Series Reactions in a CSTR with Time-Varying Input

reactor's residence time τ

1

Consider the following series reaction taking place in a CSTR (continuous stirred-tank reactor):

A

k

1

→

B

k

2

→

C

. No chemical species (

A

,

B

, or

C

) are initially present in the reactor. The reactor is fed with only species

A

at the time-varying feed rate

c

A

in

=1+sin(2t)

.

The governing equations, obtained from material balances, are

d

c

A

dt

=

1

τ



c

A

in

-

c

A

-

k

1

c

A

,

d

c

B

dt

=

-1

τ

c

B

+

k

1

c

A

-

k

2

c

B

,

d

c

C

dt

=

-1

τ

c

C

+

k

2

c

B

,

where

t

is time,

τ

is the reactor's residence time, and

k

1

and

k

2

are rate constants equal to

1

and

0.25

, respectively.

This Demonstration plots the concentration of all three species versus time for user-set values of

τ

. The blue, magenta, and brown curves correspond to species

A

,

B

, and

C

, respectively.