ch 3 - chain reaction

8/13/2019 Ch 3 - Chain Reaction

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A D V A N C E D

C H E M I C A L R E A

C T I O N E N G I N E E R I N G

Chain Reactions

Example

Initiation step

Propagation

Termination

Propagation steps occur faster than

initiation and termination steps

FACULTY OF CHEMICAL ENGINEERING CPE624 2

CH

COCH CHOCH 43

23623

32233

311343

3

][ 2

][

]][[

][ ,

CH k r H C CH

COCH k r CH COCOCH

CH Ak r COCH CH CH A

Ak r CHOCH A

t t

p p

p p

i i



A D V A N C E D



Pseudo – steady – state approximation

PSS – setting time derivative equal to zero

Mass balance equations are developed by

assuming steady state, so that PSS of intermediate

species is in steady state and concentration is small.

CPE624FACULTY OF CHEMICAL ENGINEERING 3

Example: Explain the physical meaning of pseudo-steady-state approximation, when applied to a CSTR and a PFR.

Explanation:-PSS valid if the concentration of a species is small.- In PFR or batch system, the time derivative is set equal to zero,d[CH3CO.]/dt = 0, not the concentration equal to zero.Physical meaning: The concentration of free radical is constant.-For CSTR, PSS approximation is indeed that the concentration be small or[CH3CO.]/ = 0Physical meaning: The concentration of free radical is small.



A D V A N C E D



FACULTY OF CHEMICAL ENGINEERING CPE624 5

CH

{[CH3 CO• ]-[CH3 CO• ]o/ = kp1[CH3CHO][CH3 • ] - k p2[CH3CO • ]

{[CO]-[CO ]o/ = k p2[CH3CO • ]

{[CH4]-[CH4 ]o/

= kp1[CH3CHO][CH3 • ]

[CH3 •] and [CH3CO •] are very reactive, thus the concentrations are very low.

{[CH3 CO• ]-[CH3 CO• ]o/ = kp1[CH3CHO][CH3 • ] - k p2[CH3CO • ] = 0

kp1[CH3CHO][CH3 • ] = k p2[CH3CO • ]

[CH3CO • ] = kp1/k p2 [CH3CHO][CH3 • ] …………………………(1)

{[CH3 • ]-[CH3 • ]o/ = -k i[CH3CHO] – kp1[CH3CHO][CH3 • ] + k p2[CH3CO • ]- 2k t [CH3 • ]2= 0 …………………..(2)

Insert (1) into (2)Ki[CH3CHO] - kp1[CH3CHO][CH3 • ] + k P2 x kp1/k p2 [CH3CHO][CH3 • ] - 2k t [CH3 • ]2=0

Ki[CH3CHO] - 2k t [CH3 • ]2 = 0

[CH3 • ]2= k i/2k t [CH3CHO][CH3 • ] = (k i/2k t )

1/2[CH3CHO]1/2



A D V A N C E D


C T I O N E N G I N E E R I N G Generic chain reaction

The reaction propagates by radical R·.

ni and nt are the number of molecules react in

initiation and termination steps respectively.

PSS approximation on CR yield the overall rateexpression


C B A

X R n

R C BR A

R An

t

i

,

,

t

i

n

R t t

R A p p

n

Ai i

C k r

C C k r

C k r

t

i t

n

n

A p

n

t t

i C k k n

k r

1

1

eff n

Aeff C k r



A D V A N C E D



Characteristic of chain reactions Large temperature dependences.

Sensitive to trace impurities that can alter theinitiation and termination rates

Initiators and Scavengers (promoters and poisons)

have large influences.

Initiators

Initiated by adding species I that easily forms radical

Initiate the reaction faster than reactant.

Scavengers

Termination step - radical species decomposed /reactedwith other radical species to form an inactive species X

Adding scavengers S

X is important in determining overall reaction rate

CPE624FACULTY OF CHEMICAL ENGINEERING 8SR tsts C C k r X SR ,



A D V A N C E D



Wall termination reactions

Surface reaction steps important in controlling

chain reactions.

Wall termination reactions introduce a complexity

to all chain reactions – the overall reaction rate as

a function of the size of reactor.

In a small reactor, termination reactions on surface

keep the radical intermediate small and inhibit

chain reaction.

In large reactor, the termination rate is smaller.




A D V A N C E D


C T I O N E N G I N E E R I N G Example: Briefly explain the terms initiator and

scavenger for a chain reaction

Initiator: Species (I) that can easily form radicals in a

chain reaction and can initiate the reaction faster

than the reactant.

Scavenger: Species (S) added into a chain reaction

that can readily scavenge the chain propagator to

terminate the reaction.




A D V A N C E D


C T I O N E N G I N E E R I N G Autooxidation

Autooxidation – autocatalytic process andit is an oxidation that converts alkanes into

alkyl peroxides.


ROOH OH R 2

R ROOH H R O

ROOOR

H R H R

RO

,

2

• A research student forgot to close a bottle of an organic compound tightly and kept on a table. The student left for vacation and when he came bac



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G Autooxidation


A research student forgot to close a bottle of an organic

compound tightly and kept on a table. The student left for

vacation and when he came back after one month, he saw the

table and everything on the table destroyed. Illustrate the

reaction steps and mechanism that occurred in the bottle.

Example



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G


(a) Initiation: A → R• ; r i = k iCA

Propagation: A + R• → B + C + R•; r i = k pCA CR

Termination: R•→ X; r t = k tCR

(b) Overall reaction rate:CR/ = k iCA – k tCR = 0 CR = k i/k t x CA r = k pCACR

= k ik p/k t CA2

(c) Solving CSTR equation: r = CAo – CA = (CAo – CA)/r = (CAo – CA )/CA

2 x k t/k ik p



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G


= [2 moles/L - 2(1-0.98)]/(0.04)2 x 0.05/ s/0.002/s x 10 l/s

= 1225 x 2.5 = 3062.5 s

= 51 min



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G Chain branching reaction

Produce more than one free radical species in

propagation step. Thus, the propagation steps

increase the concentration of radical species and

destabilize the kinetics.

Example:

Rapid rise in the concentration of radical species can

accelerate the reaction and possibly a chain-

branching explosion.


OH OR ROOH



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G Model of chain branching reaction

Consider the reaction of :

The mechanisms are:


C B A

X R

R C BR A

R A

,

,

R t t

R A p p

Ai i

C k r

C C k r

C k r

A pt

Ai R C k k

C k C )1(



A D V A N C E D

C H E M I C A L R E A C T I O N E N G I N E E R I N G References

Schmidt, L.D. (2005). The Engineering of Chemical

Reactions, 2nd edition, New York: Oxford University

Press.

Fogler, H.S. (2006). Elements of Chemical ReactionEngineering , 4th Edition, New Jersey: Prentice Hall.

Levenspiel, O. (1999). Chemical Reaction

Engineering , 3rd Edition, New York: John Wiley.


ch 3 - chain reaction

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