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WOLFRAM|DEMONSTRATIONS PROJECT

Optimizing Maleic Anhydride Production

​
temperature
600
cost
benzene
6
maleic anhydride
6.5
The synthesis of maleic anhydride,
C
4
H
2
O
3
, involves the following reactions in the presence of a vanadium pentoxide catalyst:
C
6
H
6
+
9
2
O
2
C
4
H
2
O
3
+2
CO
2
+2
H
2
O
(1)
C
4
H
2
O
3
+3
O
2
→4
CO
2
+
H
2
O
(2)
C
6
H
6
+
15
2
O
2
→6
CO
2
+3
H
2
O
(3)
If air is present in excess, the concentration of oxygen can be considered as constant and the reaction rates are given by
r
1
=
k
1
C
A
,
r
2
=
k
2
C
P
, and
r
3
=
k
3
C
A
, where
k
i
is the rate constant of reaction
i
(expressed in
3
m
-1
s
kg
catalyst),
C
A
is the concentration of benzene, and
C
P
is the concentration of maleic anhydride.
The temperature-dependent rate constants are given by
k
1
=4280
-12660
T
e
,
k
2
=70100
-15000
T
e
, and
k
3
=26
-10800
T
e
.
The governing equations at steady state, obtained by writing molar balances, for a packed-bed reactor modeled as a PFR (plug-flow reactor) are:
v
0
d
C
A
dW
=-
k
1
C
A
-
k
3
C
A
, with
C
A
(0)=10mol/
3
m
the concentration of benzene in the feed stream (i.e. at the entrance of the reactor), and
v
0
d
C
P
dW
=
k
1
C
A
-
k
2
C
P
, with
C
P
(0)=0
the concentration of maleic anhydride in the feed stream, where
v
0
=0.0025
3
m
/s
is the volumetric flow rate of the feed stream, which is composed mainly of air, and
W
is the weight of catalyst (expressed in kg catalyst).
The final/outlet concentrations of benzene (
C
A
) and maleic anhydride (
C
P
) are obtained by solving the steady-state equations numerically, with the weight of the catalyst ranging from 0 to 10,000 kg.
This Demonstration plots the attainable region for maleic anhydride synthesis for values of the temperature fixed by the user. A profit function is defined by
f(
C
P
,
C
A
)=(α
C
P
-β
C
A
)/
C
A
(0)
, where
α
and
β
are user-set values of the prices of benzene and maleic anhydride. When this function is maximized, the optimal catalyst weight (shown in green) and the value
f
max
(shown in magenta) are determined. The optimal outlet values of the concentrations of benzene (
C
A
) and maleic anhydride (
C
P
) are identified on the plot by the green dot. The dashed red line represents the equation
f
max
=(α
C
P
-β
C
A
)/
C
A
(0)
and is always tangent to the attainable region.
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