WOLFRAM|DEMONSTRATIONS PROJECT

Endothermic Reaction in a Heated Batch Reactor

​
initial molar ratio
0.4
steam temperature in surrounding jacket (in Kelvin)
423
option
conversion profile
temperature profile
Consider an irreversible endothermic reaction (
A+B
k

C
) in a batch reactor heated by a steam jacket at temperature
T
j
surrounding the reactor. The jacket heat transfer area and coefficient are
A=5
2
m
and
U=3.76kJ/(min
2
m
K)
. The reactor volume is
V=1200
3
dm
. The reaction rate constant is given by
k=0.001
-Ea
R
1
T
-
1
300
e
, with the activation energy
Ea=83.6kJ/mol
and the universal gas constant
R=8.314KJ/(KmolK)
. The initial concentration of
A
is
C
A
(0)=2.5mol/
3
dm
and
θ
B
=
C
B
(0)
C
A
(0)
is the initial molar ratio. The initial reactor temperature is 30°C. The mass and energy balances are
d
x
A
dt
=
-
r
A
c
A
(0)
,
dT
dt
=
UA
T
j
-T+
r
A
VΔ
H
R
N
A
(0)(
c
PA
+
θ
B
c
PB
)
,
with
r
A
=-k
c
A
2
(0)
(1-
x
A
)(
θ
B
-
x
A
)
,
where
x
A
is the conversion,
T
is the reactor temperature,
Δ
H
R
is the heat of reaction at 273.15 K,
N
A
(0)=V
C
A
(0)
is the initial molar amount of
A
,
r
A
is the reaction rate, and
c
PA
and
c
PB
are the heat capacities of species
A
and
B
, respectively.
This Demonstration plots the conversion and temperature versus time for values of the steam temperature in the jacket,
T
j
, and the initial molar ratio,
θ
B
.