10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 7: Batch Reactors
This lecture covers batch reactor equations, reactor sizing for constant volume and
variable volume processes.
Batch Reactors
Run at non-steady state conditions
Which to choose? Batch vs. CSTR?
Batch
CSTR
Figure 1. Schematics of a batch reactor and a
CSTR.
Small Amount of Material
(small quantities)
(does not tie up
equipment continuously)
Flexibility
+
-
Expensive Reactants
+
-
If product does not flow,
Materials Handling (e.g. Polymers)
+
-
Do not have to shut down and
clean, less down time
-
+
Captial costs? For size of reactor,
for given conversion
+
(concentration stays
higher longer)
Operability & Control (T, P, p4)
e.g. Exothermic reaction
-
-
+
(Manipulate only one
setpoint, steady state.
You can control additional
variables. Such as flow rates.)
Material Balance
0
In – Out + Product = Accumulation
0
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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rA V =
dN A
dt
Constant V,
dC A
dt
rA =
In terms of conversion,
Integrating,
C Ao
dX A
= rA
dt
X A dX
dC A
A
or t = C Ao ∫
0
C Ao r
r
A
A
t=∫
CA
1st Order Reaction
A ⎯k⎯
→B
− rA = kC A = kC Ao (1− x A )
t = C Ao ∫
xA
0
dx A
− kC Ao (1 − x A )
→
⎯⎯
t=
1 ⎛ 1 ⎞
ln ⎜
⎟
k ⎝ 1− x A ⎠
xA = 1 − e −kt
t90.0% =
90% conversion
(order of
1 ⎛ 1 ⎞ 2.3
ln ⎜
⎟=
k ⎝ 1 − 0.9 ⎠ k
1
)
k
2nd Order Reaction
A + A ⎯k⎯
→B
−rA = kC A2 = kC Ao 2 (1− X A )2
XA
dX A
1
=
t = C Ao ∫
2
2
0
−kC Ao
−kC Ao (1 − X A )
t=
If
XA
1
kC Ao 1− X A
XA =
∫
XA
0
dX A
(1− X A ) 2
kC Aot
1+ kC Aot
kfirst order = ksecond order C Ao , which is faster?
1st order
2nd order
1
0.63
0.50
2
0.86
0.67
3
0.95
0.75
}x
A
For a given Damkohler number, 1st order is faster. The second order reaction has
greater concentration dependence. Exponential approach (1st order) is faster.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture #
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Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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Batch Cycle
Time
t
Charge
rxn
Discharge
Clean
Downtime,
td
How long should t be?
How high should X A be?
Economic calculation:
Compare economics of further conversion to a different use
of equipment
Chemical consideration: Will product degrade? Assume product stable.
Product produced in one cycle = X AC Ao V
Pr(Rate of Production)
=
X AC Ao V
t + td
What value of t will maximize Pr?
If there is a maximum of Pr vs. t,
Assume td = constant.
(toptimum + td )
0=
d Pr
=0
dt
d Pr
= C Ao V
dt
dX A
− XA
dt
(toptimum + td ) 2
(toptimum + td )
dX A
− XA = 0
dt
Now specify kinetics. There may be no optimum.
X A = 1 − e− kt
dX A
= ke− kt
dt
− ktoptimum
− kt
(toptimum + td )ke
− (1− e optimum ) = 0
1st order
Can numerically solve for
toptimum .
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture #
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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Semi-batch Reactor
or
Figure 2. Schematics of two types of fed-batch reactors.
1) Why?
• To remove “poisonous” product
• Make room in reactor (expansion of product)
• If a reactant has a negative order effect on rate, add in small quantities
• Selectivity
A + B → Desired
(control)
A + A → Byproduct
Start with B, slowly feed A.
slow
feed of
A
Figure 3. A fed-batch
reactor with a slow feed of
one reactant.
B
•
•
•
To shift equilibrium, strip off product
To control evolution of heat
In biological cases
Fed-batch
- Feed in carbon source slowly to avoid overflow metabolism
- (glucose)
- O2 sparingly soluble, must feed.
2) Balances
B
A Balance
Figure 4. Fed-batch
reactor with a feed of B.
A
In – Out + Product = Accumulation
rA V(t ) =
d (rA V)
dt
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture #
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
dC A
dV
+ CA
dt
dt
Liquid V = V0 + v0t
rA V(t ) = V
flow
dilution
v
dC A
= rA − 0 C A
dt
V0
B Balance
v
v
dCB
= rB + 0 CBo − 0 CB
dt
V0
V0
N
Addition
Dilution
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture #
Page 5 of 5
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].