The document discusses various concepts in industrial control including: 1) A continuous stirred-tank reactor model with mass balances and dynamic equations. 2) A model of two continuous stirred-tank reactors in series and their dynamic equations. 3) A component balance model for an irreversible reaction in a reactor with flows in and out and a reaction rate. The document provides background on industrial control concepts and mathematical models for systems like continuous stirred-tank reactors, series reactors, and heated stirred tanks. It references control texts by Luyben and Chau.

1. Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2009
Tehran, Iran
Behzad Samadi (Amirkabir University) Industrial Control 1 / 7

2. Chemical Systems
Variables:
Q: volumetric flow (m3/s)
C: concentration (mol/m3)
V : volume (m3)
[Luyben, 1996] and [Chau, 2002]
Behzad Samadi (Amirkabir University) Industrial Control 2 / 7

3. Continuous Stirred-Tank Reactor
C ,Q
C ,Qin in
1 1
C ,Q1 1
C V1 1
Behzad Samadi (Amirkabir University) Industrial Control 3 / 7

4. Continuous Stirred-Tank Reactor
C ,Q
C ,Qin in
1 1
C ,Q1 1
C V1 1
Mass balance:
d(C1V1)
dt
= CinQin − C1Q1
Behzad Samadi (Amirkabir University) Industrial Control 3 / 7

5. Continuous Stirred-Tank Reactor
C ,Q
C ,Qin in
1 1
C ,Q1 1
C V1 1
Mass balance:
d(C1V1)
dt
= CinQin − C1Q1
Assuming V1 is constant and Qin = Q1 = Q,
V1
dC1
dt
= CinQ − C1Q
[Chau, 2002]
Behzad Samadi (Amirkabir University) Industrial Control 3 / 7

6. Two CSTRs in Series
C ,Qin in
C ,Q
1 1
C V1 1
C ,Q2 2
C ,Q
C V2 2
Behzad Samadi (Amirkabir University) Industrial Control 4 / 7

7. Two CSTRs in Series
C ,Qin in
C ,Q
1 1
C V1 1
C ,Q2 2
C ,Q
C V2 2
Dynamic equation: Assuming Qin = Q1 = Q2 = Q
V1
dC1
dt
= CinQ − C1Q
Behzad Samadi (Amirkabir University) Industrial Control 4 / 7

8. Two CSTRs in Series
C ,Qin in
C ,Q
1 1
C V1 1
C ,Q2 2
C ,Q
C V2 2
Dynamic equation: Assuming Qin = Q1 = Q2 = Q
V1
dC1
dt
= CinQ − C1Q
V2
dC2
dt
= C1Q − C2Q
[Chau, 2002]
Behzad Samadi (Amirkabir University) Industrial Control 4 / 7

9. Component balance
flow of moles of
jth component
into system
-
flow of moles of jth
component out of
system
+
rate of formation
of moles of jth
component from
chemical reactions
=
time rate of
change of moles
of jth component
inside system
[Luyben, 1996]
Behzad Samadi (Amirkabir University) Industrial Control 5 / 7

10. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

11. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Flow of A into system = CA0Q0
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

12. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Flow of A into system = CA0Q0
Flow of A out of system = CAQ
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

13. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Flow of A into system = CA0Q0
Flow of A out of system = CAQ
Rate of formation of A from reaction = −kVCA
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

14. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Flow of A into system = CA0Q0
Flow of A out of system = CAQ
Rate of formation of A from reaction = −kVCA
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

15. Component balance
Component A reacts irreversibly and at a specific reaction rate k to form
product, component B.
A
k
⇀ B
Flow of A into system = CA0Q0
Flow of A out of system = CAQ
Rate of formation of A from reaction = −kVCA
d(CAV )
dt
= CA0Q0 − CAQ − kVCA
[Luyben, 1996]
Behzad Samadi (Amirkabir University) Industrial Control 6 / 7

16. Heated Stirred Tank
Behzad Samadi (Amirkabir University) Industrial Control 7 / 7

17. Heated Stirred Tank
Energy balance:
ρCpV
dT
dt
= ρCpQ(Tin − T) + UA(TH − T)
T: temperature
ρ: fluid density
Cp: heat capacity
V : volume
U: heat transfer coefficient
A: heat transfer area
[Chau, 2002]
Behzad Samadi (Amirkabir University) Industrial Control 7 / 7

18. Chau, P. C. (2002).
Process Control: A First Course with MATLAB (Cambridge Series in
Chemical Engineering).
Cambridge University Press, 1 edition.
Luyben, W. L. (1996).
Process Modeling, Simulation, and Control for Chemical Engineers.
McGraw-Hill Companies, 2nd edition.
Behzad Samadi (Amirkabir University) Industrial Control 7 / 7