1. ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & REACTOR SIZING
Lecturer: Miss Anis Atikah Ahmad
Tel:

2. OUTLINE Conversion Batch Reactor Design Equation
Flow Reactors Design Equations
CSTR
PFR
PBR
Sizing Flow Reactors
Reactors in Series
Space Time
Space Velocity

3. 1. Conversion A-->B, Xmax,irr = 1 A⇌ B, Xmax,rev = Xe
aA + bB  cC + dD
Taking A as a basis,
Conversion, XA, is the number of moles A that have reacted per mole of A fed to the system
A-->B, Xmax,irr = 1
A⇌ B, Xmax,rev = Xe

4. Continuous Flow Reactor
1. Conversion
Batch Reactor
Continuous Flow Reactor

5. 2. Batch Reactor Design Equation
Moles of A reacted
Moles of A reacted
[Moles of A reacted/consumed] = [Moles of A fed]
Moles of A fed
[Moles of A reacted/consumed] = [NA0] [X]
Moles of A that have been consumed by chemical reaction
Moles of A initially
fed to reactor at t = 0
Moles of A in reactor at time t
[NA ] [NA0 ] [NA0 X]
NA NA ( X)

6. 2. Batch Reactor Design Equation
Moles of A reacted
NA NA NA0 X
[1]
Differentiating wrt time;
[2]
Recall mole balance for batch reactor (Chapter 1);
Rearranging and substituting into ;
[2]
[Design Equation in terms of conversion]

7. 2. Batch Reactor Design Equation
Design Equation (in terms of conversion, X ):
[3]
What is the time required to achieve a specific conversion?
Integrating [3] with limits (t=0, X=0; t=t, X=X )

8. 2. Batch Reactor Design Equation
For constant-volume batch reactor; V=V0
[ Design eq. from Chapter 1]
[Rearranging]
[Re-write in terms of concentration]

9. 3. Flow Reactors Design Equation
Moles of A reacted
Moles of A reacted/consumed = Moles of A fed
Moles of A reacted
time
time
Moles of A fed
= [FA0] [X]
Molar rate at which A is fed to the system
Molar rate at which A is consumed within the system
Molar flow rate at which A leaves the system
[FA ] [FA0 ] [FA0 X]
FA FA ( X)

10. 3. Flow Reactors Design Equation
FA FA FA0 X
Liquid phase
is given in mol/dm3
Gas phase
Partial Pressure

11. 3.1 CSTR FA FA0 FA0 X Recall Design Equation for CSTR (Chapter 1); [1]
Substituting into [1]
Rearranging;
FA FA FA0 X

12. 3.2 PFR FA FA0 FA0 X Recall Mole Balance for PFR (Chapter 1); [1]
We know that [2]
Differentiating [2] wrt X
FA FA FA0 X
[3]
Substituting [3] into [1]
[4]

13. 3.2 PFR
[4]
Integrating [4] with limit V=0 when X=0;

14. 3.3 PBR Design equation for PBR; Catalyst weight ; VW -rA -r’A
Similar to that of PFR except these terms:
Catalyst weight ;
VW
-rA -r’A

15. Summary of Reactor Mole Balance
Differential Form
Algebraic Form
Integral Form
Batch
CSTR -   -
PFR
PBR

16. 4. Reactor Sizing: Cstr & Pfr
With a given –rA as a function of conversion, X, we can size any type of reactor.
HOW???
Construct Levenspiel Plot
FA0/-rA vs. X
Volume of the reactors can be represented as the shaded areas in the Levelspiel Plots:

17. 4. Reactor Sizing Consider a first order reaction;
A plot of 1/-rA vs. X can be constructed;

18. An infinite reactor volume is needed to reach complete conversion
4. Reactor Sizing
Use plot of 1/-rA vs X to size flow reactors for different entering molar flow rates, FA0
Important Notes (For Irreversible Rxn, A --> B+C):
1. If the reaction is carried out isothermally,
the rate is usually greatest at the start of the reaction, when the
concentration is greatest [when X≈0, 1/-rA is small (rA is big)].
2. As X --> 1, -rA --> 0, thus 1/-rA --> ∞, V--> ∞
An infinite reactor volume is needed to reach complete conversion

19. An infinite reactor volume is needed to reach Xe
4. Reactor Sizing
Important Notes (cont):
(For Reversible Rxn, A ⇌ B+C):
1. The max conversion is the equilibrium conversion, Xe.
2. At equilibrium, rA(net)≈ 0.
X --> Xe, -rA --> 0, thus 1/-rA --> ∞, V--> ∞
An infinite reactor volume is needed to reach Xe

20. 4.1 Reactor Sizing: Sizing A Cstr
EXAMPLE 1

21. EXAMPLE 1
Calculate the volume to achieve 80% conversion in a CSTR. Given, species A enters the reactor at a molar flow rate of 0.4 mol/s.
SOLUTION:
Find –1/rA at X=0.8
2. Calculate V.

22. 4.1 Sizing A Cstr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45
EXAMPLE 1
Levelspiel Plot: X
0.1
0.2
0.4
0.6
0.7
0.8 rA
0.45
0.37
0.3
0.195
0.113
0.079
0.05
FA0/rA
0.89
1.08
1.33
2.05
3.54
5.06
8.00

23. 4.2 Reactor Sizing: Sizing A Pfr
Volume of a PFR can be calculated using integration formulas:
Trapezoidal Rule (2-point)
Simpson’s One-Third Rule (3-point)
Simpson’s Three-Eighths Rule (4-point)
Five-Point Quadrature Formula

24. 4.2 Reactor Sizing: Sizing A Pfr
Trapezoidal Rule (2-point):
Simpson’s One-Third Rule (3-point):

25. 4.2 Reactor Sizing: Sizing A Pfr
Simpson’s Three-Eighths Rule (4-point):
Five-Point Quadrature Formula:

26. 4.2 Sizing A Pfr
EXAMPLE 2
Calculate the volume to achieve 80% conversion in a PFR. Given, species A enters the reactor at a molar flow rate of 0.4 mol/s.

27. 4.2 Reactor Sizing: Sizing A Pfr
Recall the design equation of PFR:
For X=0.8,

28. 4.2 Sizing A Pfr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45
EXAMPLE 2
Levelspiel Plot: X
0.1
0.2
0.4
0.6
0.7
0.8 rA
0.45
0.37
0.3
0.195
0.113
0.079
0.05
FA0/rA
0.89
1.08
1.33
2.05
3.54
5.06
8.00

29. 4.2 Sizing A Pfr
Recall 5-Point Quadrature Rule:
Find h (∆X):

30. 4.2 Sizing A Pfr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45
EXAMPLE 2
Levelspiel Plot: X
0.1
0.2
0.4
0.6
0.7
0.8 rA
0.45
0.37
0.3
0.195
0.113
0.079
0.05
FA0/rA
0.89
1.08
1.33
2.05
3.54
5.06
8.00

31. 4.2 Sizing A Pfr Find V: Substituting the numerical values:
--> PFR with volume of m3 is required
to reach 80% conversion

32. 4.3 Comparing Volume of Cstr & Pfr
Difference btwn CSTR & PFR volumes=4.235m3
PFR

33. 4.3 Comparing Volume of Cstr & Pfr
VCSTR > VPFR for the same conversion & rxn condition.
WHY???

34. 5. Reactors in Series
The exit stream of one reactor is fed to the next one

35. 5.1 Cstr in Series Reactor 1: Mole Balance: In – Out + Generation = 0
FA0 – FA1 + rA1V1 = 0 [1]
The molar flow rate of A at point 1:
FA1 = FA0 – FA0 X [2]
Combining [1] & [2]:
(1)
(2)

36. 5.1 Cstr in Series Reactor 2: Mole Balance: In – Out + Generation = 0
FA1 – FA2 + rA2V2 = 0 [3]
The molar flow rate of A at point 2:
FA2 = FA0 – FA0 X [4]
Combining [3] & [4]:
(1)
(2)
Expressed in eq [2] & [4]
[5]

37. 5.1 Cstr in Series FA1 = FA0 – FA0 X1 [2] FA2 = FA0 – FA0 X2 [4] [5]
(1)
FA2 = FA0 – FA0 X [4]
(2)
[5]
Substituting [2] &[4] into [5];

38. 5.1 Cstr in Series
EXAMPLE 3 X
0.0
0.1
0.2
0.4
0.6
0.7
0.8
[FA0/-rA](m3)
0.89
1.08
1.33
2.05
3.54
5.06
8.0
For the two CSTRs in series, 40% conversion is achieved in the first reactor. What is the volume of each of the two reactors necessary to achieve 80% overall conversion of entering species?

39. For reactor 1, X = 0.4 For reactor 2, X = 0.8 X 0.0 0.1 0.2 0.4 0.6
EXAMPLE 3 X
0.0
0.1
0.2
0.4
0.6
0.7
0.8
[FA0/-rA](m3)
0.89
1.08
1.33
2.05
3.54
5.06
8.0
For reactor 1, X = 0.4
For reactor 2, X = 0.8
Total V= ( )m3
= 4.02 m3

40. EXAMPLE 3
5.1 Cstr in Series
Levenspiel Plot of CSTR in series V2 V1

41. 5.2 Pfr in Series V1 V2
The overall conversion of two PFRs in series is the same as ONE PFR with the same total volume.
V1, PFR
V2, PFR

42. 5.2 Pfr in Series
EXAMPLE 4 X
0.0
0.1
0.2
0.4
0.6
0.7
0.8
[FA0/-rA](m3)
0.89
1.08
1.33
2.05
3.54
5.06
8.0
Calculate the reactor volume V1 and V2 for the plug-flow sequence shown below when the intermediate conversion is 40% & the final conversion is 80%.

43. Using Simpsons One-Third Rule;X
0.0
0.1
0.2
0.4
0.6
0.7
0.8
[FA0/-rA](m3)
0.89
1.08
1.33
2.05
3.54
5.06
8.0
Using Simpsons One-Third Rule;
For reactor 1, ∆X=0.2, X0 = 0, X1 = 0.2, X2 = 0.4

44. For reactor 2, ∆X=0.2, X0 = 0.4, X1 = 0.6, X2 = 0.8 Total volume; X
0.0
0.1
0.2
0.4
0.6
0.7
0.8
[FA0/-rA](m3)
0.89
1.08
1.33
2.05
3.54
5.06
8.0
For reactor 2, ∆X=0.2, X0 = 0.4, X1 = 0.6, X2 = 0.8
Total volume;

45. 5.3 Combination of Cstr & Pfr
V3,CSTR
V1,CSTR
V2,PFR X1 X2 X3

46. 5.4 Reactor Sequencing
Which sequence is better to obtain the highest overall conversion? OR
The BEST sequence of reactors depend on
Levenspiel Plot
Reactor Size

47. Measures entering flow rate at the entrance condition
6. Space Time
Measures entering flow rate at the entrance condition
Space time/Mean residence time :
time taken for a fluid to either completely enter or completely exit the reactor
Eg: If V=0.2m3, v0= 0.01m3/s, what is τ?
Answer: τ = 20 s

48. 7. Space Velocity, SV Space velocity can be defined as:
2 types of SV that is commonly used in industry:
Liquid-hourly space velocity (LHSV) –measures liquid volumetric rate at 60°F or 75°F
Gas-hourly space velocity (GHSV)-measures gas volumetric at standard temperature & pressure (STP)

49. Summary Conversion: Batch reactor: Flow Reactors Design equation:
Batch: CSTR: PFR: PBR:
Reactor in series:
Conversion: CSTR in series: PFR in series:

50. Exercise
The irreversible gas-phase non-elementary reaction A + 2B --> C is to be carried out isothermally in a constant pressure batch reactor. The feed is at a temperature of 227°C, a pressure of 1013 kPa, and its composition is 30% A and 60% B. Laboratory data taken under identical conditions are as follows : (a) What is PFR volume necessary to achieve 30 % conversion for an entering flow rate of 2 m3/min ?
-rA (mol/dm3.s) X
0.0
0.15
0.3
0.6

51. Exercise
(a) What is PFR volume necessary to achieve 30 % conversion for an
entering flow rate of 2 m3/min ?
Given:
We know that and for gas phase:
1. Find CA0
2. Find FA0
3. Calculate VPFR using Integration Rule

52. Exercise Using Simpson One-Third Rule: -rA (mol/dm3.s) 0.00001 X
0.0
0.15
0.3
0.6
FA0/-rA (dm3)
243000
486000
Using Simpson One-Third Rule:

53. Exercise
-rA (mol/dm3.s) X
0.0
0.15
0.3
0.6
FA0/-rA (dm3)
243000
486000
(b) What is CSTR volume necessary to take the effluent from PFR above and achieve 60% total conversion (based on species A fed to the PFR)?
FA0=2.43 mol/s
X=0.3
X=0.6

54. Exercise
FA0=2.43 mol/s
X=0.3
X=0.6