# Dynamics of Two Continuous Stirred-Tank Reactors Operating in Series

Dynamics of Two Continuous Stirred-Tank Reactors Operating in Series

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 .

AB

The governing equations are [1]

d

x

1

dt

x

1

τ

1

x

1

y

1

d

y

1

dt

y

1

τ

1

x

1

y

1

β

1

y

1

η

1

d

x

2

dt

x

2

τ

2

x

2

y

2

x

1

d

y

2

dt

y

2

τ

2

x

2

y

2

β

2

y

2

η

2

y

1

with initial conditions (0)=(0)=(0)=(0)=1,

x

1

x

2

y

1

y

2

where , is dimensionless time, and are the dimensionless concentration of reactant and the temperature in reactor , is the Damköhler number, and is the ratio of reactor volumes ; the other parameters are dimensionless numbers defined in [1]. A constant inlet concentration of to the first reactor results in a periodic inlet concentration of to the second reactor and an outlet concentration that may be periodic, quasi-periodic, or chaotic, depending on the choice of parameters.

F()=exp[/(1+/ϵ)]

y

i

y

i

y

i

t

x

i

y

i

A

i

Da

α

V

1

V

2

A

A