Chemical Reaction Engineering

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
0
3
T
500 K
C
0.2 mol/dm
0
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

Batch
VV0
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

Batch
VV0
VV0
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 X0.9
11
Example 1
Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant
volume, VV0

• Reaction
• Additional Information

CA0 0.2 mol/dm3KC 100 dm3/mol
12
Example 1
Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant
volume, VV0

• Reaction
• Additional Information
• For constant volume

CA0 0.2 mol/dm3KC 100 dm3/mol
13
Example 1
Reversible Reaction, Constant Volume
Determine Xe for a batch system with constant
volume, VV0

• Reaction
• Additional Information
• For constant volume
• Solving for the equilibrium conversion
•   Xe 0.83

CA0 0.2 mol/dm3KC 100 dm3/mol
14
Example 2
Reversible Reaction, Variable Volumetric Flow Rate
Determine Xe for a PFR with no pressure drop, PP0

• Given The system is gas phase and isothermal.
• Find The reactor volume when X0.8Xe
• 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, PP0

• Given The system is gas phase and isothermal.
• Find The reactor volume when X0.8Xe
• 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, PP0

• Given The system is gas phase and isothermal.
• Find The reactor volume when X0.8Xe
• 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, PP0

• Given The system is gas phase and isothermal.
• Find The reactor volume when X0.8Xe
• Reaction
• Additional Information
• First Calculate Xe

CA0 0.2 mol/dm3 k 2 dm3/mol-min KC 100
dm3/mol FA0 5 mol/min
Xe 0.89 (vs. Xe 0.83 in Example 1) X 0.8Xe
0.711    
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((CA2)-(CB/KC))

21
Using Polymath

• Algorithm Steps Polymath Equations
• Mole Balance d(X)/d(V) -rA/FA0
• Rate Law rA -k((CA2)-(CB/KC))
• Stoichiometry CA
  (CA0(1-X))/(1epsX)
• CB (CA0X)/(2(1epsX))

22
Using Polymath

• Algorithm Steps Polymath Equations
• Mole Balance d(X)/d(V) -rA/FA0
• Rate Law rA -k((CA2)-(CB/KC))
• Stoichiometry CA
  (CA0(1-X))/(1epsX)
• CB (CA0X)/(2(1epsX))
• Parameter Evaluation eps -0.5 CA0 0.2
  k 2
• FA0 5 KC 100

23
Using Polymath

• Algorithm Steps Polymath Equations
• Mole Balance d(X)/d(V) -rA/FA0
• Rate Law rA -k((CA2)-(CB/KC))
• Stoichiometry CA
  (CA0(1-X))/(1epsX)
• CB (CA0X)/(2(1epsX))
• Parameter Evaluation eps -0.5 CA0 0.2
  k 2
• FA0 5 KC 100
• Initial and Final Values X0 0 V0 0
  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