Chemical Reaction Engineering
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1 Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce.
2 Lst Lecture Energy Blnce Fundmentls F E F E + Q! 0 0 W! Substtutng for! W 0 " $ # $ % " $ # %$ F! 0 U 0 + P! " 0 V # 0 $ F # $ U + P V! % & de dt sys + & Q & W S de sys dt F 0 0 F + Q! W! S de sys dt 2 Q! W! + 0 S F 0 0 F
3 Web Lecture 20 lss Lecture 16-hursdy 3/14/2013 Rectors wth et Exchnge User frendly Energy Blnce Dervtons dbtc et Exchnge onstnt et Exchnge Vrble o-current et Exchnge Vrble ounter urrent 3
4 dbtc Operton SR F 0 F I B Elementry lqud phse recton crred out n SR he feed conssts of both - Inerts I nd Speces wth the rto of nerts I to the speces beng 2 to 1. 4
5 dbtc Operton SR ssumng the recton s rreversble for SR, B, (K 0) wht rector volume s necessry to cheve 80% converson? If the extng temperture to the rector s 360K, wht s the correspondng rector volume? Mke Levenspel Plot nd then determne the PFR rector volume for 60% converson nd 95% converson. ompre wth the SR volumes t these conversons. Now ssume the recton s reversble, mke plot of the equlbrum converson s functon of temperture between 290K nd 400K. 5
6 SR: dbtc Exmple F 0 5 mol/mn Δ Rxn cl/mol (exothermc) K F I 10 mol/mn B? X? 1) Mole Blnces: V F r 0 X ext 6
7 Δ 1 1 R exp K K e k k K k r 2 Rx R E 1 B 1 2) Rte Lws: ( ) X X 1 0 B 0 3) Stochometry: 7 SR: dbtc Exmple
8 SR: dbtc Exmple 4) Energy Blnce dbtc, p ( Δ ) X ( Δ ) Θ Rx P 0 + P Rx + Θ I X P I ( 20,000) + ( 2)( 18) X , X X 8
9 SR: dbtc Exmple Irreversble for Prts () through (c) r k 0 ( 1 X) (.e., K ) () Gven X 0.8, fnd nd V Gven X lc lc k lc r lc K (f reversble) lc V 9
10 SR: dbtc Exmple Gven X, lculte nd V F0 X V r ext F k 0 ( 0.8) 0 X ( 1 X) 380K 10 k V 10, exp F0 X r ( 5)( 0.8) ( 3.81)( 2)( 1 0.8) dm 3
11 SR: dbtc Exmple Gven, lculte X nd V (b) lc lc Gven X k lc r lc V 11 r 360K X 100 k 1.83 mn V k ( 1 X ) ( 5)( 0.6) ( 1.83)( 2)( 0.4) lc K (f reversble) (Irreversble) 2.05 dm 3
12 SR: dbtc Exmple (c) Levenspel Plot F r 0 k F X ( 1 X) hoose X lc lc k lc lc r F 0 r 12
13 SR: dbtc Exmple (c) Levenspel Plot 13
14 SR: dbtc Exmple SR X K SR 60% SR X K 14 SR 95%
15 SR: dbtc Exmple 30 PFR X F0/R PFR 60% X PFR X 0.95 PFR 95% 15
16 SR: dbtc Exmple - Summry SR X V 2.05 dm 3 PFR X 0.6 ext 360 V 5.28 dm 3 SR X V 7.59 dm 3 PFR X 0.95 ext 395 V 6.62 dm 3 16
17 Energy Blnce n terms of Enthlpy F V F V + ΔV + U ( ) ΔV 0 d F + U ( ) 0 d F F d + df 17
18 PFR et Effects df r υ 0 + ( r ) P ( ) R d P d d υ F Δ R x F P d + υ ( r ) 18
19 PFR et Effects $ P F % & d + Δ Rx r ( ) ' ( ) +U ( ) 0 d F P Δ r U ( ) Rx d ( Δ )( Rx r ) U( ) F P 19 Need to determne
20 et Exchnge: d ( r )( Δ ) U( ) Rx F P d r ( )( Δ ) Rx U( ) F 0 Θ P 20 Need to determne
21 et Exchnge Exmple: se 1 - dbtc Energy Blnce: dbtc (U0) nd Δ P ( Δ ) Θ Rx P X (16) 21
22 User Frendly Equtons. onstnt e.g., 300K B. Vrble o-urrent d U m! ( ) P cool, V 0 (17) o 22. Vrble ounter urrent d U m! ( ) V P cool 0? Guess Guess t V 0 to mtch 0 0 t ext,.e., V V
23 et Exchnger Energy Blnce Vrble o-current oolnt Blnce: In - Out + et dded 0 m! m! V d 0 m! + U + P V + ΔV + UΔV ( ) 0 ( ) r ( ) 0 23 d d P U m! d ( ) P, V 0 0
24 et Exchnger Energy Blnce Vrble ounter-current In - Out + et dded 0 m! V +ΔV m! V + UΔV ( ) 0 m! d + U ( ) 0 24 d U m! ( ) P
25 et Exchnger Exmple se 1 onstnt Elementry lqud phse recton crred out n PFR m! c et Exchnge Flud F 0 F I B he feed conssts of both nerts I nd speces wth the rto of nerts to the speces beng 2 to 1. 25
26 1 1 R E exp k k (3) 1 1 Δ 1 1 R exp K K (4) 2 Rx 2 F r dx 1) ( 0 1) Mole Blnce: B K k r (2) 2) Rte Lws: 26 et Exchnger Exmple se 1 onstnt
27 et Exchnger Exmple se 1 onstnt 3) Stochometry: 0 ( 1 X) ( 5) B 0 X ( 6) 27 d 4) et Effects: ( R )( ) ( ) ( 7) ( Δ ) P 0 X eq θ k 1+ k Δ P r F P 0 ( 8) U θ + θ I P PI ( 9)
28 Prmeters: I PI P R r rte F U k k R E Δ,,,,,,,,,,,,,, θ et Exchnger Exmple se 1 onstnt 28
29 PFR et Effects et generted et removed d Q g Q F r P F P F ( 0 θ +υ X) P F 0 # $ θ P + Δ P X% & 29 ( )( r ) U( ) d Δ R F $ 0 % θ P + Δ P X& '
30 et Exchnger Exmple se 2 dbtc Mole Blnce: Energy Blnce: dx r F 0 dbtc nd Δ P 0 U0 0 + ( Δ ) Θ Rx P X (16) 30 ddtonl Prmeters (17) & (17B), Θ 0 P P + ΘIP I
31 31 dbtc PFR
32 Exmple: dbtc Fnd converson, X eq nd s functon of rector volume X X X eq rte V V V 32
33 et Exchnge d ( r )( Δ ) U( ) Rx F P d ( r )( Δ ) U( ) F 0 Rx Θ P (16B) 33 Need to determne
34 User Frendly Equtons. onstnt (17B) 300K ddtonl Prmeters (18B (20B): d U m!, ( ) P cool Θ B. Vrble o-urrent V. Vrble ountercurrent d U m! ( ) P, U V P cool 0 (17) 0? o 34 Guess t V 0 to mtch 0 0 t ext,.e., V V f
35 35 et Exchnge Energy Blnce Vrble ounter-current oolnt blnce: In - Out + et dded 0 m! m! d d V d m! 0 + U + P U m! P d ( ) P V + ΔV + UΔV ( ) 0 ( ) r ( ), V ll equtons cn be used from before except prmeter, use dfferentl nsted, ddng m nd P
36 et Exchnge Energy Blnce Vrble o-current In - Out + et dded 0 m! m! d V +ΔV m! + U ( ) V + UΔV 0 ( ) d 0 U m! ( ) P ll equtons cn be used from before except d / whch must be chnged to negtve. o rrve t the correct ntegrton we must guess the vlue t V0, ntegrte nd see f 0 mtches; f not, re-guess the vlue for t V0 36
37 Derve the user-frendly Energy Blnce for PBR W U ρ 0 B ( ) dw + F F Dfferenttng wth respect to W: U ρ B df dw d dw ( ) + 0 F 0 37
38 Derve the user-frendly Energy Blnce for PBR Mole Blnce on speces : df dw rʹ υ ʹ r Enthlpy for speces : ο ( ) + R R P d 38
39 Derve the user-frendly Energy Blnce for PBR Dfferenttng wth respect to W: d 0 + dw P d dw U ρ B d dw ( ) + r υ F 0 ʹ P 39
40 Derve the user-frendly Energy Blnce for PBR U ρ B υ F d dw ( ) + r ʹ υ F 0 F 0 Δ R ( ) ( Θ + υ X) Fnl Form of the Dfferentl Equtons n erms of onverson: P : 40
41 Derve the user-frendly Energy Blnce for PBR Fnl form of terms of Molr Flow Rte: d dw U ρ B ( ) F P + r ʹ Δ B: dx dw r F 0 ʹ g( X,) 41
42 Reversble Rectons + B + D he rte lw for ths recton wll follow n elementry rte lw. r k B K D Where K e s the concentrton equlbrum constnt. We know from Le hltler s lw tht f the recton s exothermc, K e wll decrese s the temperture s ncresed nd the recton wll be shfted bck to the left. If the recton s endothermc nd the temperture s ncresed, K e wll ncrese nd the recton wll shft to the rght. 42
43 Reversble Rectons K K R P ( ) δ Vn t off Equton: d lnk d P ΔR R ( ) ο Δ ( ) + ΔĈ ( ) 2 R R R 2 P R 43
44 For the specl cse of Δ P 0 Integrtng the Vn t off Equton gves: ( ) ( ) ( ) Δ ο 2 1 R R 1 P 2 P 1 1 R exp K K 44 Reversble Rectons
45 Reversble Rectons X e endothermc recton exothermc recton K P endothermc recton exothermc recton 45
46 46 End of Lecture 20
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