Chapter 6
Isothermal Reactor Design
(몰과 몰유량 )
반응공학
Chemical Reaction Engineering
Using CA (liquid) and FA (gas)
in the mole balance and rate laws
•There are many instances when it is much more convenient to
wor
k in terms of the number of moles (NA, NB) or molar flow rates (FA, FB,
etc) rather than conversion.
•Membrane reactors and multiple reactions taking place in the g
as phase are two such cases where molar flow rates are preferred
rather than conversion.
•We now modify our algorithm by using concentration for liquids
an
d molar flow rates for gases as our dependent variables.
•The main difference between the conversion algorithm and the
mo
lar flow rate/concentration algorithm is that, in the conversion algorit
hm, we needed to write a mole balance on only one species, where
as in the molar flow rate and concentration algorithm, we must
write a mole balance on each and every species.
Unsteady-State Operation of Stirred Reactors
• Startup of a CSTR : Determine the time to reach steady-state
operation
• Semibatch reactor : Predict the concentration and conversion as a function of time
A + B →C + D
B
M
C
CA0
CA
Startup of a CSTR
A
Semibatch reactor
-Ammonolysis
-Chlorination
-Hydrolysis
A, B
Reactive distillation
-Acetylation
-Esterification
Motivation of Semibatch Reactors
One of the best reasons to use semibatch reactors is to
enhance selectivity in liquid-phase reactions.
Maximizing
SD/U for two reactants
RateRate selectivityselectivity
k1
D (Desired Product)
k2
U (Undesired Product)
A+ B
The rate laws are
 r  k C 2C  k C C 2
U A B
A
D A B
r  k C 2C
D
D
A
B
2
U
U
A
B
r k C C
S D /U

rD k D C A

rU kU C B
Rate selectivity parameter=Instantaneous selectivity
Semibatch Reactors : Constant Molar feed
A B 
 C
CB0
0
B
Semibatch
reactor
volume as a
function of time
0
B
 v 0 C A  Vr A 
A
A
0
[ acc. ]

dN A
dt

(4-51)
rAV 
d C AV  VdC A  C A dV

dt
dt
dt
(4-52)
0
+ [ gen. ]

rAV (t)
[ in ]
Overall mass balance of all specials:
[ in ]
 0 v0
- [ out ] + [ gen. ] =

0
dV  v
0
dt

0

VdC A
dt
(4-56)
Mole balance on specials B:
=
- [ out ]
(4-55)
v
dC A
 rA  0 C A
dt
V
Mole balance on specials A:
[ in ]
V  V 0   0t
for    0
FB 0 
0

+ [ gen. ]
=
[ acc. ]
rB V (t )

dN B
dt
dN B
 rB V  FB 0
dt
(4-57)
dN B
d (VC B )
dV
dC B

 CB
V
dt
dt
dt
dt
[ acc. ]
d (V )
dt
- [ out ]
(4-53)
(4-54)
rB V  FB 0  rB V  v 0 C B 0
 v 0 (C B 0  C B )
dC B
 rB
V
dt
(4-58)
Example 6-3
Isothermal semibatch reactor with 2nd–order reaction
CNBr + CH3NH2  CH3Br + NCNH2
A + B

C + D
Isothermal elementary reaction
in a semibatch reactor
t=0,
dN C
 rCV  rAV
dt
dN C
d (C C V )
dC C
dV

V
 CC
dt
dt
dt
dt
CA=0.05 gmol/, CB=0.025 gmol/ℓ,
v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
V
Mole balance of A, B, C, and D
dC C
 v 0C C
dt
rA  kC A C B
C
dC C
v
 kC A C B  0 C C
dt
V
A
dC A
v
 kC A C B  0 C A
dt
V
D
dC D
v
 kC A C B  0 C D
dt
V
B
dC B
v
 kC A C B  0 (C B 0  C B )
dt
V
V  V0  v 0 t
Conversion, X
X 
A0
N A0
A

A0 0
C A0V0
A
Concentration-time trajectories
in Semibatch Reactor
0.05
CNBr + CH3NH2  CH3Br + NCNH2
(A)
(B)
(C)
(D)
0.04
Concentration
t=0,
CA=0.05 gmol/, CB=0.025 gmol/ℓ,
v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
0.03
CA
0.02
CC
0.01
CB
0.00
0
100
200
300
Time
400
500
Reaction rate-time trajectories
in Semibatch Reactor
Reaction rate [mole/s•L)
0.0025
CNBr + CH3NH2  CH3Br + NCNH2
(A)
(B)
(C)
(D)
0.0020
t=0,
C =0.05 gmol/, C =0.025 gmol/ℓ,
v0=0.05ℓ/s, k=2.2ℓ/s·mol, V0=5ℓ
0.0015
0.00010
0.00005
0.00
0
50
100
150
200
250