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 19

Web Lecture 19 Class Lecture 17 – Tuesday 3/8/2011 Energy Balance Fundamentals Adibatic reactors 2

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 3

4

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: 5 The Energy Balance

1. Adiabatic CSTR, PFR, Batch or PBR 6

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

2. CSTR with heat exchanger: UA(T a -T) and a large coolant flow rate T TaTa 8

3. PFR/PBR with heat exchange F A0 T 0 Coolant TaTa 3A. PFR in terms of conversion 9

3B. PBR in terms of conversion 3C. PBR in terms of molar flow rates 10

3D. PFR in terms of molar flow rates 4. Batch 11

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.

Reactor with no Spatial Variations Reactor

Reactor with no Spatial Variations Rate of flow of heat to the system from the surroundings Reactor

Reactor with no Spatial Variations Rate of flow of heat to the system from the surroundings Rate of work done by the system on the surroundings Reactor - -

Reactor with no Spatial Variations Rate of flow of heat to the system from the surroundings Rate of work done by the system on the surroundings Rate of energy added to the system by mass flow into the system Reactor +- +-

Reactor with no Spatial Variations Rate of flow of heat to the system from the surroundings Rate of work done by the system on the surroundings Rate of energy added to the system by mass flow into the system Rate of energy leaving system by mass flow out of the system Reactor

Reactor with no Spatial Variations Rate of flow of heat to the system from the surroundings Rate of work done by the system on the surroundings Rate of energy added to the system by mass flow into the system Rate of energy leaving system by mass flow out of the system Rate of accumulation of energy within the system Reactor =+-- =+--

Energy Balance on an open system: schematic. 19

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 in terms of the User Friendly Equations. 20

Assumptions: =0 Other energies small compared to internal 21 Recall:

22 Substituting for Steady State:

General Energy Balance: For Steady State Operation: 23

24

Enthalpy of formation at temperature T R Heat of reaction at temperature T 25 For No Phase Changes Constant Heat Capacities

Substituting back into the Energy Balance 26 Adiabatic (Q=0) and no Work

27

Substituting back into the Energy Balance 28

X T0T0 T 29 Adiabatic (Q=0) and no Work Exothermic

1) Mole balance: 2) Rate Laws: 30 A ↔ B

3) Stoichiometry: 4) Energy Balance: 31 First need to calculate the maximum conversion which is at the Adiabatic Equilibrium. A ↔ B

T XCXC Adiabatic equilibrium conversion 32 A ↔ B

33

34

Substituting back into the Energy Balance 35

X T0T0 T 36

1) Mole balance: 2) Rate Laws: 37 A ↔ B 3) Stoichiometry:

5) Energy Balance: 38 First need to calculate the maximum conversion for adiabatic operation which is at the Adiabatic Equilibrium Conversion. A ↔ B 4) Combine: At equilibrium –r A  0, solving for

T XeXe Adiabatic equilibrium conversion and temperature 40 A ↔ B

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 41

42