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L -30 Diffusion Effects in catalyst:

effectiveness factor

Prof. K.K.Pant

Department of Chemical EngineeringIIT Delhi.

kkpant@chemical.iitd.ac.in

mailto:kkpant@chemical.iitd.ac.inmailto:kkpant@chemical.iitd.ac.in

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2

For nthorder reaction

= ( 2/n+1 )

1/2

3/= R( k CASn-1/ De)

1/2

OR

2= R2kSap CASn-1/De

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Falsified Kinetics

Measurement of the apparentreaction orderand activation energy results primarily wheninternal diffusion limitations are present.

This becomes serious if the catalyst pelletshape and size between lab (apparent) andreal reactor (true) regime are too different.

Smaller catalyst pelletreduces the diffusion

limitationhigher activation energy (kinetics)more temperature sensitive

RUNAWAY REACTION CONDITIONS!!!!

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Falsified Kinetics

With the same rate of production, reaction order

and activation energy to be measured

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5

Determination of apparent order of reaction

For large value of Thiele modulus

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6

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7

Apparent order of reaction n = (ntrue+1 )/2

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Non isothermal pellet Energy balance

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Non isothermal pellet effectiveness factor

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11

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12

Slove for Cas, Conc at pellet

Surface

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Overall rate in terms of

bulk concentration

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Overall effectiveness factor and rate of reaction for a first order reaction

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Rate of reaction, -rA

= (Actual overall rate of reaction) divided by(rate that would result if the entire surface

were exposed to the bulk conditions, CAb,Ts)

"

1 a b c c

" " "A Ab 1 Ab

' " "

A A b A a b 1 Ab a b

=1+k S /k a

-r = (-r ) = k C

-r = -r = -r S = k C S

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Mass transfer and reaction in a

packed bed

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'AzA b

AbAz AB Ab

2'Ab Ab

AB A b2

dW- +r = 0

dz

where

dCW = -D +C U and

dz

U = superficial velocity

hence

d C dCD -U +r = 0

dz dz

Mole balance in flux form, where Acis

constant and FA= AcWAz =ACU CA

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Mass Balance in a Packed bed (Mass Transfer

control)

FAzFAZ+Z - (-rA) a Ac z = 0

A= surface area per unit volume, U superfecial

velocity.

U dCA/ dz = - kcCA ac

. CA= CA0exp (- kcac z/U)

Or ln (1-X) = ( -kc az/U)

0.0)()( iSGiccGiG CCakdz

dCU

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Catalytic Fixed-Bed Reactor - Design Model

Mass Balance around the catalyst

Gas-Phase component mass balance (Plug Flow model)

Gas-Phase component mass balance (Dispersion model)

Energy Model

inetSGicc RiCCak )()()(

0.0)()( iSGiccGiG CCakdzdCU

0.0)()(2

2

iSGiccGi

GGi

G CCak

dz

dCU

zd

CdiD

)()( TaTUAjHRjdzdTCpU RGGG

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Overall Rate with in the pellet (-rA= (rAb)

For first order reaction : (-rAb;= (rAb)Sa= ksSa CAb

=>(-rA)= (rAb) = Sabk CAb

2

2

0s b bAb AbA

d C dC Da U k SaC

dz dz

Neglecting Axial Dispersion

( )s aAb

AbdC k S

Cdz U

=> CAb= CAb0 exp(- Sa bks Z/U)

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Axial diffusion, can be neglected when

FAis very large

so

Finally, the conversion for

1storder reaction in PBR is

'

0 p A b p

a 0 Ab

U d -r d>>

D U C

2Ab

a 2

d CDdz

"

Ab b aAb

dC k S= - C

dz U

Remember the

forced

convection in

binary external

diffusion, JAisalso neglected

b a-( k"S L)/UAb

Ab0

CX = 1- = 1- e

C

Mass transfer and reaction in a packed bed

cont.

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Determination of limiting situation from

reaction data

Type ofLimitation

Variation of Reaction Rate with:

Velocity

Particle

Size TemperatureExternaldiffusion

U (dp)-3/2

Rate= kcac CA

Linear

InternalDiffusion Independent (dp)-1 Exponential

SurfaceDiffusion

Independent

Independent

Exponential