Chemical Reaction Engineering

Transcription

1 Lecture 19 hemcal Reacton Engneerng (RE) s the feld that studes the rates and mechansms of chemcal reactons and the desgn of the reactors n whch they take place.

2 Web Lecture 19 lass Lecture 17 uesday 3/19/2013 Energy Balance Fundamentals Adabatc reactors 2

3 oday s Lecture Energy Balance, Ratonale and Overvew Let s calculate the volume necessary to acheve a converson, X, n a PFR for a frst-order, exothermc and adabatc reacton. he temperature profle mght look somethng lke ths: k X 3 V V V

4 Energy Balance, Ratonale and Overvew Mole Balance: Rate Law: Stochometry: ombne: dx dv dx dv r A A F k r A A0 exp 1 A0 X E R E 1 1 k exp R 1 A0 1 F A0 A X 4

5 Energy Balance, Ratonale and Overvew dx dv E 1 1 k exp R 1 A0 1 F A0 X We cannot solve ths equaton because we don t have X ether as a functon of V or. We need another equaton. hat equaton s: he Energy Balance 5

6 User Frendly Equatons Relate and X or F 1. Adabatc SR, PFR, Batch or PBR W S 0 ˆ 0 P X EB P 0 H o Rx 6 X PA 0 H Rx 0 H o Rx P X EB

7 Adabatc Exothermc Endothermc X EB 0 X EB 7

8 User Frendly Equatons Relate and X or F 2. SR wth heat exchange: UA( a -) and a large coolant flow rate UA F a P 0 X EB A 0 H o Rx m 8 a

9 User Frendly Equatons Relate and X or F 3. PFR/PBR wth heat exchange F A0 0 a oolant 9 3A. PFR n terms of converson Q g Q r d r AH Q Rx Ua a g Qr dv F X F X A0 P p A0 P p

10 User Frendly Equatons Relate and X or F 3B. PBR n terms of converson d dw r A H Rx F A 0 Ua b a P p X 3. PBR n terms of molar flow rates 10 d dw r A H Rx Ua a b F P

11 User Frendly Equatons Relate and X or F 3D. PFR n terms of molar flow rates d dv r AH Rx Ua a F P Q g Q r F P 4. Batch d dt r AV H Rx UA a N P 11

12 User Frendly Equatons Relate and X or F 5. For Sembatch or unsteady SR d dt n Q W F H r V S 0 P 0 Rx A 1 n 1 N 6. For multple reactons n a PFR (q reactons and m speces) d dv q r j H Rx j 1 m j 1 Ua a F Pj 12 Let s look where these User Frendly Equatons came from. P

13 Energy Balance Reactor wth no Spatal Varatons Reactor

14 Energy Balance Reactor wth no Spatal Varatons Q Reactor Rate of flow of heat to the system from the surroundngs Q (J/s)

15 Energy Balance Reactor wth no Spatal Varatons Q W Reactor Rate of flow of heat to the system from the surroundngs - Rate of work done by the system on the surroundngs Q (J/s) - W (J/s)

16 Energy Balance Reactor wth no Spatal Varatons Q W F E n n Reactor Rate of flow of heat to the system from the surroundngs - Rate of work done by the system on the surroundngs + Rate of energy added to the system by mass flow nto the system Q (J/s) - W (J/s) + F E n n (J/s)

17 Energy Balance Reactor wth no Spatal Varatons Q W F E n n Reactor F E out out Rate of flow of heat to the system from the surroundngs Rate of work done by the system on the surroundngs Rate of energy added to the system by mass flow nto the system Rate of energy leavng system by mass flow out of the system Q (J/s) - W + F - n E n (J/s) (J/s) F E out out (J/s)

18 Energy Balance Reactor wth no Spatal Varatons Q W F E n n Reactor F E out out Rate of accumulaton of energy wthn the system Eˆ d sys dt (J/s) Rate of flow of heat to the system from the surroundngs = Q - W + F - (J/s) Rate of work done by the system on the surroundngs (J/s) Rate of energy added to the system by mass flow nto the system = n E n (J/s) Rate of energy leavng system by mass flow out of the system F E out out (J/s)

19 Energy Balance F H n e.g., n e.g., F H A0 A0 W S Q F out e.g., F H e.g., H out A A Energy Balance on an open system: schematc. Q W S F 0 E 0 n FE out de system dt 1 19

20 OK folks, here s what we are gong to do to put the above equaton nto a usable form. 1. Replace U by U =H -PV 2. Express H n terms of heat capactes 3. Express F n terms of ether converson or rates of reacton 4. Defne ΔH Rx 5. Defne Δ P 6. Manpulate so that the overall energy balance s n terms of the User Frendly Equatons. 20

21 Intro to Heat Effects Assumptons: E W U PE KE flow work shaft work flow work =0 =0 Other energes small compared to nternal F 0 P V ~ 0 0 FPV ~ m V ~ 3 mol Recall: H U PV 21

22 Intro to Heat Effects Substtutng for W F 0U 0 FU Q F 0PV 0 0 F PV WS de dt sys H 0 F 0 U 0 PV 0 0 F U PV Q WS H de dt sys F H F H Q W 0 0 S de dt sys 22 Steady State: Q W F H FH 0 S 0 0

23 Intro to Heat Effects General Energy Balance : Q W S F 0 H 0 FH de system dt For Steady State Operaton: Q W F H FH 0 S

24 Intro to Heat Effects F 0 H 0 F A 0 H F H F X H F H F X H A A A H Rx S A A Rx Q W F H H F X H

25 Intro to Heat Effects For No Phase hanges H H 0 R R P d onstant Heat apactes Enthalpy of formaton at temperature R H H 0 R P R 25 H 0 H P 0 H 0 H P R Heat of reacton at temperature

26 Intro to Heat Effects H 0 H P R H R H R ˆ P ˆ P R ˆ P R d a ˆ PD c a ˆ P b a ˆ PB ˆ PA Substtutng back nto the Energy Balance Q W ˆ S FA 0X H R R P R F A0 P Adabatc (Q=0) and no Work ( 0) W S

27 Intro to Heat Effects H Rx d a H D c a H b a H B H A P d a PD c a P b a PB PA 27

28 Intro to Heat Effects S A A Rx Q W F H H F X H Substtutng back nto the Energy Balance Q W ˆ S FA 0X H R R P R F A0 P

29 X 0 P P R P P R P R R X H X X H X ˆ ~ ˆ ~ ˆ 0 0 Adabatc Energy Balance 29 Adabatc (Q=0) and no Work ) ( 0 W S Exothermc

30 A0 A F r dv dx 1) Mole Balance: 1 1 k H exp k k R E exp k k k k r 2 0 X 2 P 1 1 B A A 2) Rate Laws: Example: Adabatc PFR 30 A B

31 Example: Adabatc PFR A B 3) Stochometry: A 4) Energy Balance B 0 A0 A0 1 X X 0 HXX P 31 Frst need to calculate the maxmum converson whch s at the adabatc equlbrum converson.

32 Example: Adabatc PFR

33 Example: Adabatc PFR A B 0 0 H X X P X e Adabatc equlbrum converson and temperature 33 X eq K 1 K

34 Example: Adabatc PFR We can now form a table. Set X, then calculate, -V A, and F A0 /-r A, ncrement X, then plot F A0 /-r A vs. X: F A0 /-r A 34 X

35 End of Web Lecture 19 lass Lecture 17 35