchange volume,Reactor 1:,Reactor 2:,,,where,,閱讀：p693-694,參看Levenspiel: Chemical Reaction Engineering (3rd), Chap12

34、-Compartment Models, p283.,Summary,The models for predicting conversion from RTD data are:a. Zero adjustable parameters(1) Segregation model(2) Maximum mixedness modelb. One adjustable parameter(1) Tanks-in-series m

35、odel(2) Dispersion modelc. Two adjustable parameters: real reactor modeled as combinations of ideal reactors,2. Tanks-in-series model: use RTD data to estimate the number of tanks in series,,,For a first-order reaction

36、,3. Dispersion model: for a first-order reaction, use the Danckwerts boundary conditions,,,,,4. Determine Da,(a) For laminar flow the dispersion coefficient is,,(b) Correlations.,(c) Experiment in RTD analysis to find tm

37、 and ?2,,Closed-closed,,Open-open,5. If a real reactor is modeled as a combination of ideal reactors, the model should have at most two parameters.,6. The RTD is used to extract model parameters.,7. Comparison of convers

38、ions for a PFR and CSTR with the zero-parameter and two-parameter models. Xseg symbolizes the conversion obtained from the segregation model and Xmm that from the maximum mixedness model for reaction orders greater than