L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering...

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L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. [email protected]

Transcript of L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering...

Page 1: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

L 29-Heterogeneous Catalysis and Reactor Design

Prof. K.K.PantDepartment of Chemical Engineering

IIT [email protected]

Page 2: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Diffusion and Reaction in a spherical pellet (Reading assignment: Fogler, Ch 12))

dr

dCD

dr

dycDW A

eA

eAr

0)( 22

rrdr

rWdcA

Ar

0])/([ 22

rrdr

rdrdCDdcA

Ae =r+Δr

Moles = WAr (4 πr2)r

Boundary conditions

-rA=c(-r’A)

r=0, CA finite, r=R, CA=CAS

Molar flux

In – out – disappearance =0 (spherical shell balance)

WAr (4 πr2)r - WAr (4 πr2)r+∆ r - rA’ (4 πr2 c

∆r) =0Dividing by -4 π ∆ r

Page 3: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

consider 1st order

0])/([ 22

rrdr

rdrdCDdcA

Ae

0])/([

12

2

AAe Ckr

dr

rdrdCDd

c(-r’A) =-rA

-rA=kCA

What about n-th order ?

0])/([ 22

n

AnAe Ckr

dr

rdrdCDd

Differentiation &Divide by –r2De

Differentiation &Divide by –r2De

Page 4: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Dimensionless eq. – 1st order

About for n-th order ?

02

2

2

n

Ae

nAA CD

k

dr

dC

rdr

Cd

02 1

2

2

A

e

AA CD

k

dr

dC

rdr

Cd 2212

20

d d

d d

22

2

20n

n

d d

d d

Thiele Module

Thiele Module

eD

Rk 21

e

nAsn

D

CRk 12

Page 5: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Y = , , =>= y/ d/ d = 1/ (dy/d)- y/ 2

d2/ d2 = 1/ (d2y/d2)- 2/ 2 dy/d + 2y/3 Þd2y/d 2 - ø2y=0Þy= A Cosh ø + B Sinh ø ÞA=0 as φ must be finite at the centre, (B. C. =0, coshø 1; and ÞSinh ø 0.And at =1, =1,=> B= 1/Sinh ø

Thus , = CA/CAs = 1/ [Sinh ø / Sinh ø]

2212

20

d d

d d

Page 6: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Thiele Modulus, n

2 n-1 n2 n As n Asn

e e As

k R C k RC "a" surface reaction rateφ = = =

D D [(C -0)/R] "a" diffusion rate

A 1

As 1

C sinhφ λ1ψ = =

C λ sinhφ

• If n is large – internal diffusion limits the overall rate• If n is small – the surface reaction limits the overall rate

Page 7: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Internal Effectiveness Factor

• Internal effectiveness Factor, is: ranged 0 – 1

• for a first-order reaction in a spherical catalyst pellet

As s

Actual overall rate of reactionη =

Rate of reaction that would result if entire

interior surface were exposed to the external

pellet surface conditions C ,T

' "A A A

' "As As As

-r -r -rη = = =

-r -r -r

1 121

3η = φ cothφ -1

φ

Page 8: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Calculation of Catalytic Effectiveness Factor

)1(3 Coth

η = Actual overall rate(RA /Rate in the absence of diffusion resistance (RAs )

Global rate RA = 4 πR2 De (dCA/dr) at r=R

Or RA = 4 πR De (d /d ) at =1

Þ ((d /d )at =1 = (ø cot h ø-1)

ÞRA = 4 πR De CAS (ø cot h ø-1) Global Rate.ÞThus η = [4 πR De CAS (ø cot h ø-1)] / k’ ρc CAS 4/3 πR 3

Þ η = 3 (ø cot h ø-1)/ k’ ρc R2/De RÞ η = 3 (ø cot h ø-1)/ ø2

for ø> 20, η= 3/ ø strong pore diffusion resistance

Page 9: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Calculation of Catalytic Effectiveness Factor

Catalytic Effectiveness Factor:

wheref- Thiele Modulus

1st order reaction rate:

Spherical Pellet

Cylindrical Pellet

Slab Pellet

)313(1 Coth

DekSaRp /

3

DekSaRp /

2

DekSaL p /

Page 10: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Internal Effectiveness Factor

Page 11: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Uses the measured values of the rate of reaction to determine if Internal diffusion controls the rate.

Weisz-Prater Parameter CWP

ηø2 = 3(Ø Coth Ø-1)ηø2 = (observed rate/rate cal. at CAS) x (rate calculated at CAS) / diffusion Rate)

η = (-r’A(obs)/ -r’As

Ø2= -r”AS Sa ρp R2/De CAs = -r’AS ρp R2/De CAs

Weisz – Prater Criterion for internal diffusion

Page 12: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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ÞCWP= (-r’A(obs)/ -r’As )(-r’AS ρp R2/De CAS)

Þ CWP = (-r’A(obs) (ρp R2/De CAS)

Þ These are measured or known terms.

Þ if CWP << 1, No diffusion limitations and no concentration gradient exists in the pellet.

ÞCWP >> 1, Internal diffusion limits the rate.

Page 13: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Non isothermal pellet Energy balance

0])/([ 22

rrdr

rdrdCDdcA

Ae Mass Balance

Energy balance

Page 14: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Non isothermal pellet effectiveness factor

Page 15: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Falsified Kinetics

• Measurement of the apparent reaction order and activation energy results primarily when internal diffusion limitations are present.

• This becomes serious if the catalyst pellet shape and size between lab (apparent) and real reactor (true) regime were Too different.

• Smaller catalyst pellet reduces the diffusion limitation higher activation energy more temperature sensitive

• RUNAWAY REACTION CONDITIONS!!!!

Page 16: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

Falsified Kinetics•With the same rate of production, reaction order and activation energy to be measured (apparent rate)

Page 17: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Overall effectiveness factor (Both internal and external diffusion are important

Page 18: L 29-Heterogeneous Catalysis and Reactor Design Prof. K.K.Pant Department of Chemical Engineering IIT Delhi. kkpant@chemical.iitd.ac.in.

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Overall Effectiveness Factor

At Steady state, Moles transported from bulk fluid to the

external surface of the Catalyst (WAr Ap )= Net Rate of

reaction with in and on the pellet,

MA = WAr Ap = -r”A(As+ Ap),=( Molar Flux x Ext. Surface

Area of pellet)

For a single spherical pellet of Radius R,

AP= 4π R2, and As= SA x mass of pellet,(As >>Ap)

AP = (ext. SA/reactor volume) (reactor volume) = ac ∆V

As= (int. SA/.mass of catalyst) (mass cat./vol. cat) (vol

cat/reactor vol.) . Rect vol.) => AS= SA ρ c (1- ø) ∆V