1. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 17

2. Today’s lecture Energy Balance Fundamentals Adibatic reactors 2

3. Energy Balances, Rationale and Overview Let’s calculate the volume necessary to achieve a conversion, X, in a PFR for a first-order, exothermic and adiabatic reaction. The temperature profile might look something like this: T V k V X V Todays Lecture 3

4. The combined mole balance, rate law and stoichiometry yield: Energy Balances, Rationale and Overview 4

5. We cannot solve this Equation because we don’t have X either as a function of V or T. We need another Equation. That Equation is: Energy Balances, Rationale and Overview 5 The Energy Balance

6. User Friendly Equations Relate T and X or F i 1. Adiabatic CSTR, PFR, Batch or PBR 6

7. 7 Adiabatic T X EB Exothermic T0T0 0 T X EB Endothermic T0T0 0

8. 2. CSTR with heat exchanger, UA(T a -T) and a large coolant flow rate T TaTa User Friendly Equations Relate T and X or F i 8

9. 3. PFR/PBR with heat exchange F A0 T 0 Coolant TaTa User Friendly Equations Relate T and X or F i 3A. PFR in terms of conversion 9

10. User Friendly Equations Relate T and X or F i 3B. PBR in terms of conversion 3C. PBR in terms of molar flow rates 10

11. User Friendly Equations Relate T and X or F i 3D. PFR in terms of molar flow rates 4. Batch 11

12. User Friendly Equations Relate T and X or F i 5. For Semibatch or unsteady CSTR 6. For multiple reactions in a PFR (q reactions and m species) 12 Let’s look where these User Friendly Equations came from.

13. Rate of energy in by flow Rate of energy out by flow Heat added to the system Work done by the system Rate of energy accumulation --+= Energy Balance 13

14. Energy Balance on an open system: schematic. Energy Balance 14

15. OK folks, here is what we are going to do to put the above equation into a usable form. 1. Replace U i by U i =H i -PV i 2. Express H i in terms of heat capacities 3. Express F i in terms of either conversion or rates of reaction 4. Define Δ H Rx 5. Define Δ C P 6. Manipulate so that the overall energy balance is either in terms of the User Friendly Equations. 15

16. Assumptions: =0 Other energies small compared to internal Intro to Heat Effects 16 Recall:

17. Intro to Heat Effects 17 Substituting for

18. General Energy Balance: For Steady State Operation: 18 Intro to Heat Effects

19. Flow Rates, F i For the generalized reaction: In general, 19 Intro to Heat Effects

20. 20 Intro to Heat Effects

21. Enthalpy of formation at temperature T R Heat of reaction at temperature T Intro to Heat Effects 21 For No Phase Changes Constant Heat Capacities

22. 22 Intro to Heat Effects

23. 23 Intro to Heat Effects

24. Substituting back into the Energy Balance 24 Intro to Heat Effects

25. X T0T0 T Adiabatic Energy Balance: 25

26. 1) Mole balance: 2) Rate Laws: Example Adiabatic PFR 26 A ↔ B

27. 3) Stoichiometry: 4) Energy Balance: 27 Example Adiabatic PFR First need to calculate the maximum conversion which is at the Adiabatic Equilibrium. A ↔ B

28. T XCXC Adiabatic equilibrium conversion 28 Example Adiabatic PFR A ↔ B

29. We can now form a table. Set X, then calculate T, -V A, and F A0 /- r A, increment X, then plot F A0 /-r A vs. X: F A0 /-r A X 29

30. End of Lecture 17 30