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.
Lst Lecture Energy Blnce Fundmentls F 0 E 0 F E Q W de dt sys Substtutng for W H 0 F 0 U 0 PV 0 0 F U PV Q WS F H F H Q W 0 0 S H de dt sys de dt sys Q W F H F H 0 S 0 0 2
Web Lecture 20 lss Lecture 16-hursdy 3/14/2013 Rectors wth Het Exchnge User frendly Energy Blnce Dervtons dbtc Het Exchnge onstnt Het Exchnge Vrble o-current Het Exchnge Vrble ounter urrent 3
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
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
SR: dbtc Exmple F 0 = 5 mol mn F 0 F I 0 = 300 K ΔH Rxn = 20000 cl mol (exothermc) F I = 10 mol mn B =? X =? 1) Mole Blnces: V F r 0 X ext 6
1 1 R H exp K K e k k K k r 2 Rx 1 1 1 R E 1 B 1 2) Rte Lws: X X 1 0 B 0 3) Stochometry: 7 SR: dbtc Exmple
SR: dbtc Exmple 4) Energy Blnce dbtc, p =0 0 300 H X H P 20,000 164 18 Rx 2 X 0 P Rx I X 20,000 300 164 36 P I X 300 100 X 8
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 V lc K (f reversble) 9
SR: dbtc Exmple Gven X, lculte nd V V k V F r 0 F0 X r X ext 0.1exp F k 0.8 0 10,000 1.989 300 100 0 X 1 X 1 298 380K 1 380 50.8 3.812 1 0.8 3.81 2.82 dm 3 10
SR: dbtc Exmple Gven, lculte X nd V (b) Gven X lc lc lc k r lc V 11 r 360K 0 300 X 100 k 1.83 mn V k 1 1 X 50.6 1.832 0.4 0.6 (Irreversble) 2.05 dm lc K (f reversble) 3
SR: dbtc Exmple (c) Levenspel Plot F r 0 k F0 1 0 300 100X X hoose X lc lc k lc F 0 lc r r 12
SR: dbtc Exmple (c) Levenspel Plot 13
SR: dbtc Exmple SR X = 0.6 = 360 K SR 60% SR X = 0.95 = 395 K 14 SR 95%
SR: dbtc Exmple 30 PFR X = 0.6 25 20 -F0/R 15 10 5 PFR 60% 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 X PFR X = 0.95 PFR 95% 15
SR: dbtc Exmple - Summry SR X = 0.6 = 360 V = 2.05 dm 3 PFR X = 0.6 ext = 360 V = 5.28 dm 3 SR X = 0.95 = 395 V = 7.59 dm 3 PFR X = 0.95 ext = 395 V = 6.62 dm 3 16
Energy Blnce n terms of Enthlpy F H V F H V V U V 0 d F H U 0 d F H F dh H df 17
PFR Het Effects df H r H 0 P r R dh P d d F H F P d H r H H R x 18
PFR Het Effects P F d H R r U 0 F P d H R r U d H r U R F P 19 Need to determne
Het Exchnge: d r H U Rx F P d r H U F 0 Rx P (16B) 20 Need to determne
Het Exchnge Exmple: se 1 - dbtc Energy Blnce: dbtc (U=0) nd Δ P =0 0 HRx P X (16) 21
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 P cool V 0? Guess Guess t V = 0 to mtch 0 = 0 t ext,.e., V = V
Het Exchnger Energy Blnce Vrble o-current oolnt Blnce: In - Out + Het dded = 0 m H m H V dh H 0 m H U P V V UV 0 r 0 23 dh d P d U m P, V 0 0
Het Exchnger Energy Blnce Vrble o-current In - Out + Het dded = 0 m H V V m H V UV 0 m dh U 0 24 d U m P
Het Exchnger Exmple se 1 onstnt Elementry lqud phse recton crred out n PFR m c Het Exchnge Flud F 0 F I B 25 he feed conssts of both nerts I nd speces wth the rto of nerts to the speces beng 2 to 1.
Het Exchnger Exmple se 1 onstnt 1) Mole Blnce: dx ( 1) r F 0 2) Rte Lws: (2) r k K B (3) k k 1 exp E R 1 1 1 26 (4) K K 2 exp H R Rx 1 2 1
27 Het Exchnger Exmple se 1 onstnt 3) Stochometry: B 0 0 P 0 X eq k 1 k P 1 X P X 8 5 I 6 4) Het Effects: d H r U R F 0 P PI 9 7
Prmeters: I PI P R r rte F U k k R E H,,,,,,,,,,,,,, 0 0 2 1 2 1 Het Exchnger Exmple se 1 onstnt 28
PFR Het Effects Het generted Het removed d Q g Q F r P F P F 0 X F X P 0 P P 29 d H R r U F X 0 P P
Het Exchnger Exmple se 2 dbtc Mole Blnce: Energy Blnce: dx r F 0 dbtc nd Δ P =0 U=0 0 HRx P X (16) 30 ddtonl Prmeters (17) & (17B), 0 P P IP I
31 dbtc PFR
Exmple: dbtc Fnd converson, X eq nd s functon of rector volume X X X eq rte V V V 32
Het Exchnge d r H U Rx F P d r H U F 0 Rx P (16B) 33 Need to determne
User Frendly Equtons. onstnt (17B) = 300K ddtonl Prmeters (18B (20B): d P cool, B. Vrble o-urrent U m V. Vrble ountercurrent d U m P cool V P, U 0 (17) 0? o 34 Guess t V = 0 to mtch 0 = 0 t ext,.e., V = V f
35 Het Exchnge Energy Blnce Vrble o-current oolnt blnce: In - Out + Het dded = 0 m m H H dh d V dh H m 0 H U P P d U m P V V UV 0 r, V 0 0 0 ll equtons cn be used from before except prmeter, use dfferentl nsted, ddng m nd P
Het Exchnge Energy Blnce Vrble o-current In - Out + Het dded = 0 m m H dh V V m U H V UV 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 V=0, ntegrte nd see f 0 mtches; f not, re-guess the vlue for t V=0 36
Derve the user-frendly Energy Blnce for PBR W U 0 B dw F H FH 0 0 0 Dfferenttng wth respect to W: U B df dw dh dw 0 H F 0 37
Derve the user-frendly Energy Blnce for PBR Mole Blnce on speces : df dw r r Enthlpy for speces : H H R R P d 38
Derve the user-frendly Energy Blnce for PBR Dfferenttng wth respect to W: dh dw 0 P d dw U B d dw r H F 0 P 39
Derve the user-frendly Energy Blnce for PBR U B F d dw r H F 0 H F 0 H R X Fnl Form of the Dfferentl Equtons n erms of onverson: P : 40
Derve the user-frendly Energy Blnce for PBR Fnl form of terms of Molr Flow Rte: d dw U B F P r H B: dx dw r F 0 g X, 41
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
Reversble Rectons K K R P Vn t Hoff Equton: d ln K d P HR R H Ĉ 2 R R R 2 P R 43
For the specl cse of Δ P =0 Integrtng the Vn t Hoff Equton gves: 2 1 R R 1 P 2 P 1 1 R H exp K K 44 Reversble Rectons
Reversble Rectons X e endothermc recton exothermc recton K P endothermc recton exothermc recton 45
46 End of Lecture 20