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.