Seminar II [Schreibgeschützt]II_neu.pdf · Dipl.-Ing. Andreas Jörke1 Tutorial Chemical Reaction Engineering: 2. Stoichiometry 1Institute of Process Engineering, G25-217, [email protected]

Dipl.-Ing. Andreas Jörke1

Tutorial Chemical Reaction Engineering:

2. Stoichiometry

1Institute of Process Engineering, G25-217, [email protected]

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


# 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


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


Key Reactions


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


Key Reactions



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

+


Key Reactions



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

+


Key Reactions



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


Key Reactions


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


Key Reactions


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


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!




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




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!


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



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


1 2 -1 2 1 2 11 2 -1 2 0 0

13 kmol/h13 kmol/h


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


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


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


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


0 kmol/h13 kmol/h

0 0 1 2 1-1 2 1 2 0 0


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


E 1 0 -1 2

8315


ij

j

nxn

013

n 2

M 0,142CO 0,037H 0,138


2

2

,H O 0,337

A 0,061EA 0 053

10 1 -1 00 0 1 -1


57 kmol/hEA 0,053E 0,232

1 0 -1 2


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


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


70 kmol/h83 kmol/h

-1 2 1 2 -1 2 00 0 -1 2 0


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


E 0 -1 2 0

9883


ij

j

nxn

7083

n 2

M 0,142CO 0,037H 0,138


2

2

,H O 0,337

A 0,061EA 0 053

11 -1 0 00 1 -1 0


57 kmol/hEA 0,053E 0,232

0 -1 2 0


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


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


-28 kmol/h-15 kmol/h

0 1 -1 2 01 2 1 2 -1 2 0


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


E 1 -1 2 0

9815


ij

j

nxn

2815

n 2

M 0,142CO 0,037H 0,138


2

2

,H O 0,337

A 0,061EA 0 053

10 -1 0 00 1 -1 0


57 kmol/hEA 0,053E 0,232

1 -1 2 0


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


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


-13 kmol/h0 kmol/h

1 2 1 2 1 2 10 0 -1 2 -1


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


E 1 0 2 0

8315


ij

j

nxn

130n

2

M 0,142CO 0,037H 0,138


2

2

,H O 0,337

A 0,061EA 0 053

10 1 0 00 0 -1 0


57 kmol/hEA 0,053E 0,232

1 0 2 0

Documents

Seminar II [Schreibgeschützt]II_neu.pdf · Dipl.-Ing. Andreas Jörke1 Tutorial Chemical Reaction Engineering: 2. Stoichiometry 1Institute of Process Engineering, G25-217, [email protected]