Lecture 13 Chemical Reaction Engineering (CRE) is the field that - - PowerPoint PPT Presentation

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 13

Le Lect ctur ure e 13 3 – Tue uesd sday y 2/ 2/26 26/2 /2013

 Complex Reactions:

A +2B  C A + 3C  D

 Example A: Liquid Phase PFR  Example B: Liquid Phase CSTR  Example C: Gas Phase PFR  Example D: Gas Phase Membrane Reactors Sweep Gas Concentration Essentially Zero Sweep Gas Concentration Increases with Distance  Example E: Semibatch Reactor

2

Gas Phase Multiple Reactions

3

Ne New w th things ngs for

• r mu

multip tiple le reactions eactions are: e:

4

• 1. Number Every Reaction
• 2. Mole Balance on every species
• 3. Rate Laws

(a) Net Rates of Reaction for every species

(b) Rate Laws for every reaction (c) Relative Rates of Reaction for every reaction For a given reaction i: (i) aiA+biB ciC+diD:







N i iA A

r r

1

3 2 2 2 2 1 1 C A C C B A A A

C C k r C C k r    

i iD i iC i iB i iA

d r c r b r a r     

Reactor Mole Balance Summary

5

Reactor Type

Gas Phase Liquid Phase

V r dt dN

A A 

A A

r dt dC 

Batch

V r dt dN

A A 

V C r dt dC

A A A

  

Semibatch

B B B

F V r dt dN  

 

V C C r dt dC

B B B B

   

Reactor Mole Balance Summary

6

Reactor Type

Gas Phase Liquid Phase

A A A

r F F V   

 

A A A

r C C V    

CSTR

A A

r dV dC  

A A

r dV dF  PFR

A A

r dW dC   

A A

r dW dF   PBR

Note: The reaction rates in the above mole balances are net rates.

V N C

B B 



B B

F C  T T P P N N V V

T T

 T T P P V N N N C

T T B B

 T T P P N N C C

T B T B

 T T P P F F

T T

   T T P P F F C C

T B T B

 T T P P F F F C

T T B B

 

Batch Flow

7

Note: We could use the gas phase mole balances for liquids and then just express the concentration as: Flow: Batch:

Stoichiometry

8

Concentration of Gas:

D C B A T T A T A

F F F F F T T y F F C C                   



A A

F C  V N C

A A 

Example A: Liquid Phase PFR

9

NOTE: The specific reaction rate k2C is defined with respect to species C.

2 3 ) 2 ( D A C  

2 3 2 2 A C C C

C C k r  

2 ) 1 ( C B A  

2 1 1 B A A A

C C k r  

NOTE: The specific reaction rate k1A is defined with respect to species A.

The complex liquid phase reactions follow elementary rate laws:

Example A: Liquid Phase PFR

10 10

Complex Reactions 1) Mole Balance on each and every species

฀ (1) A 2B  C (2) A 3C  D

D D C C B B A A

r dV dF r dV dF r dV dF r dV dF     ) 4 ( ) 3 ( ) 2 ( ) 1 (

Example A: Liquid Phase PFR

11 11

2) Rate Laws:

Net Rates Rate Laws Relative Rates Reaction 1

D D C C C B B B A A A

r r r r r r r r r r r

2 2 1 2 1 2 1

) 8 ( ) 6 ( ) 7 ( ) 5 (        

3 2 2 2 2 1 1

) 10 ( ) 9 (

C A C C B A A A

C C k r C C k r    

1 1 1 1 1 1 1

1 2 1 (11) 2 (12)

C A B B A C A

r r r r r r r       

Example A: Liquid Phase PFR

12 12

Relative Rates Reaction 2

3 ) 14 ( 3 2 ) 13 ( 1 3 2

2 2 2 2 2 2 2 C D C A D C A

r r r r r r r       

3 2 2 3 2 2 1 2 1 3 2 2 2 1

3 2 3 2

C A C D C A C B A A C B A A B C A C B A A A

C C k r C C k C C k r C C k r C C k C C k r        

Example A: Liquid Phase PFR

13 13

3) Stoichiometry Liquid

 

else then 00001 . ~ ) 19 ( ) 18 ( ) 17 ( ) 16 ( ) 15 (              

D C D C D D C C B B A A

F F V if S F C F C F C F C    

Example A: Liquid Phase PFR

14 14

Others 4) Parameters Needed Not – Liquid ) 20 ( Needed Not – Liquid ) 19 ( Needed Not – Liquid

0 

 

T T

C F 

100 ) 26 ( 200 ) 28 ( 200 ) 26 ( 2500 ) 25 ( Liquid ) 24 ( Liquid ) 23 ( 20 ) 22 ( 10 ) 21 (

2 1

         

B A f T C A

F F V C k k

Example B: Liquid Phase CSTR

15 15

Same reactions, rate laws, and rate constants as Example A

2 ) 1 ( C B A  

2 1 1 B A A A

C C k r  

NOTE: The specific reaction rate k1A is defined with respect to species A. NOTE: The specific reaction rate k2C is defined with respect to species C.

2 3 ) 2 ( D A C  

2 3 2 2 A C C C

C C k r  

Example B: Liquid Phase CSTR

16 16

The complex liquid phase reactions take place in a 2,500 dm3 CSTR. The feed is equal molar in A and B with FA0=200 mol/min, the volumetric flow rate is 100 dm3/min and the reaction volume is 50 dm3. Find the concentrations of A, B, C and D existing in the reactor along with the existing selectivity. Plot FA, FB, FC, FD and SC/D as a function of V

Example B: Liquid Phase CSTR

17 17

(1) A + 2B →C (2) 2A + 3C → D

3 2 2 2 2 1 1 C A C C B A A A

C C k r C C k r     ) 4 ( ) 3 ( ) 2 ( ) 1 (             V r C D V r C C V r C C B V r C C A

D D C C B B B A A A

     

1) Mole Balance

Example B: Liquid Phase CSTR

18 18

2) Rate Laws: (5)-(14) same as PFR 3) Stoichiometry: (15)-(18) same as Liquid Phase PFR 4) Parameters:

0001 . 0001 . ) 19 (

/

   

D C D C D C

C C F F S  

2 1

, , , , ,  V C C k k

B A C A

Example B: Liquid Phase CSTR

19 19

(1) A + 2B →C (2) 2A + 3C → D

3 2 2 2 2 1 1 C A C C B A A A

C C k r C C k r    

00001 . ) 19 ( ) 18 ( ) 17 ( ) 16 ( ) 15 (      

D C D C D D C C B B A A

F F S F C F C F C F C    

1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)

 

V r F F F f

A A A A

   ) 1 (

(=0)

 

V r F F F f

B B B B

   ) 2 (

(=0)

 

V r F F f

C C C

   0 ) 3 (

(=0)

 

V r F F f

D D D

   0 ) 4 ( (=0)

In terms of molar flow rates

Same as Example A

Example B: Liquid Phase CSTR

20 20

(1) A + 2B →C (2) 2A + 3C → D

3 2 2 2 2 1 1 C A C C B A A A

C C k r C C k r    

1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)

In terms of concentration

 

V r C C C f

A A A A

   ) 1 (  

(=0)  

V r C C C f

B B B B

   ) 2 (  

(=0)

 

V r C C f

C C C

   ) 3 (  (=0)

 

V r C C f

D D D

   ) 4 (  (=0) 00001 . ) 15 (  

D C D C

F F S

Same as Example A

Example C: Gas Phase PFR, No ΔP

21 21

Same reactions, rate laws, and rate constants as Example A:

2 ) 1 ( C B A  

2 1 1 B A A A

C C k r  

NOTE: The specific reaction rate k1A is defined with respect to species A. NOTE: The specific reaction rate k2C is defined with respect to species C.

2 3 ) 2 ( D A C  

2 3 2 2 A C C C

C C k r  

Example C: Gas Phase PFR, No ΔP

22 22

1) Mole Balance 2) Rate Laws: (5)-(14) same as CSTR

) 4 ( (2) ) 3 ( ) 1 (

D D B B C C A A

r dV dF r dV dF r dV dF r dV dF    

Example C: Gas Phase PFR, No ΔP

23 23

3) Stoichiometry: Gas: Isothermal T = T0 Packed Bed with Pressure Drop

D C B A T T D T D T C T C T B T B T A T A

F F F F F y F F C C y F F C C y F F C C y F F C C         ) 19 ( ) 18 ( ) 17 ( ) 16 ( ) 15 (

2 2

T T T T

F F y T T F F y dW dy                      

Example C: Gas Phase PFR, No ΔP

24 24

4) Selectivity

 

21 1  y

     

20 else then 00001 . if           

D C D C

F F V F F S

Example D: Membrane Reactor with ΔP

25 25

Same reactions, rate laws, and rate constants as Example A:

2 ) 1 ( C B A  

2 1 1 B A A A

C C k r  

NOTE: The specific reaction rate k1A is defined with respect to species A. NOTE: The specific reaction rate k2C is defined with respect to species C.

2 3 ) 2 ( D A C  

2 3 2 2 A C C C

C C k r  

Example D: Membrane Reactor with ΔP

26 26

Because the smallest molecule, and the one with the lowest molecular weight, is the one diffusing out, we will neglect the changes in the mass flow rate down the reactor and will take as first approximation: 1) Mole Balances

       

4 2 3 1

D D B B C C C A A

r dV dF D r dV dF B R r dV dF C r dV dF A     

C Csg

R dV dF 

We also need to account for the molar rate of desired product C leaving in the sweep gas FCsg

m m   

We need to reconsider our pressure drop equation. When mass diffuses out of a membrane reactor there will be a decrease in the superficial mass flow rate, G. To account for this decrease when calculating our pressure drop parameter, we will take the ratio of the superficial mass velocity at any point in the reactor to the superficial mass velocity at the entrance to the reactor.

           

 

i i i i

MW F MW F G G   

27

Example D: Membrane Reactor with ΔP

The superficial mass flow rates can be obtained by multiplying the species molar flow rates, Fi, by their respective molecular weights, Mwi, and then summing over all species:

       

   

    

i i i i C i i C i i C C

MW F MW F A MW F A MW F A m A m G G

1 1 1 1

Example D: Membrane Reactor with ΔP

28 28

Example D: Membrane Reactor with ΔP

29 29

2) Rate Laws: (5)-(14) same as Examples A, B, and C. 3) Stoichiometry: (15)-(20) same as Examples A and B (T=T0) 4) Sweep Gas Balance:

 

CSweep C C C

C C k R    

21 2 2

T T T T

F F y dV dy F F y dW dy      

C Csg C V V Csg V Csg

R dV dF V R F F     

 

Example E: Liquid Phase Sem emibatch batch

30 30

Same reactions, rate laws, and rate constants as Example A:

2 ) 1 ( C B A  

2 1 1 B A A A

C C k r  

NOTE: The specific reaction rate k1A is defined with respect to species A. NOTE: The specific reaction rate k2C is defined with respect to species C.

2 3 ) 2 ( D A C  

2 3 2 2 A C C C

C C k r  

The complex liquid phase reactions take place in a semibatch reactor where A is fed to B with FA0= 3 mol/min. The volumetric flow rate is 10 dm3/min and the initial reactor volume is 1,000 dm3. The maximum volume is 2,000 dm3 and CA0=0.3 mol/dm3 and CB0=0.2 mol/dm3. Plot CA, CB, CC, CD and SS/D as a function of time.

31 31

Example E: Liquid Phase Sem emibatch batch

1) Mole Balances: (1) A + 2B →C (2) 2A + 3C → D

A A A

F V r dt dN   V r dt dN

B B 

V r dt dN

C C 

V r dt dN

D D  0  A

N 000 . 2   V C N

B B 0  C

N

0  D

N

32

B FA0

Example E: Liquid Phase Sem emibatch batch

2) Rate Laws: (5)-(14)

         

19 18 17 16 15 V N C V N C V N C V N C t v V V

D D C C B B A A

     

Net Rate, Rate Laws and relative rate – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR

 

20 ) ( else then ) 0001 . ( if

/

         

D C D C

N N t S

min dm 10

3 0 



3

dm 100 V  min mol 3 F 0

A 

33

Example E: Liquid Phase Sem emibatch batch

3) Selectivity and Parameters:

En End o d of Le Lect ctur ure e 13

34 34