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WOLFRAM|DEMONSTRATIONS PROJECT

Dynamics of a Forced Exothermic Chemical Reaction

​
time t
50
forcing amplitude
α
0.125
forcing frequency
ω
Pi
This Demonstration shows the effect of varying the coolant temperature of a continuous stirred-tank reactor in which an irreversible first-order exothermic chemical reaction
A⟶B
takes place.
The system is governed by the following dimensionless equations [1]:
dc
dt
=-c+Da(1-c)
T/(1+ϵT)
e
,
dT
dt
=-T+BDa(1-c)
T/(1+ϵT)
e
-β(T-
T
c
)
,
T
c
=
T
c
+αsinωt
,
where
c
is the conversion of reactant
A
,
T
is the reactor temperature,
Da
is the Damköhler number,
ϵ
is the inverse activation energy,
B
is the heat of reaction,
β
is the heat transfer coefficient,
T
c
is the coolant forcing function,
T
c
is the average coolant temperature during forcing,
α
is the forcing amplitude,
ω
is the forcing frequency, and
t
is time. The following parameters are considered:
Da=0.085
,
B=22
,
β=3
,
ϵ=0
,
T
c
=0
, with
T
c
(0)=c(0)=0
. The unforced system,
α=0
, has a single oscillatory state; increasing the amplitude of the forcing function results in quasi-periodic behavior, followed by a sequence of period-doubling bifurcations leading to chaos. Furthermore, bistability can occur where both states are periodic or one state is periodic and the other chaotic.
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