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].