Lecture 10
Chemical Reaction Engineering (CRE) is the
field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in
which they take place.
Lecture 10 – Tuesday 2/12/2013




Block 1:
Block 2:
Block 3:
Block 4:
Mole Balances
Rate Laws
Stoichiometry
Combine
 Definition of Selectivity
 Semibatch Reactors
2
Selectivity in Multiple Reactions
D
A  B 
D
rD  k D C A C B
(Desired)
A  B  U
rU  k U C A C
(Undesired
k
2
kU
Selectivity
)
Yield
Instantaneous
SD/U = rD/rU
Y D  rD /  r A
Overall
ŜD/U = FD/FU
YˆD  F D /( F A 0  F A )
S D /U 
3
2
B
rD
rU
2

k D C AC B
k u C AC
2
B

kDC A
kU C B
Keep CA high and CB low.
Semibatch Reactors
 Semibatch reactors can be very effective in
maximizing selectivity in liquid phase reactions.
 The reactant that starts in the reactor is always
the limiting reactant.
4
Semibatch Reactors
Semibatch reactors
A+B→C+D
B, v0
m
Initial V
A
Liquid level and volume increase
5
Semibatch Reactors
1) Mass Balance:
dm
 m
dt
m   0  0
dm
dt
dV
dt
 0
and
dV
dt
  0 0
 0
t  0 V  V0
6
V  V0   0t
m  V 0
Semibatch Reactors
1) Mole Balance on Species A:
[in] – [out] + [gen] = [acc]
0  0  r AV 
dN
A

d [ C AV ]
dt
dV
dt
dC A
7
dt
V
dt
 0C A
V
A
dt
dC A
dt
 0
 rA 
dN
 CA
dV
dt
Semibatch Reactors
1) Mole Balance on Species B:
F B 0  0  rB V 
dN B

dt
d [ C BV ]
dt
dN
B
dt
V
dC B
dt
dV
F B 0  C B 0 0
dC B
8
dt
 rB 
dt
 CB
 0
C B 0  C B  0
V
dV
dt
Semibatch Reactors
1) Mass and Mole Balance Summary
9
 0C A
1 
dC
2 
dC B
3 
dC C
4 
dC D
5 
V  V0   0t
A
dt
dt
dt
dt
 rA 
 rB 
 rC 
 rD 
V
 0 (C B 0  C B )
V
 0C C
V
 0C D
V
Semibatch Reactors
2) Rate Laws
3) Stoichiometry
10
4) Parameters
6 
 rA
1
r A  kC A C B

 rB
rC

1

1
7 
rB  r A
8 
rC   rA
9 
rD   r A
rD
1
N A0  N A
10 
X 
11 
N A 0  C A 0V 0
12 
N A  C AV
N A0
C A0 , V0 ,  0 , k , C B 0
Semibatch Reactors
11
Semibatch Reactors
12
Equilibrium Conversion in Semibatch
Reactors with Reversible Reactions
Consider the following reaction:


A  B 
 C  D
Everything is the same as for the irreversible case,
except for the rate law:


CCC D 
 rA  k A  C A C B 

K
C


13
Equilibrium Conversion in Semibatch
Reactors with Reversible Reactions
Where:
C A
C B
N A 0 1  X
V
 FB 0 t  N A 0 X 
V
C C CD 
At equilibrium,  r
K C
C Ce C De
C Ae C Be

A
N Ce N De
N Ae N Be
0
N A0 X
V
then
2

N A0 X e
1  X e  F B 0 t  N A 0 X e 
Xe changes with time.
14

P6-6B - Semibatch Reactors
Sodium Bicarbonate + Ethylene Chlorohydrin  Ethylene Glycol + NaCl + CO2
NaCHO3 + CH2OHCH2Cl  (CH2OH)2 + NaCl + CO2 
A + B  C + D + CO2 
15
P6-6B - Semibatch Reactors
Semibatch Reactors in terms of Moles
A + B  C + D + CO2
Mole Balances
A
B
C
D
(1)
(2)
(3)
(4)
(5 )
Stoichiometry
a
dt
dN b
dt
dN c
 r AV
 F B 0  rB V
 rC V
dt
ND  NC
0   FCO 2  rCO 2 V
CO 2
16
dN
FCO 2  rCO 2 V
 r A   rB  rC  r D  rCO 2
(6)
dV
  0   CO 2
dt
(7 )
Rate Laws
2
RHO
(8 )
MW  44
(9 )
RHO  1000
(10 )
Ca  N A V
(11 )
CB  N B V
(12 )
r A   kC A C B
N a0  N a
X 
N a0
N a 0  V0C a 0
(13 )
(14 )
17
 CO 
FCO 2 MWCO
Rest of the Polymath Statements
Similar to Concentration Program
2
P6-6 Semibatch: Moles, Na, Nb, etc.
19
20
21
P6-6 Semibatch: Concentrations CA, CB, CC
23
24
Semibatch Reactors
Three Forms of the Mole Balances applied to Semibatch Reactors:
dN
1. Molar Basis
A
 r AV
B
 F B 0  rB V
dt
dN
dt
2. Concentration
Basis
dC A
dt
 rA  C A
dC B
3. Conversion
25
dt
dN
V
dt
 rB  C B 0  C B 
dt
dX
0

 r AV
N A0
0
dN
V
dt
A
 r AV
B
 F B 0  rB V
Semibatch Reactors
Consider the following elementary reaction:
A+B  C+D
-rA=kCACB
The combined Mole Balance, Rate Law, and
Stoichiometry may be written in terms of number
of moles, conversion, and/or concentration:
Conversion
dX
dt

k 1  X
 N Bi
 FB 0 t  N A 0 X
V0   0t

dC A
dt
dC B
26
No. of Moles
Concentration
dt
 rA  C A
0
dN
V
dt
 r A  C B 0  C B 
0
dN
V
dt
A
 r AV
B
 F A 0  rB V
Polymath Equations
27
End of Lecture 10
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