chapter 3 - chain reaction pnmeela

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Chain Reactions

CPE624 FACULTY OF CHEMICAL ENGINEERING

�  Example : Decomposition of acetaldehyde

Initiation step Propagation #1 Propagation #2 Termination step

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CH

COCHCHOCH +→ 43

23623

32233

311343

3

][ 2

][ ]][[

][ ,

•=→•

•=•+→•

•=•+→•+

=•+•→

CHkrHCCH

COCHkrCHCOCOCH

CHAkrCOCHCHCHAAkrCHOCHA

tt

pp

pp

ii

23

AkCr =

� Propagation steps occur faster than initiation and termination steps

� Radical species are very reactive and concentrations are always very low.

� Major products generated by propagation step

� Minor products made by initiation and termination steps.

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Mass balance

�  PFTR/Batch : Time derivative,

�  CSTR : Concentration gradient,

�  Mass balance = - reactant + product

dtdCA

OAA CCr −=τ

Mass balance : PFTR ]][[][][

311 •−−=−−= CHAkAkrrdAd

pipiτ

tppi rrrrdCHd 2][

213 −+−=•

τ2

33231 ][2][]][[][ •−•+•−= CHktCOCHkCHAkAk ppi

][]][[][323121

3 •−•=−=• COCHkCHAkrr

dCOCHd

ppppτ

][][322 •== COCHkr

dCOd

ppτ

]][[][311

4 •== CHAkrdCHd

ppτ

23623

32233

311343

3

][ 2

][ ]][[

][ ,

•=→•

•=•+→•

•=•+→•+

=•+•→

CHkrHCCH

COCHkrCHCOCOCH

CHAkrCOCHCHCHAAkrCHOCHA

tt

pp

pp

ii

Recall:

Activity in Class : Write mass balance for CSTR

When the concentration of the two radicals are low (very reactive) :

� Hence :

Rates of two propagation steps are exactly equal

0][][ 33 =•−•

τoCOCHCOCH

0][]][[ 3231 =•−• COCHkCHAk pp

][]][[ 3231 •=• COCHkCHAk pp

�  Hence adding the two propagation steps:

0][][][][ 3333 =•−•

=•−•

ττoo COCHCOCHCHCH

233231 ][2][]][[][ •−•+•− CHktCOCHkCHAkAk ppi

][]][[ 3231 •−•= COCHkCHAk pp

23 ][2][ •= CHktAki

The initiation and termination step are exactly equal

�  The major processes are the propagation steps

�  Adding p1 and p2 steps yield:

�  Autocatalytic – the reaction generates the catalyst that promotes the reaction.

�  The overall rate is enhanced by large ki and inhibited by large kt even though ki, kt << kp

�  Kinetic chain length – ratio of rp to rt. CPE624 FACULTY OF CHEMICAL ENGINEERING

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•++→•+ 343 CHCOCHCHA

�  PSS valid when the concentration of the species is small.

�  In batch/PFR – setting time derivative equal to zero

�  In CSTR - Mass balance equations are developed by assuming steady state, so that PSS of intermediate species is in steady state and concentration is small.

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�  Hence :

0][][][][ 3333 =•−•

=•−•

ττoo COCHCOCHCHCH

233231 ][2][]][[][ •−•+•− CHktCOCHkCHAkAk ppi

][]][[ 3231 •−•= COCHkCHAk pp

23 ][2][ •= CHktAki

t

i

kAkCH2][][ 2

3 =•

2/12/1

3 ][2

][ AkkCHt

i⎟⎟⎠

⎞⎜⎜⎝

⎛=•

τ][][ 44 oCHCH

r−

=

]3][[1 •= CHAkp

2/12/1

1 ][2

][ AkkAkt

ip ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

2/12/3

1 2][ ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

t

ip k

kAk

�  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 rate expression

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CBA +→

XRnRCBRA

RAn

t

i

→•

•++→•+

•→

,, [ ]

[ ][ ][ ] t

i

nRtt

RApp

nAii

Ckr

CCkrCkr

=

=

=

[ ] t

it

nn

Ap

n

tt

i Ckknkr +

⎟⎟⎠

⎞⎜⎜⎝

⎛= 1

1

[ ] effnAeff Ckr =

Generic Chain Reaction

ntni

Ap

nt

tt

inAeff Ck

knkCkr eff

+

⎟⎟⎠

⎞⎜⎜⎝

⎛==

1

1

][][ p

nt

tt

ieff k

knkk

1

⎟⎟⎠

⎞⎜⎜⎝

⎛=

t

ieff n

nn +=1, ,

⎟⎠

⎞⎜⎝

⎛ −=RTEkk o exp

Replacing each k in initiation, propagation and termination with :

Effective activation energy has become :

pt

t

t

ieff E

nE

nEE +−=

Generic Chain Reaction

2][Akkkr pt

i⎟⎟⎠

⎞⎜⎜⎝

⎛=

If ni=nt=1 :

RTE

effot

ieff ekp

kkk

−==

Hence the new effective rate coefficient :

ptieff EEEE +−=

Example 10-1 (Schmidt pg 404) �  Consider the chain reaction in a CSTR:

a)  Write the mass balance equations for A, B, R and X in a CSTR assuming constant density.

b)   What is the overall reaction rate with respect to CA? c)  Find τ for 90% conversion of A in CSTR assuming pseudo

steady state if CA0 = 2 moles/liter, ki = 0.001 sec-1, kp = 20 liter/mole sec and kt = 0.1 sec-1.

d)   What are CR and Cx for this conversion? CPE624 FACULTY OF CHEMICAL ENGINEERING

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XRRCBRA

RA

→

++→+

→

,, [ ]

[ ][ ][ ]Rtt

RApp

Aii

Ckr

CCkrCkr

=

=

=

Exercise in class

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§  Large temperature dependences.

§  Sensitive to trace impurities that can alter the initiation and termination rates

§  Initiators and Scavengers (promoters and poisons) have large influences.

§  Initiators ú  Initiated by adding species I that easily forms radical ú  Initiate the reaction faster than reactant.

§  Scavengers ú  Termination step - radical species decomposed /reacted with other

radical species to form an inactive species X ú  Adding scavengers S ú  X is important in determining overall reaction rate

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SRtsts CCkrXSR =→+ ,

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.

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� 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.

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Wall termination reactions

SRtt CCkrXSRss

=→+ ,

)(, """sbS RRmRtttt CCkCkrr

volarear −==⎟

⎠

⎞⎜⎝

⎛=

DDSkk AhD

mt ==" Mass transfer controlling

mt kvolareak

volareak ** " == Process control by surface

termination

Example Consider the chain reaction in a CSTR:

a)  Write the mass balance equations for A, B, R and X in a CSTR

assuming constant density. b)  What is the overall reaction rate with respect to CA? c)  Find τ for 98% conversion of A in CSTR assuming pseudo

steady state if CA0 = 2 moles/liter, ki = 0.002 sec-1, kp = 10 liter/mole sec and kt = 0.05 sec-1.

d)  What are CR and Cx for this conversion?

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XRRCBRA

RA

→

++→+

→ [ ][ ][ ][ ]Rtt

RApp

Aii

Ckr

CCkrCkr

=

=

=

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(a) Initiation: A → R• ; ri = kiCA

Propagation: A + R• → B + C + R•; ri = kpCA CR Termination: R•→ X; rt = ktCR (b) Overall reaction rate: CR/τ = kiCA – ktCR = 0 ∴ CR = ki/kt x CA ∴ r = kpCACR = kikp/kt CA

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

2 x kt/kikp = [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

Q#1 Test 2– Oct 2012

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�  Fast and exothermic that proceeds by free radical chain reactions

�  Chains reactions, once ignited, process proceeds very quickly and becomes very non-isothermal

�  Release large amounts of energy

�  Applications in the production of power, heat in incineration

�  Involve multiphases: oxidants is air, fuel is liquids/solids

�  Example is oxidation of H2 and alkanes

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� Autooxidation – autocatalytic process and it is an oxidation that converts alkanes into alkyl peroxides.

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ROOHOHR →+− 2

•+→−+•

•→+•

•+•→−

RROOHHROROOORHRHR

RO

,

2

� Lab safety : � Organic chemicals will react with oxygen

in the air at room temperature in chain reactions

� Hence forming organic peroxides (fuel /C & H atoms in the compounds)

� Consequences : spontaneous react, explosion upon shaking or opening the cap

�  Organic peroxide have very exothermic heats of decomposition

�  The reactions can only occur if oxygen is present

�  The reaction depends crucially on the initiation steps, and different molecules have vastly different capabilities of dissociation

�  The initiation step can be photoinduced. If a bottle is sitting in sunlight, UV photons can cause photo dissociation to initiate the chain reaction much faster than in the dark

�  Organic molecule (R-H) where R. could be an alkyl or any fragment containing C, H and O atoms

�  In the presence of O2, this molecule undergo auto oxidation reaction :

�  The chain reactions proceeds at high temperature to break the R-H strong bond (>80 kcal/mole)

ROOHOHR →+− 2

� Consider the chain reaction sequence :

ROOHOHR

RROOHHRROOROOORHCHR

→+−

•+→−+•

•→+•

•+→−

2

2

__________________________,

,, initiation

oxidation

radical transfer

Thermal and chemical autocatalysis

�  Chemical autocatalysis – reactions accelerates chemically such as in enzyme-promoted fermentation, or chain branching reaction

�  Enzyme reaction nearly isothermal but combustion processes are both chain branching and auto thermal

�  Autocatalysis – reactive intermediate or heat can act as catalyst to promote the reaction

�  Catalyst is generated by the reaction , by adding promoters or heat to initiate the and accelerate the process

�  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.

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•+•+•→ OHORROOH

�  Produce two reactive free radicals from one

�  Propagation steps produce more radical species that start with. ie:

The hydroperoxy radical .OOH reacts immediately at high temperature

�  Most combustion reactions involve chain branching

•+•→•→+• OOHOOHOH 2

�  Consider the reaction of :

�  The mechanisms are:

�  derive

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CBA +→

XRRCBRA

RA

→

++→+

→

,,

α

Rtt

RApp

Aii

Ckr

CCkrCkr

=

=

=

Apt

AiR Ckk

CkC)1( −−

=α

�  For α > 1 and CA is large enough and not in SS :

�  If the propagation term is large compares to others:

�  Sample of chain branching reaction : Combustion of Hydrogen to form water

Apt Ckk )1( −= α

ktRR

RApR

eCC

CCkdtdC

ot=

−+=

)(

)1(α

Exercise in Class : Problem 10-16 (Schmidt) pg 440

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�  Chemical industry is the safer industry compare to the risk if you drive on the road

�  Some example of disaster

-Texas City disaster I and II

-Flixborough & Philips polyethylene plane explosion

-Bhopal incident

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References

�  Schmidt, L.D. (2005). The Engineering of Chemical Reactions, 2nd edition, New York: Oxford University Press.

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

�  Levenspiel, O. (1999). Chemical Reaction Engineering, 3rd Edition, New York: John Wiley.

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CBA +→

Aii CkrRA =→ ,A+ R→ B+C +αR , rp = kpC ACR

Rtt CkrXR =→ ,

Apt

AiR Ckk

CkC)1( −−

=α

0)1( =−−+= RtRApAiR CkCCkCkdtdC

α

For linear chain :

t

AiR k

CkC =

Exam Q#1-June 2012

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