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Chaos in a Continuous Stirred Tank Reactor

​
time
1.
Damköhler number
Da
1
5
Damköhler number
Da
2
2.75
Chaotic behavior can be exhibited by a very simple chemical reactor model in which two exothermic reactions are carried out in a nonisothermal continuous-flow stirred tank reactor.
The parallel conversion of the two reactants
A
and
B
can be written:
A→C
,
B→D
.
The governing equations are [1]:
dY
dt
=1-Y-Y
Da
1
γ
1
T/(1+T)
e
,
dZ
dt
=1-Z-Z
Da
2
γ
2
T/(1+T)
e
,
dT
dt
=α
β
1
Y
Da
1
γ
1
T/(1+T)
e
+
β
2
Z
Da
2
γ
2
T/(1+T)
e
-T
,
with initial conditions
Y(0)=Z(0)=T(0)=1
.
Here
Y
and
Z
represent dimensionless concentrations of
A
and
B
,
T
is the dimensionless temperature,
t
is the dimensionless time, and the Damköhler numbers [2] for the two reactions are
Da
1
and
Da
2
; the other parameters are dimensionless numbers defined in [1].
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