ITK-330 Chemical Reaction Engineering
Isothermal Reactor Design
Dicky Dermawan
www.dickydermawan.net78.net
dickydermawan@gmail.com
Algorithm for Isothermal Reactor Design
Example of Application:
First-order Gas Phase Reaction in PFR
An Example: Effect of Reactor Type
The elementary gas phase reaction
2A+BC
with rate constant k=10 L2/mol2.s
takes place in a CSTR at constant temperature (500 K) and
constant pressure (16.4 atm). The feed is equal molar
in A and B. The feed volumetric flow rate vo=25 L/s. In
order to achieve 90% conversion:
a.
Estimate the CSTR volume
b.
What is the reactor volume if PFR is used?
c.
How long would it take if the reaction is carried out in
a constant volume batch reactor?
P4-5A
P4-7A
General Guidelines for California Problems
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.
1. Group unknown parameters/values on the same side of
the equation
example:
[unknowns] = [knowns]
2. Look for a Case 1 and a Case 2 (usually two data points)
to make intermediate calculations
3. Take ratios of Case 1 and Case 2 to cancel as many
unknowns as possible
4. Carry all symbols to the end of the manipulation before
evaluating, UNLESS THEY ARE ZERO
P4-11B
P4-12B Changing Feed Ratio
P4-13B Arranging Additional Reactor
L5-13: Scale Up Problem
(a)
The homogeneous gas reaction A  3 R follows secondorder kinetics. For a feed rate of 4 m3/hr of pure A at 5
atm and 350oC, an experimental reactor consisting of a
2.5 cm ID pipe 2 m long gives 60% conversion of feed. A
commercial plant is to treat 320 m3/hr of feed consisting
of 50% A, 50% inerts at 25 atm and 350oC to obtain 80%
conversion.
How many 2-m lengths of 2.5 cm ID pipe are required?
Should they be placed in parallel or in series?
Assume plug glow in the pipe, negligible pressure drop,
and ideal gas behavior
L5-18: Scale Up & Laboratory Experiment
The homogeneous gas reaction A  2B is run at 100oC at a
constant pressure of 1 atm in an experimental batch
reactor. The data in below were obtained starting with
pure A.
What size plug flow reactor operated at 100oC and 10 atm would
yield 90% conversion of A for a total feed rate of 10
mol/sec, the feed containing 40% inert?
Time, min
V/V 0
0
1
1
1.2
2
1.35
3
1.48
4
1.58
5
1.66
6
1.72
Time, min
V/V 0
8
1.82
9
1.86
10
1.88
11
1.91
12
1.92
13
1.94
14
1.95
7
1.78
P4-14C Similarity: Adaptation, Scale Up etc.
P4-15A Similarity: Adaptation, Scale Up etc.
P4-16B: Reactor Nonideality
Pressure Drop
in Packed Bed Reactors
Ergun:
     0  0     0 
P
T FT
  0  0 

P T0 FT 0
Catalyst weight:
P T0 FT0


P0 T FT
FT
 1   X
FT 0
Isothermal Fixed (i.e. Packed) Bed Reactors
Design
Example for First Order Reaction
Performance equation:
Kinetics:
Stoichiometry:
Pressure drop:
Combine:
dX  rA

dW FA 0
 rA 
Gas
k
E
k  k1  exp a
R
 CA
CA  CA0 
1  X P T0
 
1    X P0 T
liquid
dP
 T P
    0  (1    X)
dW
2 T0 P / P0
dX
 f (  rA )  f (X, P)
dW
dP
 g ( X, P )  g ( X, P )
dW
 1 1 
   
 T1 T 
CA  CA0  (1  X)
for small DP: P/P0 = 1
Thus…
The combination results in
2 simultaneous
differential equations
Polymat 5.0
Introduction to Simultaneous
Ordinary Differential Equation
Solver
P4-18B
Example: PBR Design
Reforming reactors are used to increase the octane number of
petroleum. In a reforming process 20.000 barrels of
petroleum are to be processed per day. The corresponding
mass and molar feed rates are 44 kg/s and 440 mol/s,
respectively. In the reformer, dehydrogenation reactions such
as:
Paraffin  Olefin + H2
occur. The reaction is first-order in paraffin with k’ = 0.02
L/kgcat.s. Assume that pure paraffin enters the reactor at a
pressure of 2000 kPa and the corresponding concentration of
0.32 mol/L. This reaction is carried out in a tubular packed
bed 2.4 m in diameter and 25 m in length containing 173870
kg catalyst
P
B
R
D
e
s
i
g
n
The hydrodemethylation of toluene is to be carried out in a
packed bed reactor. Plot the conversion, pressure ratio
P/P0, and the partial pressures of toluene, hydrogen, and
benzene as a function of catalyst weight. The molar feed
rate of toluene to the reactor is 50 mol/min and the reactor
is operated at 40 atm and 640oC. The feed consist of 30%
toluene, 45% hydrogen, and 25% inerts. Hydrogen is used
in excess to help prevent coking. The pressure drop
parameter is 9.8x10-5 kg-1. Also determine the catalyst
weight in a CSTR with a bulk density of 400 kg/m3
C 6H5 CH 3  H2  C 6H6  CH 4
 r ' C6H5CH3 
k'  0.00087
k 'PH2  PC6H5CH3
1  K C6H6  PC6H6  K C6H5CH3  PC6H5CH3
mol
atm 2  kgcat  min
K C6H6  1.39 / atm
K C6H5CH3  1.038 / atm
P4-19B
Exercises
1.
The first-order homogeneous gaseous
decomposition A  2.5 R is carried out in an
isothermal batch reactor at 2 atm with 20%
inerts present, and the volume increases by
60% in 20 min. In a constant- volume
reactor, find the time required to reach 8 atm
if the initial pressure is 5 atm, 2 atm of which
consist of inerts.
Exercises
2. Kinetika reaksi dekomposisi zat A pada fasa larutan dipelajari
menggunakan indikator warna yang berubah saat konsentrasi
A turun hingga kurang dari 0,1 mol/L. Umpan yang
mengandung 0,6 mol A perliter dialirkan ke dalam tangki
pertama dari dua reaktor tangki berpengaduk yang disusun
secara seri, masing-masing bervolume 400 cm3. Perubahan
warna terjadi dalam reaktor pertama pada keadaan tunak saat
laju alirnya 10 cm3/menit. Perubahan yang sama baru terjadi
di reaktor kedua pada keadaan tunak saat laju alir mencapai
50 cm3/menit. Larutan yang mengandung 0,8 mol A perliter
direaksikan dalam susunan reaktor di atas. Berapa laju alir
umpan agar dicapai konversi 95%?
Exercises
3. The first order reversible liquid reaction:
AR
CA0 = 0.5 mol/L, CR0 = 0
Takes place in a batch reactor.
After 8 minutes, conversion of A is 33.3%,
while equilibrium conversion is 66.7%.
Find the rate equation for this reaction.
Design in Term of other than Conversion
In some instance it is more convenient to work in term of
NA, NB,… (batch) or FA, FB,… (continue) rather than conversion.
Use
Rather than
dN A
 rA  V
dt
or
dFA
 rA
dV
VCSTR 
FA 0  FA
 rA
NA 0 
dX
 rA  V
dt
dX
FA 0 
 rA
dV
for each species involved
rB 
b
 rA
a
NT
N T0
or
rc  
c
 rA
a
FT
FT 0
Fj
P T0
C j  CT0 


FT P0 T
rD  
d
 rA
a
or
VCSTR  FA 0 
only for A
  da  ac  ba  1
1   X
C j  C A0
Θ j  j  X
P T0



1   X P
T
X
 rA
Working in Terms of Molar Flow
Rates in a PFR
The gas phase reaction:
A 2B
is carried out isothermally at 500 K & 10 atm without pressure drop
in a PFR and follows an elementary rate law.
Determine:
a. Equilibrium conversion
b. The molar flow rates along the length of a 100 L reactor.
c. Reactor volume required to achieve 95% of equilibrium conversion
Additional information:
kA = 2.7 min-1
KC = 1.2 mol/L
FA0 = 10 mol/min
Illustration of Application:
Semibatch Reactors
Mole balances & stoichiometry:
dNA
 0  0  rA  V
dt
dNB
 FB0  rA  V
dt
dNC
 rA  V
dt
dND
 rA  V
dt
Mass balances: dV  0
dt

CC  CD 


Kinetics:  rA  k   CA  CB 
K C 

Illustration of Application:
Semibatch Reactors
P4-26B
Illustration of Application:
Unsteady State Operations Semibatch Reactors
P4-27B
Illustration of Application:
Membrane Reactors
Mole balances & stoichiometry:
dFA
 rA
dV
dFB
 rB
dV
dFC
 rC  RC
dV
rA  rB  rC
Mass transfer: RC  k cC  CC
C6H12  C6H6  H2
A

B
 C
Illustration of Application:
Membrane Reactors
P4-30B
Illustration of Application:
Membrane Reactors
P4-31C