10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 10: Non ideal Reactor Mixing Patterns

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1 1.37 Chemical and Biological Reacion ngineering, Spring 27 Prof. K. Dane Wirup Lecure 1: Non ideal Reacor Mixing Paerns This lecure covers residence ime disribuion (RTD), he anks in series model, and combinaions of ideal reacors. Non Ideal Mixing CSTR PFR Figure 1. Ideal PFR wih pulse inpu. A pulse inpu will yield an oupu profile ha is a pulse inpu. Figure 2. Ideal CSTR wih pulse inpu. A pulse inpu will yield an oupu profile ha is a sharp peak wih a ail. Real mixed ank bypassing mixing recirculaion eddies sagnan volumes Figure 3. A real mixed ank. In a real mixed ank here are porions ha are no well mixed due o sagnan volumes, recirculaion eddies, and mixing bypasses. In a real PFR here is back mixing and axial dispersion. In a packed bed reacor (PBR) channeling can occur. This is where he fluid channels hrough he solid medium. Residence Time Disribuion A useful diagnosic ool is he residence ime disribuion (RTD). The residence ime is how long a paricle says in he reacor once enering. ()d Probabiliy ha a fluid elemen enering he vessel a = exis beween ime and +d. Probabiliy densiy funcion for exi ime,, as a random variable. Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

2 d Probabiliy ha fluid elemen exis before ime. ( ) d Probabiliy of exiing a ime laer han. ( ) mean = ( ) d = normalized = ( ) d = 1 variance =σ 2 = ( ) ( ) 2 d (measures he broadness of he disribuion) before 1 afer 1 1 Figure 4. () versus. A a given ime poin, some maerial has exied and some maerial will sill exi a a laer ime. xperimenal Deerminaion of () Inflow should be somehing measurable Absorbance Fluorescence ph sal conduciviy radioaciviy Use one of wo ypes of inpu concenraion curves: Pulse Sep Figure 5. Two ypes of inpu. A pulse inpu is a spike of infinie heigh bu zero widh, ideally. A sep inpu is a consan concenraion over a period of ime Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 2 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

3 A pulse inpu allows for easy inerpreaion because all maerials ener he reacor a once. deecor inpu curve Figure 6. Schemaic of a residence ime disribuion experimen. The inpu curve eners he reacor; a deecor deecs concenraion changes in he oupu sream. ( ) C ou () = C ou ( ) d PFR (Ideal) Figure 7. Pulse inpu in ideal PFR. A pulse inpu in an ideal PFR becomes a pulse oupu. ()=δ ( ) = x δ( x) = = x = δ( ) x dx = 1 f ( x ) δ ( x a) dx = f ( a ) CSTR (Ideal) Transien maerial balance: In Ou+Producion=Accumulaion 1.37 Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 3 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

4 Since all he maerial is added a once, In=. The racer used is non reacive. Therefore here is no producion. This gives: C + = dc d ( ) C = Ce ( ) = C ( ) ( ) C d CSTR, = = e Figure 8. Pulse inpu in an ideal CSTR. In an ideal CSTR, a pulse inpu leads o a sharp peak wih a ail. mean residence ime = e d = CSTR (non ideal mixing) Bypassing: Divide inpu ino 2 sreams B SB Figure 9. A bypass is modeled by dividing he inpu sream ino wo sreams, one of which does no ener he reacor Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 4 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

5 bypass porion mixed combine Perfec mixing = Bypass = Figure 1. Residence ime disribuion deerminaion for a bypass. Dead volumes: Sagnan regions no geing mixed SB SD ideal D dead volume presen Figure 11. Residence ime disribuion for dead volumes. When a dead volume is presen, a decreased amoun of maerial is observed in he oupu sream. measureable = SD + D SD = SD <ideal PFR (Non ideal) Channeling channeling bed channel PFR like Figure 12. Channeling. In channeling, he residence ime disribuion will show peaks for each channel as well as he one for he main porion of he reacor Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 5 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

6 Axial Dispersion Figure 13. A pulse inpu can become an axially dispersed pulse oupu in a non ideal PFR. There are wo common models for dispersion in a ubular reacor: Tanks in a series Taylor dispersion model (based on he Pecle number) To model he PFR as several anks in a series, break he reacor volume,, ino n CSTRs of volume n each n Figure 14. n anks in series. The oupu of ank 1 is he inpu o ank 2. The oupu is sampled a ank n for dispersion. ( ) n 1 i = e ( n 1)! n i, i = n () 1 1 PFR 2 4 Figure 15. () plos for 1, 2, 4, and 1 anks and a PFR. Noice how he () curve approaches he PFR pulse as more anks are used. The numbers above represen numbers of CSTRs. Wihou enough CSTRs, he peak is no a good approximaion o he narrow peak for a PFR when here is a pulse inpu Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 6 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].

7 2 2 σ = n 2 n = σ 2 We can physically measure and we can deermine σ from experimenally measuring (). RTD (residence ime disribuion) are useful for diagnosis, bu no for reacor design. To calculae conversion, he mos sraighforward acic is o model he non ideal sysem as comparmenal combinaions of ideal reacors. Figure 16. Recirculaion. Recirculaion can be modeled by a PFR followed by a CSTR wih a recycle sream. Figure 17. Parially dead volumes. Dead volumes can be modeled as separae CSTRs ha exchange maerial wih each oher. Figure 18. Bypass. A bypass can be modeled as a CSTR along one roue wih a PFR along he bypass roue Chemical and Biological Reacion ngineering, Spring 27 Lecure 1 Prof. K. Dane Wirup Page 7 of 7 Cie as: K. Dane Wirup, course maerials for 1.37 Chemical and Biological Reacion ngineering, Spring 27. MIT OpenCourseWare (hp://ocw.mi.edu), Massachuses Insiue of Technology. Downloaded on [DD Monh YYYY].