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

AB

.

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.