1. Chemical Reaction Engineering
Chapter 4, Part 2:
1. Applying the Algorithm to a Batch Reactor, CSTR, and PFR
2. Calculating the Equilibrium Conversion

2. Using the Algorithm for Isothermal Reactor Design
Now we apply the algorithm to the reaction below occurring in a Batch Reactor, CSTR, and PFR.
Gas Phase Elementary Reaction
Additional Information
only A fed P
= 8.2 atm T
= 500 K 3 C
= 0.2 mol/dm A0 3 3
k = 0.5 dm
/mol-s v0
= 2.5 dm /s

3. Isothermal Reactor Design
Batch
CSTR
PFR
Mole Balance:

4. Isothermal Reactor Design
Batch
CSTR
PFR
Mole Balance:
Rate Law:

5. Isothermal Reactor Design
Batch
CSTR
PFR
Mole Balance:
Rate Law:
Stoichiometry: Gas: V = V0 Gas: T =T0, P =P0 Gas: T = T0, P = P0
(e.g., constant volume
steel container)
Per Mole of A: Per Mole of A:
Flow
Batch
V=V0

6. Isothermal Reactor Design
Batch
CSTR
PFR
Mole Balance:
Rate Law:
Stoichiometry: Gas: V = V0 Gas: T =T0, P =P0 Gas: T = T0, P = P0
(e.g., constant volume
steel container)
Per Mole of A: Per Mole of A:
Flow
Batch
V=V0
V=V0

7. Isothermal Reactor Design
Batch
CSTR
PFR
Stoichiometry (continued):

8. Isothermal Reactor Design
Batch
CSTR
PFR
Stoichiometry (continued):
Combine:

9. Isothermal Reactor Design
Batch
CSTR
PFR
Stoichiometry (continued):
Combine:
Integrate:

10. Isothermal Reactor Design
Batch
CSTR
PFR
Stoichiometry (continued):
Combine:
Integrate:
Evaluate:
Batch
CSTR
PFR
For X=0.9:

11. Example 1 Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant volume, V=V0
Reaction:
Additional Information:
CA0 = 0.2 mol/dm3 KC = 100 dm3/mol

12. Example 1 Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant volume, V=V0
Reaction:
Additional Information:
For constant volume:
CA0 = 0.2 mol/dm3 KC = 100 dm3/mol

13. Example 1 Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant volume, V=V0
Reaction:
Additional Information:
For constant volume:
Solving for the equilibrium conversion:
  Xe = 0.83
CA0 = 0.2 mol/dm3 KC = 100 dm3/mol

14. Example 2 Reversible Reaction, Variable Volumetric Flow Rate
Determine Xe for a PFR with no pressure drop, P=P0
Given: The system is gas phase and isothermal.
Find: The reactor volume when X=0.8Xe
Reaction:
Additional Information:
CA0 = 0.2 mol/dm3 k = 2 dm3/mol-min
KC = 100 dm3/mol FA0 = 5 mol/min

15. Example 2 Reversible Reaction, Variable Volumetric Flow Rate
Determine Xe for a PFR with no pressure drop, P=P0
Given: The system is gas phase and isothermal.
Find: The reactor volume when X=0.8Xe
Reaction:
Additional Information:
First Calculate Xe:
CA0 = 0.2 mol/dm3 k = 2 dm3/mol-min
KC = 100 dm3/mol FA0 = 5 mol/min

16. Example 2 Reversible Reaction, Variable Volumetric Flow Rate
Determine Xe for a PFR with no pressure drop, P=P0
Given: The system is gas phase and isothermal.
Find: The reactor volume when X=0.8Xe
Reaction:
Additional Information:
First Calculate Xe:
CA0 = 0.2 mol/dm3 k = 2 dm3/mol-min
KC = 100 dm3/mol FA0 = 5 mol/min

17. Example 2 Reversible Reaction, Variable Volumetric Flow Rate
Determine Xe for a PFR with no pressure drop, P=P0
Given: The system is gas phase and isothermal.
Find: The reactor volume when X=0.8Xe
Reaction:
Additional Information:
First Calculate Xe:
Solving for Xe:
CA0 = 0.2 mol/dm3 k = 2 dm3/mol-min
KC = 100 dm3/mol FA0 = 5 mol/min
Xe = 0.89 (vs. Xe= 0.83 in Example 1)
X = 0.8Xe =    

18. Using Polymath
Algorithm Steps Polymath Equations

19. Using Polymath Algorithm Steps Polymath Equations
Mole Balance d(X)/d(V) = -rA/FA0

20. Using Polymath Algorithm Steps Polymath Equations
Mole Balance d(X)/d(V) = -rA/FA0
Rate Law rA = -k*((CA**2)-(CB/KC))

21. Using Polymath Algorithm Steps Polymath Equations
Mole Balance d(X)/d(V) = -rA/FA0
Rate Law rA = -k*((CA**2)-(CB/KC))
Stoichiometry CA = (CA0*(1-X))/(1+eps*X)
CB = (CA0*X)/(2*(1+eps*X))

22. Using Polymath Algorithm Steps Polymath Equations
Mole Balance d(X)/d(V) = -rA/FA0
Rate Law rA = -k*((CA**2)-(CB/KC))
Stoichiometry CA = (CA0*(1-X))/(1+eps*X)
CB = (CA0*X)/(2*(1+eps*X))
Parameter Evaluation eps = CA0 = k = 2
FA0 = KC = 100

23. Using Polymath Algorithm Steps Polymath Equations
Mole Balance d(X)/d(V) = -rA/FA0
Rate Law rA = -k*((CA**2)-(CB/KC))
Stoichiometry CA = (CA0*(1-X))/(1+eps*X)
CB = (CA0*X)/(2*(1+eps*X))
Parameter Evaluation eps = CA0 = k = 2
FA0 = KC = 100
Initial and Final Values X0 = V0 = Vf = 500

24. General Guidelines for California Problems

25. General Guidelines for California Problems
Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.

26. General Guidelines for California Problems
Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.
Some Hints:
Group unknown parameters/values on the same side of the equation example: [unknowns] = [knowns]

27. General Guidelines for California Problems
Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.
Some Hints:
Group unknown parameters/values on the same side of the equation example: [unknowns] = [knowns]
Look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations

28. General Guidelines for California Problems
Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.
Some Hints:
Group unknown parameters/values on the same side of the equation example: [unknowns] = [knowns]
Look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations
Take ratios of Case 1 and Case 2 to cancel as many unknowns as possible

29. General Guidelines for California Problems
Every state has an examination engineers must pass to become a registered professional engineer.  In the past there have typically been six problems in a three hour segment of the California Professional Engineers Exam. Consequently one should be able to work each problem in 30 minutes or less. Many of these problems involve an intermediate calculation to determine the final answer.
Some Hints:
Group unknown parameters/values on the same side of the equation example: [unknowns] = [knowns]
Look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations
Take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
Carry all symbols to the end of the manipulation before evaluating, UNLESS THEY ARE ZERO