Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of

chemical reactions and the design of the reactors in which they take place.

Lecture 12

Lecture 12 – Tuesday 2/19/2013 �  Multiple Reactions

� Selectivity and Yield

� Series Reactions

� Complex Reactions

2

A DkD

A UkU

A B C

A + B C + D

A + C E

�  Series: A → B → C �  Parallel: A → D

A → U

�  Independent: A → B

C → D

�  Complex: A + B →C + D

A + C → E

With multiple reactors, either molar flow or number of moles must be used (no conversion!)

3

4 Types of Multiple Reactions

Instantaneous Overall

Selectivity

Yield

There are two types of selectivity and yield: Instantaneous and Overall.

U

DDU r

rS =U

DDU F

FS =~

A

DD r

rY−

=AA

DD FF

FY−

=0

~

4

Selectivity and Yield

ABA

BA

U

DUD C

kk

CCkCCk

rrS

2

1

2

21 ===

To maximize the selectivity of D with respect to U run at high concentration of A and use PFR.

DBA 1k⎯→⎯+ BAD CCkr 21=Example: Desired Product:

UBA 2k⎯→⎯+BAU CCkr 2=Undesired Product:

Selectivity and Yield

5

Gas Phase Multiple Reactions

6

Multiple Reactions

7

Flow Batch

BB

AA

rdVdF

rdVdF

=

=

VrdtdN

VrdtdN

BB

AA

=

=

A) Mole Balance of each and every species

Multiple Reactions

8

B) Rates a) Rate Law for each reaction: b) Net Rates: c) Relative Rates:

ACAA

BAAA

CCkrCCkr

22

11

=−

=−

AAi

iAA rrrr 211

+==∑=

riA−ai

= riB−bi

= riCci

= riDdi

Multiple Reactions

9

C) Stoichiometry Gas:

Liquid:

⎟⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

TT

PP

FFCCA

ATA

0

000

0υAA FC =

Example: A → B → C

(1) A → B k1

(2) B → C k2

Batch Series Reactions

10

1) Mole Balances

VrdtdN

VrdtdN

VrdtdN

CC

BB

AA

=

=

=

AC

AB

AA r

dtdC r

dtdC r

dtdC

===

V=V0 (constant batch)

Batch Series Reactions

11

2) Rate Laws

B2B1B

A1A

BB1B1

AA1A1

rrrrr

CkrCkr

+=

=

=−

=−Laws

Net rates

1r

1r

1r

1r

C2B2

B1A1

=−

=−

Relative rates

Example: Batch Series Reactions

12

A → B → C

(1) A → B

(2) B → C

1) Mole Balances

CC

BB

AA r

dtdC r

dtdC r

dtdC

===

t topt

Ci

A B C

OVV =

Example: Batch Series Reactions

13

2) Rate Laws

1r

1r

1r

1r C2B2B1A1 =

−=

−Relative:

B2B2

A1A1

CkrCkr

−=

−=Laws:

Example: Batch Series Reactions

14

3) Combine Species A: Species B:

A1AA CkrdtdC

=−=−

( )tkexpCC 10AA −=

BB rdtdC

=

B2A1B2B1NET BB CkCkrrrr −=+==

( )tkexpCkCkdtdC

10A1B2B −=+

Example: Batch Series Reactions

15

Using the integrating factor, ( ) ( )tkdtkFI 22 expexp.. == ∫( )[ ] ( )tkkCk

dttkCd A

B1201

2 expexp−=

at t = 0, CB=0

CB =k1CA0

k2 − k1exp −k1t( )− exp −k2t( )⎡⎣ ⎤⎦

BAAC CCCC −−= 0

( ) ( )[ ]tktkAC ekek

kkCC 21 11 12

12

0 −− −−−−

=

Example: CSTR Series Reactions

16

AàBàC What is the optimal ? τ

00 =+− τAAA rCC

000 0

=+−

=+−

τBB

BB

rCVrCv

00

000

0

=+−

=+−

VrvCvCVrFF

AAA

AAA

1) Mole Balances A:

B:

Example: CSTR Series Reactions

17

AàBàC 2) Rate Laws

B2B2

A1A1

CkrCkr

−=

−=Laws:

1 1

1 2 1 2

0A A A

B A B A B

r r k Cr r r k C k C= + = −

= − + = −

Net:

1r

1r

1r

1r C2B2B1A1 =

−=

−Relative:

Example: CSTR Series Reactions

18

AàBàC 3) Combine

�

CA 0 −CA − k1CAτ = 0

CA =CA 0

1+ k1τ

−CB + k1CA − k2CB( )τ = 0

CB =k1CAτ1+ k2τ

CB =k1CA 0τ

1+ k2τ( ) 1+ k1τ( )

Example: CSTR Series Reactions

19

AàBàC

€

dCB

dτ= 0

€

τmax =1k1k2

Find that gives maximum concentration of B

( )( )τττ

12

01

11 kkCkC A

B ++=

τ

20

End of Lecture 12

21

22

Supplementary Slides

Blood Coagulation

23

24

25

Notations

26

Notations

Mole Balances

27

28

Mole Balances

29

Mole Balances

30

Results

Many metabolic reactions involve a large number of sequential reactions, such as those that occur in the coagulation of blood.

Cut → Blood → Clotting

Figure A. Normal Clot Coagulation of blood (picture courtesy of: Mebs, Venomous and Poisonous

Animals, Medpharm, Stugart 2002, Page 305) 31

Blood Coagulation

32

Schematic of Blood Coagulation

Cut

A + B C D E F

Clot 33