# Multiple Reactions in a Continuous Stirred-Tank Reactor with Heat Effects

Multiple Reactions in a Continuous Stirred-Tank Reactor with Heat Effects

Consider a continuous stirred-tank reactor (CSTR) with multiple reactions: . Only species is fed to the reactor with an inlet concentration equal to .

ABC

k

1

→

k

2

→

A

C=1

A0

The Demonstration finds the steady states using both the mass and energy balance equations. From snapshot 1, up to five steady states can be obtained.

The mass balance equations for the species and are:

A

B

C(T)=C/(1+k(T)τ)

A

A0

1

C(T)=k(T)τC(T)/(1+k(T)τ)

B

1

A

2

where is the residence time and and are the reaction rate constants given by the Arrhenius law.

τ

k(T)

1

k(T)

2

The energy balance can be written as ,

Q(T)=Q(T)

in

out

where ,

Q(T)=-ΔHVk(T)C(T)-ΔHVk(T)C(T)

in

1

1

A

2

2

B

and .

Q(T)=FρCT-FρCT+UA(T-T)

out

P

0

P,0

0

j

Here, and are the heat of reactions, is the molar flow rate, is the heat capacity, is the density, the subscript indicates inlet conditions, and are the overall heat transfer coefficient and the area of the cooling jacket, respectively, is the temperature of cooling, and is the reactor's volume.

ΔH

1

ΔH

2

F

C

P

ρ

0

U

A

T=278K

j

V

The two heat quantities and are plotted versus in red and blue; is a simple linear function (shown by the blue line).

Q(T)

in

Q(T)

out

T

Q(T)

out

The steady states are shown by the green dots in two different plots: (1) and versus ; and (2) . You can vary the inlet temperature and the parameter .

Q(T)

in

Q(T)

out

T

Q(T)-Q(T)=ΔQ(T)

out

in

T

0

β=FρC+UA

P