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Dynamics of Two Continuous Stirred-Tank Reactors Operating in Series

​
time, t
5
Damköhler number
D
a
0.26
ratio of reactor volumes
V
1
V
2
19.8676
time plots
Chaotic behavior can be exhibited in a model of two nonisothermal continuous stirred-tank reactors (CSTRs) operating in series with constant input and following first-order reaction kinetics
AB
.
The governing equations are [1]
d
x
1
dt
=-
x
1
+
τ
1
Da(1-
x
1
)F(
y
1
)
,
d
y
1
dt
=-
y
1
+
τ
1
DaB(1-
x
1
)F(
y
1
)-
β
1
(
y
1
-
η
1
)
,
d
x
2
dt
=α(-
x
2
+
τ
2
Da(1-
x
2
)F(
y
2
)+
x
1
)
, and
d
y
2
dt
=α(-
y
2
+
τ
2
DaB(1-
x
2
)F(
y
2
)-
β
2
(
y
2
-
η
2
)+
y
1
)
,
with initial conditions
x
1
(0)=
x
2
(0)=
y
1
(0)=
y
2
(0)=1
,
where
F(
y
i
)=exp[
y
i
/(1+
y
i
/ϵ)]
,
t
is dimensionless time,
x
i
and
y
i
are the dimensionless concentration of reactant
A
and the temperature in reactor
i
,
Da
is the Damköhler number, and
α
is the ratio of reactor volumes
V
1
V
2
; the other parameters are dimensionless numbers defined in [1]. A constant inlet concentration of
A
to the first reactor results in a periodic inlet concentration of
A
to the second reactor and an outlet concentration that may be periodic, quasi-periodic, or chaotic, depending on the choice of parameters.
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