CRE II L20-21

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L -21 External Mass Transfer

Effects

Prof. K.K.Pant

Department of Chemical EngineeringIIT Delhi.

[email protected]
mailto:[email protected]:[email protected]

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Thermofer Catalytic cracking unit (MBR,Used for reactions with moderate

decay)

Fresh/regenerated catalyst enters from top

of reactor=> gets coked as moves down

and exits in a furnace where air is uded toburn off carbon (C+ O2-CO2 )

Catalyst pellet size ~ 1/8 in inch in dia)

CATALYST DEACTIVATION

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L -21 External Mass Transfer

Effects

Prof. K.K.Pant

Department of Chemical EngineeringIIT Delhi.

[email protected]
mailto:[email protected]:[email protected]

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Thermofer Catalytic cracking unit (MBR,Used for reactions with moderate

decay)

Fresh/regenerated catalyst enters from top

of reactor=> gets coked as moves down

and exits in a furnace where air is uded toburn off carbon (C+ O2-CO2 )

Catalyst pellet size ~ 1/8 in inch in dia)

CATALYST DEACTIVATION

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Ist Order deactivation

IInd order Rate

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Straight through Transport Reactor

(Circulating Fluidized bed reactor)

Used when deactivation is rapid.Used for production of gasoline

Catalyst pellet and feed enter

together and transported rapidly.Bulk density of the catalyst is low

compared to Moving bed.

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STTR : Used when coking is rapid.

Bulk density of catalyst is smaller than

MBR. Particle velocity = gas velocity.

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Mole balance

rA= brA

Or

Z= Height (m),and Up is velocity of catalyst

(m/s)

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a

1 R 1= ln +T E Ta o

Temperature/Time Trajectories

A control strategy involves maintaining a constant

conversion with catalyst decay by increasing

operating temperature.

develop a temperature/time trajectory to find T -t

relationship: How T should increase with time.

-rA (t=0,T0) = -rA (t= t,T) = a(t ,T)[-rA (t=0,T) ]

k T a T,t = ko

E1 1a -

R T To

k e a = ko o

Arrhenius type T dependence

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a

0

E1 1d -

R T Tda o n

r = - = k ed ddt

decay law is:

a

Ed- lnaE

da a n- = k e

ddt o

a

E

dn-Ea

= kdo

a

1 R 1= ln +

T E Ta o

Substitute T value

Integrate with a=1 at t=0

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1- n+ E Ead1- at =

k 1-n+ E Ead d

o

a

1 R 1= ln +T E T

a o

E 1 1a -R T T

oa = e

E -n E +Ea a 1 1d -R T T

o1-e

=E

dk 1-n+d

Eo a

aa

E

d-n+E

a tda = -k dt1 0d

o

Ed-n 1

Ea

For

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13

External Diffusion effects in Heterogeneous Reactions

TWO TYPES of Diffusion Resistance

1. External diffusion

2. Internal Diffusion

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14

Mass Transfer FundamentalsDiffusion : Spontaneous intermingling or mixing of Atoms or molecules

by random thermal motion.

Gives rise to motion of the species relative to motion of mixtures.

WA or NA= Molar flux of A relative to a fixed coordinates (Vector)

Molar flux of A = Diffusive flux (J A) + Convective flux (BA)(in direction of concn. Gradient)

BA = CAV due to bulk fluid motin, V = Molar average velocity , V= yivi

For Binary system

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Or

For Equi molar Counter Diffusion (EMCD): WA= -WB

EMCD

Ficks Law of diffusion

B d C diti

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Boundary Conditions

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For Equi molar counter diffusion

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Ist Order deactivation

IInd order Rate

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Straight through Transport Reactor

(Circulating Fluidized bed reactor)

Used when deactivation is rapid.

Used for production of gasoline

Catalyst pellet and feed enter

together and transported rapidly.Bulk density of the catalyst is low

compared to Moving bed.

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STTR : Used when coking is rapid.

Bulk density of catalyst is smaller than

MBR. Particle velocity = gas velocity.

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a

1 R 1= ln +T E Ta o


A control strategy involves maintaining a constant

conversion with catalyst decay by increasingoperating temperature.

develop a temperature/time trajectory to find T -t

relationship: How T should increase with time.

-rA (t=0,T0) = -rA (t= t,T) = a(t ,T)[-rA (t=0,T) ]

k T a T,t = ko

E

1 1a -R T To

k e a = ko o

Arrhenius type T dependence

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a

0

E1 1d -

R T Tda o n

r = - = k ed ddt

decay law is:

a

Ed- lnaE

da a n- = k e

ddt o

a

E

dn-Ea

= kdo

a

1 R 1= ln +

T E Ta o

Substitute T value

Integrate with a=1 at t=0

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1- n+ E Ead1- at =

k 1-n+ E Ead do

a

1 R 1= ln +

T E Ta o

E 1 1a -R T T

oa = e

E -n E +Ea a 1 1d -R T T

o1-e

=E

dk 1-n+d

Eo a

aa

E

d-n+Ea t

da = -k dt1 0do

Ed-n 1

Ea

For

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26

External Diffusion effects in Heterogeneous Reactions

TWO TYPES of Diffusion Resistance

1. External diffusion

2. Internal Diffusion

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Mass Transfer FundamentalsDiffusion : Spontaneous intermingling or mixing of Atoms or molecules

by random thermal motion.

Gives rise to motion of the species relative to motion of mixtures.

WA or NA= Molar flux of A relative to a fixed coordinates (Vector)

Molar flux of A = Diffusive flux (J A) + Convective flux (BA)(in direction of concn. Gradient)

BA = CAV due to bulk fluid motin, V = Molar average velocity , V= yivi

For Binary system

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Or

For Equi molar Counter Diffusion (EMCD): WA= -WB

EMCD

Ficks Law of diffusion

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Boundary Conditions

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Boundary Conditions

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For Equi molar counter diffusion

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32Solve for concentration profile CAvs z

=>

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Diffusion through Stagnant Gas (Evaporation or

gas absorption)

Gas B is stagnant then there is no net flux of B

with respect to a fixed coordinate.

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External mass transfer / boundary layer

Diffusion through a film to a catalyst particle

CAb= concn of gas A at the ext. boundary of gas film B (dilute gas)

Cas = at the external cat surface

Correlation for mass transfer for flow around a

spherical pellet

Frossling correlation

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Boundary layer around a catalyst pellet

External Resistance to Mass Transfer

Diffusion and Reaction

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Isomerisation Reaction

Diffusion and reaction

LHHW surface

reaction

For weak adsorption or at high T,

=>

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For rapid reaction : sp. reaction rate constant is much greater than mass

transfer coefficient

For slow reaction

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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

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Diffusion and Reaction in a Porous Catalyst

c

D p cD =e

where

Actual distance a molecule travels btw 2 points = tortousity =

Shortest distance btw 2 points

Volume of void space = pellet porosity =p

Total volume(voids and solids)

= Constriction factor,c f( )

Effective Diffusivity: Bulk diffusion ( Large pore)and

Knudsen diffusion(small pore) Dk(cm2/s)=9.7 *103r (cm) (TK/M)

1/2

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Effective Diffusivity: Pores are not straight cylindrical.

These are a series of Tortuous, interconnecting paths of

varying cross sectional area.

Pellet porosity = volume of void space/ total volume

(voids and solids)

Constriction factor , ( )accounts for the variation in thecross sectional area that is normal to the diffusion. It is a

function of the ratio of maximum to minimum pore areas

().

= f(), =1 if =1. =0.5 if = 10. Typical value=0.8.

tortuosity,t = 3.0

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Derivation of the Differential Equation

~ Diffusion and Reaction in a spherical pellet

dr

dCD

dr

dycDW Ae

AeAr

0)( 22 rr

dr

rWdcA

Ar

0])/([ 22

rrdrrdrdCDd cAAe

=r+r

Moles = WAr(4 r2)r

Boundary

conditions

Order of

reaction?-rA=c(-rA)

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

Molar flux

Inoutdisappearance =0

WAr(4 r2)r - WAr(4 r

2)r+ r - rA (4 r2c

r) =0

Dividing by -4 r

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Lets simply consider 1storder

0])/([ 22

rrdr

rdrdCDdcA

Ae

0])/([ 122

AAe CkrdrrdrdCDd

c(-rA)=-rA volumetric

-rA=kCA

What about n-th order ?

0])/([ 2

2

n

AnAe Ckr

dr

rdrdCDd

Differentiation &

Divide byr2De

Differentiation &

Divide byr2De

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Lets simply consider 1storder

What about n-th order ?

02

2

2

n

A

e

nAA CD

k

dr

dC

rdr

Cd

02 12

2

A

e

AAC

D

k

dr

dC

rdr

Cd

Di i l F f th E ti

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Dimensionless Form of the Equation

Dimensionless symbol was normally introduced to

Reduce complexity in equation

Simplify operation of calculation Scale-up the reactor

Let = CA/CAs and =r/R

dCA/dr= (dCA/d)(d/dr)= (d/d)(dCA/d

)x

(d/dr)

=> dCA/dr = (d/d)(CAS/R)d2CA/dr

2= d/dr(dCA/dr)= (d2/d2)(CAS/R2)

When

CA=CAsat r=R, =1 and =1

CA=finite at r=0, =finite and =0

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Dimensionless eq.1storder

About for n-th order ?

0

22

2

n

A

e

nAA

CD

k

dr

dC

rdr

Cd

02 1

2

2

A

e

AAC

D

k

dr

dC

rdr

Cd0

2 212

2

dr

d

rd

d

0

2 22

2

n

ndr

d

rd

d

Thiele

Module

Thiele

Module

eDRk 2

1

e

n

Asn

D

CRk 12

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Thiele Modulus, n

2 n-1 n

2 n As n Asn

e e As

k R C k RC "a" surface reaction rate = = =D D [(C -0)/R] "a" diffusion rate

A 1

As 1

C sinh 1 = =

C sinh

If n is largeinternal diffusion limits the

overall rate

If n is smallthe surface reaction limits theoverall rate

y=

d2y/d 2- 2y=0

y= A Cosh + B Sinh

A=0 as must be finite

at the centre

(B. C =0, cos h 1;

1/ , and Sinh 0.

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Calculation of Catalytic Effectiveness FactorCatalytic Effectiveness Factor:

where

- Thiele Modulus

1storder reaction rate:

Spherical Pellet

Cylindrical Pellet

Slab Pellet

)313(1

Coth

DekSaR p/3

DekSa

Rp

/2

DekSaL p/

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Internal Effectiveness Factor

InternaleffectivenessFactor, is:ranged 01

for a first-orderreaction in aspherical catalystpellet

As s

Actual overall rate of reaction

= 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 -r = = =

-r -r -r

1 121

3 = coth -1

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Internal Effectiveness Factor

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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 pellet

shape and size between lab (apparent) andreal reactor (true) regime were Too different.

Smaller catalyst pelletreduces the diffusion

limitationhigher activation energy moretemperature sensitive

RUNAWAY REACTION CONDITIONS!!!!

F l ifi d Ki i

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Falsified Kinetics

Apostrophe/ prime sign denotes the

apparent parameter vice versa

With the same rate of production, reaction

order and activation energy to be measured

R t f ti

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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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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

2

Aba 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.

Determination of limiting situation from

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Determination of limiting situation from

reaction data

Type ofLimitation

Variation of Reaction Rate with:

Velocity

Particle

Size TemperatureExternaldiffusion

U (dp)-1/2 Linear

InternalDiffusion Independent (dp)-1 Exponential

SurfaceDiffusion

IndependentIndepende

ntExponential

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CRE II L20-21