1 Chemical Reaction Engineering Lecture 14 Lecturer 2 This course focuses on models for nonideal reactors.
Three concepts used to describe nonideal reactors
the distribution of residence times in the system (two bounds (i.e. the segregation and maximum mixedness) were determined)
the quality of mixing
the model used to describe the system
3 Models for nonideal reactors
reactor with bypassing and dead volume
Combination and/or modification of ideal reactors
The RTD is used to evaluate the parameter(s) in the model.
4 Models for real reactors
realistic describe the characteristics of the reactor
no more than 2 adjustable parameters
the less the better
Give me four adjustable parameters and I can fit an elephant give me five and I can include his tail!
5 One-parameter model
the reactor dead volume VD
the fraction of fluid bypassing the reactor f
the number of tanks for the tanks-in-series model n
the dispersion coefficient for the dispersion model Da
Modeling of a tubular reactor
real the velocity profile is not flat there is axial mixing
tanks-in-series model the dispersion model
6 Tanks-in-series model If there are three tanks Pulse injection For a single CSTR a material balance (V V1 V2 V3 1 2 3) on the first reactor gives on the second reactor gives on the third reactor gives The fraction of material leaving the system of three reactors that has been in the system between time t and t t is 7 n tanks-in-series n 10 E() n 4 n 2 dimensionless
How many tanks are needed for modeling P 875 8 The number of tanks in series is determined by the tracer experiment 1 1 The number of tanks necessary to model the real reactor as n ideal tanks in series. 9 Dispersion model It is used to describe nonideal tubular reactors. In addition to transport by bulk flow UCAc every component is transported through any cross section of the reactor at a rate resulting from molecular and convective diffusion. The molar flow rate of tracer is Mole balance on the inert tracer This compensates not only axial mixing but also radial mixing and other nonflat velocity profiles 10 Dispersion in a tubular reactor with laminar flow For a laminar flow reactor the axial velocity varies in the radial direction the Hagen-Poiseuille equation For a laminar flow reactor the RTD function is IF there is axial and radial dispersion what will the RTD be The P.D.E describing the concentration at a particular r x and t 11 Similarly the P.D.E describing the variation of the average concentration with t and x is The value of Da for turbulent flow is shown in Fig. 14-6 and for PBR is shown in Fig. 14-7. 12 Determination of Da from the RTD experimental data dimensionless We want to solve this P.D.E. with certain B.C.s characteristic length Per the reactor Peclet number U/ the average interstitial velocity Pef the fluid Peclet number (in a packed bed) (in an empty tube) 13 Boundary conditions (1) closed-closed vessel B.C. at x 0 the Danckwerts boundary conditions in dimensionless form at 0 at x L at 1 at t 0 14 B.C. at 0 at 1 at t 0 A pulse injection We can theoretically solve the P.D.E.. How to obtain Per for the equation The mean residence time tm Bischoff and Levenspiel 1963 From experiments 15 (1) open-open vessel B.C. at x 0 at x L at t 0 16 together with the B.C.s in the previous we have the dimensionless effluent tracer concentration The mean residence time We obtain Per and then Da. 17 When there are dispersion and reaction in a tubular reactor U Ac z L zz z z 0 At steady-state the mass balance on A over the volume element VAcz is rate in - rate out rate of generation rate of accumulation dimensionless where Da is the Damköhler number for convection 18 B.C. (use the Danckwerts boundary conditions for close-close system) at 0 at 1 The O.D.E. is solved 19 The comparison between the dispersion and tanks-in-series models The first-order reaction is carried out in a 10-cm-diameter tubular reactor 6.36 m in length. The specific reaction rate is 0.25 min-1. The results of a tracer test carried out on this reactor are (the effluent tracer concentration as a function of time) Calculate conversion using (a) the closed vessel dispersion model (b) PFR (c) the tanks-in-series model (d) a single CSTR 2 C(t) E(t) tm tm close-close vessel dispersion model cf open-open vessel dispersion model 20 (a) the closed vessel dispersion model We have Per from Per 7.5 Da 1.29 We need Da We have X 0.68 (b) ideal PFR We have X 0.725 21 (c) the tanks-in-series model The number of tanks necessary to model The conversion for n tanks-in-series is We have X 0.677 (d) a single CSTR n 1 22 Two-parameter models
A real reactor might be modeled by one of two different combinations of ideal reactors.
A tracer experiment is used to evaluate the model parameters.
23 A real CSTR is modeled as an ideal CSTR with a bypassing and a dead space CA0 vs (1-)v0 v0 Bypass Vd (1-)V vb v0 Vs V deadzone CA0 CAs CA v0 A first-order reaction Mole balance on species A Mole balance on species A in the reactor Assume We want to determine the values of these two parameters (using RTD). 24 For an inject of tracer T as a positive-step input the unsteady-state mass balance on T is Positive injection (B.C.) 25 Example CSTR with dead space and bypassing The elementary reaction is carried out in a CSTR with bypassing and a stagnant region in the reactor. The measured reactor volume is 1 m3 and the flow rate is 0.1 m3/min to the reactor. The reaction rate constant is 0.28 m3/kmol.min. The feed is equimolar in A and B with an entering concentration of A equal to 2.0 kmol/m3. The tracer output for the reactor is in the table. Calculate the conversion expected in this reactor. CT0 2000 0.7 0.2 26 Calculation of conversion use this 2-parameter model Mole balance on reactor volume Mole balance on species A Combining From we obtain the values of vs s cf if an ideal CSTR X 0.66 27 A real CSTR modeled as two-ideal-CSTR-interchange v0 v0 v0 v1 CSTR 2 CSTR 1 CA2 CA1 v1 V V2 V1 CA1 v0 Mole balance on reactor 1 Mole balance on reactor 2 For a first-order reaction These equations are solved together We want to determine the values of and (using RTD) 28 A tracer pulse injection at t 0 is used to determine the value of the two parameters Mole balance on reactor 1 Mole balance on reactor 2 We also have They are used to determine the values of and ! Numerical method might be used (page 9023) 29 Other models of nonideal reactors using CSTRs and PFRs
almost all agitated tank reactors have a well-mixed zone in the vicinity of the agitator and can be represented by a CSTR
A number of combinations can be obtained.
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