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Chemical Engineering DepartmentCCB3043 KINETICS AND REACTOR DESIGN
CHAPTER 2: CONVERSION AND REACTOR SIZING(part 1)
1
Basic knowledge
Application
3
1. Define conversion
2. Develop design equation for batch reactor
3. Develop design equation for flow reactor
4. Applying design equation to solve reactor problems
5. Applying design equation to reactors in series
6. Differentiate between space time and space
velocity
OBJECTIVES OF CHAPTER 2
4
Overview on Objective of Chapter 2
Re-write reactor sizing
in terms of conversion
Reactor sizing in terms of
mole balance
Relating mole balance to conversion
CHAPTER 1
CHAPTER 2
APPLYING DESIGN
EQUATION TO SOLVE
PROBLEMS RELATED TO FLOW REACTOR AND REACTOR IN SERIES
What is conversion?
• Consider the general equation (irreversible eqn)
aA + bB cC + dD
• We will choose A as our basis of calculation
DadC
acB
abA
How do we define
conversion?
Conversion
• Conversion is define as:
feedA of molesreactedA of moles
AX
MAXIMUM CONVERSION?
Irreversible ReactionX = 1
Reversible ReactionX = Xe
7
Conversion
How do we relate
conversion with flow rate or
moles of reactant?
8
Relating conversion with moles of reactant
Batch reactor
XNXN
A
A
0
0
.
reacted A of Mole
onversionC fed A of Moles reacted A of Mole
reacted A of Mole - fed A of Mole timeany at A of Mole t
XNNN AAA 00 -
0
0 - A
AA
NNNX
9
Relating conversion with molar flow rate
Flow reactor (CSTR and PFR/PBR)
XFXF
A
A
0
0
.
reacted A of flowrate Molar
onversionC fed A of flowrate Molar reacted A of flowrate Molar
t Molar flowrate A at any time Molar flowrate A fed - Molar flowrate A reacted
XFFF AAA 00 -
0
0 - A
AA
FFFX
10
Now, recap back our design equation:
Relating V to X
dtdN
Vr AA
HOW TO RE-WRITE
V = f(X)
WHAT WE HAVE JUST DISCOVERED:
0
0 - A
AA
NNNX
0
0 - A
AA
FFFX
Develop Design Equation for batch reactor
• Batch reactor
X
AA
AA
VrdXNt
Vrdt
dN
00
• PFR
0
AA
AA
A
dF rdV
dXV Fr
• CSTR
A
A
AAA
rXF
V
VrFF
0
0 0
Develop Design Equation for flow reactor
Design Equation(Summary)
Reactor Differential Algebraic Integral
Batch
CSTR
PFR
PBR
Example:
• E. 2-1: Using ideal gas law to calculate CAO and FA0
A gas of pure A at 830 kPa (8.2 atm) enters a reactor with a
volumetric flow rate, v0 of 2 dm3/s at 500K. Calculate the
entering concentration of A and its molar flow rate.
15
APPLYING DESIGN EQUATIONS TO SOLVE REACTOR PROBLEMS
For F LOW R EAC TO R , we can estimate the reactor
size using a L E V E N S P I E L P LOT .
What is LEVENSPIEL plot?
• From a given data of and X, and a know value of FA0:
16
Reactor Sizing for flow reactor
–rA X FA0/-rAFA0/-rA
X
Reactor Sizing for flow reactor
• Knowing –rA = f(XA), reactor size can be determine
using Levenspiel plot
• Consider the design equation for CSTR
A
0Ar
XFV
• Consider the design equation of a PFR
Reactor Sizing for flow reactor
A0A rdVdXF
19
Example 2-2 / 2-3: Sizing a CSTR / PFR
The gas phase reaction A B is carried out in a
CSTR and the entering molar flow rate of A is
0.4 mol/s. Using data in Table 2-1:
1. Calculate the volume required to achieve
80% conversion. Shade the area on the
Levenspiel plot that corresponds to this
conversion.
2. Re-do the problem if the reaction is carried
out in a PFR.
3. Any comment on the reactor size?
Reactor Sizing for flow reactor
XA -rA (mol/m3.s)0.0 0.450.1 0.370.2 0.300.4 0.1950.6 0.1130.7 0.0790.8 0.05
TABLE 2.1
Solution Ex 2-2: Sizing for CSTRTABLE 2.1
XA -rA (mol/m3.s) 1/-rA (m3..s/mol) FA0/-rA (m3..s/mol)
0.0 0.45 2.22 0.890.1 0.37 2.70 1.080.2 0.30 3.33 1.330.4 0.195 5.13 2.050.6 0.113 8.85 3.540.7 0.079 12.70 5.060.8 0.05 20.00 8.00
XFr
V AA
01
DESIGN EQUATION OF CSTR!!
Solution Ex 2-2: Sizing for PFRTABLE 2.1
XA -rA (mol/m3.
s)
FA0/-rA (m3..s/mol)
0.0 0.45 0.890.2 0.30 1.330.4 0.195 2.050.6 0.113 3.540.8 0.05 8.00
0.80
0A
A
FV dXr
DESIGN EQUATION OF PFR!!
Use 5-point quadrature formula:
4
00 1 2 3 44 2 4
3X
X
hf X dX f f f f f
4 0
4X X
h
Summary what we have learned:Important things to remember
Volume CSTR
Volume PFR
• General mole balance• Mole balance equations for
each reactor• Design equations for each
reactor• Conversion• Reactor sizing
Reactors in Series
• Knowing –rA = f(XA), we can design any sequence of
reactors
• Provided there’s no side reactors, conversion at any
reactor outlet is define as:
reactorfirst tofedA of moleipoint toup reactedA of moles total
iX
Reactors in series
Try and develop these design equations……..
2 CSTR in series
1 2
0
2
4
6
8
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Conversion, X
FA0/
-rA
FA2
X2=0.8
FA0
FA1
X1=0.4
2 PFR in series
0
2
4
6
8
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Conversion, XFA
0/-rA
1
2
FA0
FA1
X1=0.4
FA2
X2=0.8
CSTR in series = 1 PFR
54321
1 2 3 4 5
Equals to
As no. of CSTR in series increases, the total volume required for a given conversion is similar to the volume of one PFR
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
Conversion, X
FA0/
-rA
CSTR in series = 1 PFR
CSTR 1CSTR 2
CSTR 3
CSTR 4
CSTR 5
PFR
Reactors in series• Example 2-5: Comparing volumes for CSTR in
series– From data below, calculate the volume of CSTR if 2 CSTR in series
is use for the reaction. Given that the intermediate conversion is 40% and the final conversion is 80%. Then, use the Levenspiel plot to help you explain on the difference of the reactor volume for single CSTR and CSTR in series.
– Will there be any difference in volume if the reaction is carried out in 2 PFR in series? Use the Levenspiel plot to explain your answer.
X 0.0 0.1 0.2 0.4 0.6 0.7 0.8FA0/-rA
0.89 1.09 1.33 2.05 3.54 5.06 8.0
0
2
4
6
8
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Conversion, X
FA0/
-rA
3
1
31
3
4.0
0
8.0
4.00.2
0.2
mV
mV
mr
F
XA
A
332
122
02
3
8.0
0
2.34.08.00.8
0.8
mmV
XXr
FV
mr
F
A
A
XA
A
VT = V1 +V2 = 0.82 + 3.2 = 4.02 m3
Answer Example 2-5
Reactors in series
• Example 2-6: Sizing plug flow reactors in series
– Redo Example 2-5 but using 2 PFR in series. The
intermediate and final conversion remains the same.
The flow rate, FA0, also remains the same.
Answer Example 2-6
• Use Simpson’s three-point rule
331
0001
4.0
001
551.005.233.1489.032.0
)4.0()2.0(4
)0(3
mmV
rF
rF
rFXV
rdXFV
A
A
A
A
A
A
AA
331
0002
8.0
4.002
614.10.854.3405.232.0
)8.0()6.0(4
)4.0(3
mmV
rF
rF
rFXV
rdXFV
A
A
A
A
A
A
AA
210 43
)(2
0
XfXfXfXdXxfX
X
3321 165.2614.1551.0 mmVVVT
This is the same volume if we were to calculate for a single PFR to achieve the same conversion.
•Example 2.7 – An adiabatic liquid phase isomerisation
The isomerisation of butane was carried out adiabatically in the liquid phase and the data in Table 2-7 was obtained. The entering molar flow rate of n-butane of 50 kmol/hr.
Given the reactor scheme in Figure E 2-7.1, use Levenspiel plot to show how to calculate the reactor volume
Reactors in series
2538595339-rA (kmol/m3.hr)
0.650.60.40.20XTable 2-7
Reactors in series
V1
X1=0.2
X2=0.6
X3=0.65
Figure E2-7.1
35
Levenspiel plot for adiabatic reactors in series
0.00
0.50
1.00
1.50
2.00
2.50
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70
Conversion, X
FA0/
-rA
Can you suggest a better reactor combination?
1st CSTR 2nd CSTRPFR
CSTR PFR
Some further definitions
• Relative rate of reaction– Obtained from stoichiometric ratio– Example:
dr
cr
br
ar DCBA
Space time
ReactorFluid
•Also know as Mean Residence Time or Holding Time •Defined as the time necessary to process one reactor volume of fluid based on entrance condition (volumetric flow rate)
0 V
Volume of reactor
Volumetric flowrate
Space time = time it for the fluid to enter the reactor completely
• Space velocity (SV)– 2 common measures of space velocity
• Liquid hourly space velocity (LHSV)–Liquid flowrate measured at 60 - 70oF
• Gas hourly space velocity (GHSV)–Gas flow rate measured at STP
– Given by:
Some further definitions
Vv
SV o1
39
END OF LECTURE
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