Chemical Engineering Department
CDB2043 REACTION ENGINEERING
CHAPTER 2: CONVERSION AND REACTOR SIZING(part 1)
1
Basic
knowledge
Application
At the end of the lecture, students should be able to:
1. define conversion
2. developed the design equation for batch and flow reactor
3. apply the design equation to calculate the volume of reactors for a particular process
4. evaluate the best reactor arrangement
5. differentiate between space time and space velocity
3
Course Learning Outcome
4Overview 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
Batch CSTR PFR PBR
5
Recap from Lecture 1
Design Equation in terms of mole
dt
dNVr AA
How do we relate conversion with flow rate or moles of reactant?
What is conversion?
Consider the general equation (irreversible eqn)
aA + bB cC + dD
We will choose A as our basis of calculation
Da
dC
a
cB
a
bA
How do we define conversion?
Conversion
Conversion is define as:
feedA of moles
reactedA of molesAX
MAXIMUM CONVERSION?
Irreversible Reaction
X = 1
Reversible Reaction
X = Xe
8Relating conversion with moles of reactant
Batch reactor
Flow reactor (CSTR and PFR/PBR)
reactedA of Mole - fedA of Mole any timeat A of Mole t
XNNN AAA 00 -
XFFF AAA 00 -
outletat A of rate flowMolar
-inlet at A of rate flowMolar any timeat A of rate flowMolar t
Now, recap back our design equation:
9
Relating V to X
dt
dNVr AA
HOW TO RE-WRITE
V = f(X)
WHAT WE HAVE JUST DISCOVERED:
XNNN AAA 00 -
XFFF AAA 00 -
Develop Design Equation for batch reactor
Batch reactor
PFR CSTR
Develop Design Equation for flow reactor
Design Equation(Summary)
Reactor Differential Algebraic Integral
Batch
CSTR
PFR
PBR
13
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 knowN value of FA0:
14
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
0A
r
XFV
Consider the design equation of a PFR
Reactor Sizing for flow reactor
A0A rdV
dXF
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?
17
Reactor Sizing for flow reactor
XA -rA (mol/m3.s)
0.0 0.45
0.1 0.37
0.2 0.30
0.4 0.195
0.6 0.113
0.7 0.079
0.8 0.05
TABLE 2.1
Solution Ex 2-2: Sizing for CSTR
TABLE 2.1
XA -rA (mol/m3.s) 1/-rA
(m3..s/mol)FA0/-rA
(m3..s/mol)
0.0 0.45 2.22 0.89
0.1 0.37 2.70 1.08
0.2 0.30 3.33 1.33
0.4 0.195 5.13 2.05
0.6 0.113 8.85 3.54
0.7 0.079 12.70 5.06
0.8 0.05 20.00 8.00
XFr
V AA
0
1
DESIGN EQUATION OF CSTR!!
Solution Ex 2-2: Sizing for PFR
TABLE 2.1
XA -rA(mol/m3.s)
FA0/-rA(m3..s/mol)
0.0 0.45 0.89
0.2 0.30 1.33
0.4 0.195 2.05
0.6 0.113 3.54
0.8 0.05 8.00
0.80
0
A
A
FV dX
r
DESIGN EQUATION OF PFR!!
Use 5-point quadrature formula:
4
00 1 2 3 44 2 4
3
X
X
hf X dX f f f f f
4 0
4
X Xh
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 theres no side reactors, conversion at any
reactor outlet is define as:
reactorfirst tofedA of mole
ipoint toup reactedA of moles totaliX
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
FA
0/-
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, XF
A0
/-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
02
4
6
8
10
0 0.2 0.4 0.6 0.8 1
Conversion, X
FA
0/-
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 Levenspielplot 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 0.8
FA0/-rA 0.89 1.09 1.33 2.05 3.54 5.06 8.0
02
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
FA
0/-
rA
3
1
3
1
3
4.0
0
8.0
4.00.2
0.2
mV
mV
mr
F
XA
A
332
12
2
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 Simpsons three-point rule
331
0001
4.0
0
01
551.005.233.1489.03
2.0
)4.0()2.0(4
)0(3
mmV
r
F
r
F
r
FXV
r
dXFV
A
A
A
A
A
A
A
A
331
0002
8.0
4.0
02
614.10.854.3405.23
2.0
)8.0()6.0(4
)4.0(3
mmV
r
F
r
F
r
FXV
r
dXFV
A
A
A
A
A
A
A
A
210 43
)(2
0
XfXfXfX
dXxf
X
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 Levenspielplot to show how to calculate the reactor volume
Reactors in series
2538595339-rA (kmol/m3.hr)
0.650.60.40.20X
Table 2-7
Reactors in series
V1
X1=0.2
X2=0.6
X3=0.65
Figure E2-7.1
33
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
FA
0/-
rA
1st CSTR 2nd CSTRPFR
CSTR PFR
Some further definitions
Relative rate of reaction
Obtained from stoichiometric ratio
Example:
d
r
c
r
b
r
a
r 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
V
vSV o
1
END OF LECTURE
37
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