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Dipl.-Ing. Andreas Jörke1
Tutorial Chemical Reaction Engineering:
2. Stoichiometry
1Institute of Process Engineering, G25-217, andreas.joerke@ovgu.de24-Jun-14
Tutorial CRE: Stoichiometry
Problem: Ethanol synthesis
M+CO+2H E+H O I2 2M+CO+2H E+H O
M+CO AA E EA H O
I
II
2 A+E EA+H O
EA+M 2E+CO
III
IV
M: 120 kmol/h 200 °C
2CO+2H M V
Products
M: 120 kmol/h
CO: 120 kmol/h
200 C
H2: 200 kmol/h
24-Jun-14CRE: Stoichiometry 2
Key Components
# key components = # species – rank(element-species-matrix)
rankR N rankR N
2 2M CO H E H O A EAC 1 1 0 2 0 2 4H 4 0 2 6 2 4 8O 1 1 0 1 1 2 2
-
O 1 1 0 1 1 2 2
2 2M CO H E H O A EAC 1 1 0 2 0 2 4H 4 0 2 6 2 4 8
O 0 0 0 1 1 0 2
det 2 0 rank 3
24-Jun-14CRE: Stoichiometry 3
# Key components = 7 – 3 = 4
Key Reactions
# key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # key reactions = # key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2M CO H E H O A EA2 2
I 1 1 2 1 1 0 0II 1 1 0 0 0 1 0
-II 1 1 0 0 0 1 0
III 0 0 0 1 1 1 1IV 1 1 0 2 0 0 1
IV 1 1 0 2 0 0 1V 1 1 2 0 0 0 0
24-Jun-14CRE: Stoichiometry 4
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2M CO H E H O A EA2 2
I 1 1 2 1 1 0 0II 1 1 0 0 0 1 0
*
II 1 1 0 0 0 1 0III 1 1 2 2 0 1 1IV 1 1 0 2 0 0 1
IV 1 1 0 2 0 0 1V 1 1 2 0 0 0 0
24-Jun-14CRE: Stoichiometry 5
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2H O M CO H E A EA2 2
I 1 1 1 2 1 0 0II 0 1 1 0 0 1 0
*
II 0 1 1 0 0 1 0III 0 1 1 2 2 1 1IV 0 1 1 0 2 0 1
+
IV 0 1 1 0 2 0 1V 0 1 1 2 0 0 0
24-Jun-14CRE: Stoichiometry 6
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2H O M CO H E A EA2 2
I 1 1 1 2 1 0 0II 0 1 1 0 0 1 0
**
II 0 1 1 0 0 1 0III 0 0 0 2 2 0 1IV 0 1 1 0 2 0 1
IV 0 1 1 0 2 0 1V 0 1 1 2 0 0 0
+
24-Jun-14CRE: Stoichiometry 7
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2H O M CO H E A EA2 2
I 1 1 1 2 1 0 0II 0 1 1 0 0 1 0
**
II 0 1 1 0 0 1 0III 0 0 0 2 2 0 1IV 0 1 1 0 2 0 1
+*
IV 0 1 1 0 2 0 1V 0 0 0 2 2 0 1
+
24-Jun-14CRE: Stoichiometry 8
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2H O M CO H E A EA2 2
I 1 1 1 2 1 0 0II 0 1 1 0 0 1 0
**
II 0 1 1 0 0 1 0III 0 0 0 2 2 0 1IV 0 1 1 0 2 0 1
+
**
IV 0 1 1 0 2 0 1V 0 0 0 0 0 0 0
24-Jun-14CRE: Stoichiometry 9
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2 2H O CO M H E A EA2 2
I 1 1 1 2 1 0 0II 0 1 1 0 0 1 0
**
*
II 0 1 1 0 0 1 0III 0 0 0 2 2 0 1IV 0 0 2 0 2 1 1
**
IV 0 0 2 0 2 1 1V 0 0 0 0 0 0 0
24-Jun-14CRE: Stoichiometry 10
Key Reactions
# Key reactions = rank(stoichiometric-matrix) To fulfill the atom balances: # Key reactions = # Key components Test rank(stoichiometric matrix) 4? Test rank(stoichiometric matrix) = 4?
2H O CO H2 E M A EA2
I 1 1 2 1 1 0 0II 0 1 0 0 1 1 0
**
*
II 0 1 0 0 1 1 0III 0 0 2 2 0 0 1IV 0 0 0 2 2 1 1
**
IV 0 0 0 2 2 1 1V 0 0 0 0 0 0 0
• One reaction is linear dependend N l ( bi h ) i W l i IV
det 4 0 rank 4
Neglect an (arbitrary chosen) reaction We neglect reaction IV
24-Jun-14CRE: Stoichiometry 11
Summary task a)
4 Key components
Select key components so, that the remaining non-key
components contain elements (C,H,O) rank 3
5 reactions, but 4 key reactions are sufficient to
rank 4 5 reactions, but 4 key reactions are sufficient todescribe the network , # key components = # key reactions
rank 4
One reaction is linear dependend and can be neglected!
Decision for neglection is arbitrary! We neglect reaction IV!
24-Jun-14CRE: Stoichiometry 12
Tutorial CRE: Stoichiometry
Problem: Ethanol synthesis
M+CO+2H E+H O I2 2M+CO+2H E+H O
M+CO AA E EA H O
I
II
2 A+E EA+H O
EA+M 2E+CO
III
IV
M: 120 kmol/h 200 °C
2CO+2H M V
Products
M: 120 kmol/h
CO: 120 kmol/h
200 C
H2: 200 kmol/h
24-Jun-14CRE: Stoichiometry 13
Tutorial CRE: Stoichiometry
Problem: Ethanol synthesis
2 2M+CO+2H E+H O I2 2 M CO 2H E H O
M+CO A
A+E EA+H O
II
III2 A+E EA+H O
EA+M 2E+CO
III
IV
2CO+2H M V
E ilib i i b k d i f d i ( 1)Equilibrium reactions: backward reaction = forward reaction·(-1)
Linear dependend doesn´t change can be neglected! rank
no use for equilibria in stoichiometry!
24-Jun-14CRE: Stoichiometry 14
Product composition/extend of reaction
From measurements: Information about key components
0 708MX 35 kmol/hn Conversion0,7080,9250,830
M
CO
H
XXX
0
0i i
ii
n nXn
35 kmol/h9 kmol/h34 kmol/h
M
CO
H
nnn
2
2
0,830
83 kmol/hH
H O
X
n 2
2
34 kmol/h
83 kmol/hH
H O
n
n
From molar changes we calculate the extend of reaction ξi
85 kmol/hMn #KR85 kmol/h111 kmol/h166 kmol/h
M
CO
H
nnn
#
,1
KR
i i j ij
n n
12
2
166 kmol/h
83 kmol/hH
H O
n
n
1
n
24-Jun-14CRE: Stoichiometry 15
Product composition/extend of reaction
Stoichiometric matrix for key components:I II III V I II III V
M -1 -1 0 1CO -1 -1 0 -1H 2 0 0 2
1M -1 2 1 2 -1 2 0
CO 0 -1 1 2 0H 1 2 1 2 1 2 1
2
2
H -2 0 0 -2H O 1 0 1 0
2
2
H 1 2 -1 2 1 2 1H O 1 2 -1 2 0 0
8 Calculate theextend of reaction vector:
85111166
1 16683
70 kmol/h
1
n
-1 2 1 2 -1 2 00 -1 1 2 0
1 2 1 2 1 2 1
70 kmol/h28 kmol/h13 kmol/h
24-Jun-14CRE: Stoichiometry 16
1 2 -1 2 1 2 11 2 -1 2 0 0
13 kmol/h13 kmol/h
Product composition/extend of reaction
Stoichiometric matrix for non-key components:I II III V
A 0 1 -1 0EA 0 0 1 0E 1 0 1 0
Calculate the molar changes of the non-key components:
E 1 0 -1 0
7028
Outlet composition:i
ij
j
nxn
1313
n 2
M 0,142CO 0,037H 0,138
15 kmol/h13 kmol/h nKCn
0 1 -1 00 0 1 0
2
2
,H O 0,337
A 0,061EA 0 053
1
24-Jun-14CRE: Stoichiometry 17
57 kmol/h1 0 -1 0EA 0,053E 0,232
Isothermal reactor operation
Which heat has to be removed to keep the reactor isothermal?
2 2M CO H H O A EA E
2 2
200 / kJ/mol 192,3 -105,9 5,08 -234,05 -463,3 -450,3 285,6f iH T C
, R j i j f i R fi
H H H H 231,61 kJ/molR IH 165,10 kJ/mol
64,55 kJ/molk / l
R II
R III
HH
T
R j j Rj
Q H H
96,56 kJ/molR VH
3231,61 kJ/mol 70 10 mol/h Q 3
3
, 165,10 kJ/mol 28 10 mol/h 64,55 kJ/mol 13 10 mol/h
Q
24-Jun-14CRE: Stoichiometry 18
3 6 96,56 kJ/mol 13 10 mol/h 21, 25 10 kJ/h 6 MW
Appendix: Which reaction can be neglected?
Neglect V: Stoichiometric matrix for key components:I II III IV I II III IV
M -1 -1 0 -1CO -1 -1 0 1H 2 0 0 0
1M 0 0 -1 2 0
CO -1 2 -1 2 1 2 0H 0 0 1 2 1
2
2
H -2 0 0 0H O 1 0 1 0
2
2
H 0 0 1 2 1H O -1 2 1 2 0 0
8 Calculate theextend of reaction vector:
85111166
1 16683
83 kmol/h
1
n
0 0 1 2 0 83 kmol/h15 kmol/h0 kmol/h
0 0 -1 2 0-1 2 -1 2 1 2 0
0 0 1 2 1
24-Jun-14CRE: Stoichiometry 19
0 kmol/h13 kmol/h
0 0 1 2 1-1 2 1 2 0 0
Appendix: Which reaction can be neglected?
Neglect V: Stoichiometric matrix for non-key components:I II III IV
A 0 1 -1 0EA 0 0 1 -1E 1 0 1 2
Calculate the molar changes of the non-key components:
E 1 0 -1 2
8315
Outlet composition:i
ij
j
nxn
013
n 2
M 0,142CO 0,037H 0,138
15 kmol/h13 kmol/h nKCn
2
2
,H O 0,337
A 0,061EA 0 053
10 1 -1 00 0 1 -1
24-Jun-14CRE: Stoichiometry 20
57 kmol/hEA 0,053E 0,232
1 0 -1 2
Appendix: Which reaction can be neglected?
Neglect I: Stoichiometric matrix for key components:II III IV V II III IV V
M -1 0 -1 1CO -1 0 1 -1H 0 0 0 2
1M -1 2 -1 2 0 0
CO 0 0 0 1H 1 2 1 2 1 2 0
2
2
H 0 0 0 -2H O 0 1 0 0
2
2
H -1 2 1 2 -1 2 0H O 0 0 -1 2 0
8 Calculate theextend of reaction vector:
85111166
1 16683
98 kmol/h
1
n
1 2 1 2 0 0 98 kmol/h83 kmol/h70 kmol/h
-1 2 -1 2 0 00 0 0 1
-1 2 1 2 -1 2 0
24-Jun-14CRE: Stoichiometry 21
70 kmol/h83 kmol/h
-1 2 1 2 -1 2 00 0 -1 2 0
Appendix: Which reaction can be neglected?
Neglect I: Stoichiometric matrix for non-key components:II III IV V
A 1 -1 0 0EA 0 1 -1 0E 0 1 2 0
Calculate the molar changes of the non-key components:
E 0 -1 2 0
9883
Outlet composition:i
ij
j
nxn
7083
n 2
M 0,142CO 0,037H 0,138
15 kmol/h13 kmol/h nKCn
2
2
,H O 0,337
A 0,061EA 0 053
11 -1 0 00 1 -1 0
24-Jun-14CRE: Stoichiometry 22
57 kmol/hEA 0,053E 0,232
0 -1 2 0
Appendix: Which reaction can be neglected?
Neglect II: Stoichiometric matrix for key components:I III IV V I III IV V
M -1 0 -1 1CO -1 0 1 -1H 2 0 0 2
1M -1 2 -1 2 0 0
CO 1 2 1 2 0 1H 0 1 1 2 0
2
2
H -2 0 0 -2H O 1 1 0 0
2
2
H 0 1 -1 2 0H O 1 2 1 2 -1 2 0
8 Calculate theextend of reaction vector:
85111166
1 16683
98 kmol/h
1
n
1 2 1 2 0 0 98 kmol/h-15 kmol/h28 kmol/h
-1 2 -1 2 0 01 2 1 2 0 10 1 -1 2 0
24-Jun-14CRE: Stoichiometry 23
-28 kmol/h-15 kmol/h
0 1 -1 2 01 2 1 2 -1 2 0
Appendix: Which reaction can be neglected?
Neglect II: Stoichiometric matrix for non-key components:I III IV V
A 0 -1 0 0EA 0 1 -1 0E 1 1 2 0
Calculate the molar changes of the non-key components:
E 1 -1 2 0
9815
Outlet composition:i
ij
j
nxn
2815
n 2
M 0,142CO 0,037H 0,138
15 kmol/h13 kmol/h nKCn
2
2
,H O 0,337
A 0,061EA 0 053
10 -1 0 00 1 -1 0
24-Jun-14CRE: Stoichiometry 24
57 kmol/hEA 0,053E 0,232
1 -1 2 0
Appendix: Which reaction can be neglected?
Neglect III: Stoichiometric matrix for key components:I II IV V I II IV V
M -1 -1 -1 1CO -1 -1 1 -1H 2 0 0 2
1M 0 0 0 1
CO -1 2 -1 2 0 -1H 1 2 1 2 1 2 1
2
2
H -2 0 0 -2H O 1 0 0 0
2
2
H -1 2 1 2 -1 2 -1H O 0 0 -1 2 -1
8 Calculate theextend of reaction vector:
85111166
1 16683
83 kmol/h
1
n
0 0 0 1 83 kmol/h15 kmol/h13 kmol/h
0 0 0 1-1 2 -1 2 0 -1-1 2 1 2 -1 2 -1
24-Jun-14CRE: Stoichiometry 25
-13 kmol/h0 kmol/h
1 2 1 2 1 2 10 0 -1 2 -1
Appendix: Which reaction can be neglected?
Neglect III: Stoichiometric matrix for non-key components:I II IV V
A 0 1 0 0EA 0 0 -1 0E 1 0 2 0
Calculate the molar changes of the non-key components:
E 1 0 2 0
8315
Outlet composition:i
ij
j
nxn
130n
2
M 0,142CO 0,037H 0,138
15 kmol/h13 kmol/h nKCn
2
2
,H O 0,337
A 0,061EA 0 053
10 1 0 00 0 -1 0
24-Jun-14CRE: Stoichiometry 26
57 kmol/hEA 0,053E 0,232
1 0 2 0
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