Diffusion n Adsorption

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PRINCIPLES OFCATALYSIS

Part 1c: Diffusion


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Steps in the Catalytic Reaction

A schematic diagram of a tubular packed bed withcatalyst pellets is shown below:

The overall rate of reaction is equal to the sloweststep in the mechanism (Step 1-7): Physical kinetics

Chemical kinetics (rate of adsorption, rate of desorption,rate of chemical reaction)

Pores

Packed catalyst bed Catalyst pellet Catalyst pellet surface


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STEPS IN A CATALYTIC REACTION (Table Form)

1. Mass transferof the reactant(s) or External Diffusion In from the

bulk fluid to the external surface of the catalyst pellet.

2. Diffusion of the reactant or Internal Diffusion In from the pore

mouth through the catalyst pores to the immediate vicinity of the

internal catalytic surface.

3. Adsorption of reactant A onto the catalyst surface.

4. Reaction on the surface of the catalyst (e.g.,A B)

5. Desorption of product B from the catalyst surface

6. Diffusion of the products or Internal Diffusion Out from the interiorof the pellet to the pore mouth at the external surface.

7. Mass transfer of the products or External Diffusion Out from the

external pellet surface to the bulk fluid.


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Steps in Catalytic Reaction

1. Diffusion of the reactant(s) (e.g., species A) from the bulk fluid to the

external surface of the catalyst pellet

2. Diffusion of the reactant from the pore mouth through the cat. pores to the

immediate vicinity of the internal catalytic surface

3. Adsorption of reactant onto the catalyst surface

4. Reaction on the surface of the catalyst (e.g., A B)

5. Desorption of the product

6. Diffusion of the products from the interior of the pellet to the pore mouth atthe external surface

7. Diffusion of the products from the external pellet surface to the bulk fluid

62

A

B

2

B

7

53

A

1

6

External

diffusion

Internal

diffusion

Catalytic

surface

4

A B

A

B


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Steps in the catalytic reaction can be dividedinto two categories:

Diffusion steps (1, 2, 6, and 7 in table in the next

slide)

Reaction steps (3, 4, and 5)

The overall process can be broken down into

sequence of individual steps.


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Types of Adsorption

Types of

Adsorption

Characteristic

Physical adsorption(physisorption)

Unselective, low energy of adsorption.

Extent of adsorption related to boiling point ofgas, not nature of solid surface.

No breaking of bonds in molecules andnegligible changes in bond energies.

Associative

chemicaladsorption

(chemisorption)

Selective, strongly dependent on both gas and

solid surface.Higher energies of adsorption than those ofphysisorption.

Bonds in the adsorbed molecules are changedin strength but not broken, i.e. moleculesadsorbed whole molecular fragments

Dissociativechemical

adsorption

(chemisorption)

Selective, strongly dependent on both gas andsolid surface.

Higher energies of adsorption than those ofphysisorption.

Bonds are in the adsorbed molecules arebroken, i.e. molecules adsorbed as two or more

molecular fragments


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C - O

C - O

C O

C

O

C O

Increasing interaction with metal surface

Molecule

approaches

surface

Physical

adsorption

Associative

chemisorption

Dissociative

chemisorption

Reaction and

adsorption

Types of Adsorption (contd)

Representation of adsorption, and possible subsequent reaction of CO onvarious solid surfaces

Example: CO adsorption on Al2O3 ,Bu ,Ni

Associative Chemisorption: CO + 3H2 CH4 +H2OCO + H2 CH3OHCu

Dissociative Chemisorption: CO C + ONi


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Reaction Steps

Example:The decomposition of cumene to form benzene and

propylene.

C6H5CH(CH3)2 C6H6 + C3H6


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Reaction Steps (Adsorption)STEP 3

The catalytic mechanism extends beyond the surface to involvephysical diffusion to & inside the particle leading to the following:

Adsorption on the surface:

kads Chemisorption

Results from chemical bonds between the molecule (adsorbate-reactant/product) and the solid surface (adsorbent-catalyst)

Very specific because receptive sites for chemisorption must exist

Physical adsorption Comes from Van der Waals forces & physical in origin

Weaker than chemisorption & not specific Adsorption on the catalyst surface:

rate of adsorption = rateattachment ratedetachment= kadsf(reactant,products)

kads = adsorption equilibrium constant

R ti St (S f R ti )


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Reaction Steps (Surface Reaction)VARIOUS TYPES OF KINETIC MODELS

Single siteA S B S

Dual site (Langmuir-Hinshelwood kinetics):

1. A S + B S C S + D S

1. A S + B S C S + D S

Eley Rideal

A S + B(g) C S + D(g)

A B C D

B A C D

A C DB

A B


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R(g) + OL P + and + O2

OL

OL = Lattice oxygen

Mechanistic Transformation at The Surface of Catalyst


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Steps in the Catalytic Reaction (4)

The catalytic mechanism extends beyond the surface toinvolve physical diffusion to & inside the particle leading to

the following: (cont.)

SURFACE REACTION: ks

Single site (A S B S)A B


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Reaction Step 5 (Desorption)

The catalytic mechanism extends beyond thesurface to involve physical diffusion to & inside

the particle leading to the following: (cont.)

Desorption of product/sB S B + S

Rate of desorption = -rate of adsorption

B B


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Diffusion Steps (1 & 7) (External)

The catalytic mechanism extends beyond the surface to

involve physical diffusion to & inside the particle leadingto the following:

External Diffusion of Molecule A:

k ext.diff. = kg Sext.

Motion of A through the fluid outside the particle is governed byexternal or bulk diffusion or mass transfer diffusion

Decreasing particle diameter/size, density & viscosity result inan increase in the external diffusion rate


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Diffusion Step (External)

Ficks first law of diffusion:

In term of molar flux of species A:

AoffractionmoleyBinAofydiffusivitD

ionconcentrattotalc

AspeciesoffluxdiffusivemolarJ

cD-J

A

AB

A

yABA A

BoffluxmolarW

AoffluxmolarW

)W(WyJW

B

A

BAAAA


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Diffusion Steps 6 & 7 (External)

Types of molar flux

1. Equimolar Counterdiffusion

2. Dilute concentration

When the mole fraction of the diffusing solute and the bulkmotion in the direction of the diffusion are small. Then,

A B

A B

C-DW-W AABBA

C-DJWAABAA


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Diffusion Steps 6 & 7 (External)

Types of molar flux

3. Diffusion Through a Stagnant Gas

The diffusion of a solute A through a stagnant gas B oftenoccurs in systems in which two phases are present. If gas B isstagnant, there is no net flux of B with respect to a fixedcoordinate: that is,

WB = 0then,

4. Forced Convection

Wyy-cDW AAAABA

JAZ

JAx

AofionConcentratC

areanalCrossectioA

velocityTerminalV

flowbulkB

CAVCBW

A

c

z

AZ

A

C

zAAZA


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Diffusion Steps 2 & 6 (Internal)

Overview of the internal diffusion

Porous

catalyst pellet External

surface

Internal

diffusion

External

diffusion

A

A B

A

External

diffusion

B B


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Diffusion Step (Internal)

The catalytic mechanism extends beyond the surface to

involve physical diffusion to & inside the particle leadingto the following: (cont)

Internal Pore Diffusion:

k int.diff. = ks Sint.h

Second step in the mechanism is diffusion into the poresleading to the reacting surface sites

Resistance to this diffusion is through collisions either withother molecules (bulk diffusion) or with the walls of the pore(Knudsen Diffusion)

Rates of pore diffusion-controlled reactions can be increasedby decreasing the particle radius or increasing the diffusivity

(by increasing the pore radius)


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External Diffusion

Diffusion of the reactants and products between the bulk fluid and the external

surface of the catalyst. An essential condition for successful kinetic

measurements is to ensure that the reaction is free of mass transfer limitations

(external and internal diffusion)

Detecting a limitation in ExternalDiffusion

conversion

Limitation by

external diffusion

No limitation from

externaldiffusion

v 2v 3v 4v

F1

G1

F2

G2

F3G3

F4

G4 conversion

5v

F

G

5F

5G

v

Limitation by

external diffusion

No limitation by

external diffusion

Two diagnostic tests to indicate if a reaction is limited by external diffusion (a) if the flow rate is

increased proportionately to the catalyst volume, so that the space velocity is constant as the mass flow

increases; a constant conversion indicates no limitation by external diffusion. (b) if plots conversion

versus contact time for two markedly different catalyst volumes are compared, superimposable curves

indicate no limitation by external diffusion

(a) (b)


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Internal Diffusion

Diffusion of the reactants or products from the external pellet surface (pore mouth)

to the interior of the pellet

Detecting a limitation in InternalDiffusion

dp/4dp/3dp/2

conversion

Limited by internal

diffusion

Chemical

kinetic control

dp

F

G

F

G

FG

F

G

dp

Experiment to find out whether reaction kinetics or internal diffusion limits a conversion.

Maintain constant all operating variables (volumetric gas flow, space velocity, contact time,

reaction temperature, inlet gas composition, and catalyst volume) as the particle sizes of the

catalyst are progressively varied, as dp, dp/2, dp/3, and dp/4. Then plot conversion against particle

size; and if the conversion varies, internal diffusion is limiting, whereas a constant conversion

indicates limitations of reaction kinetics only


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- Reaction takes place only on the catalyst and not in the fluid surrounding it

- The fluid velocity in the vicinity of the spherical pellet will very with position around the

sphere

As illustrated, the change in concentration of A from CAb to CAs takes place in a very narrow fluid

layer next to the surface of the sphere

- At low velocities the mass transfer boundary layer thickness is large and diffusion

limits the reaction

-As the velocity past the sphere is increased, the boundary layer thickness decreases and

the mass transfer across the boundary layer no longer limits the rate of reaction

- Reaction-limiting conditions can be achieved by using very small particles, but the

smaller particle size, the greater the pressure drops in a packed bed.

Phenomena of Diffusion

The flow of gas

Boundary

layer

Catalyst

pellet

CAb

CAs


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Rate-controlling

When heterogeneous reactions are carried out at steady state, the

rates of each of the three reaction steps in series (adsorption, surface

reaction, and desorption) are equal to one another. However, oneparticular step in the series is usually found to be rate-limitingor

rate-controlling.

0

1

2

3

4

5

6

0 1 2 3 4 5 6

initial concentration of reactant

initialrate

Adsorption-limited reaction

0

0 . 0 5

0. 1

0 . 1 5

0. 2

0 . 2 5

0. 3

0 . 3 5

0. 4

0 . 0 9 2 . 0 9 4 . 0 9 6 . 0 9 8 . 0 9 10 . 0 9 12 . 0 9


initialrate

Surface-reaction-limited

0

0. 5

1

1.5

2

2. 5

3

3. 5

0 1 2 3 4 5 6


initialrate

Desorption-limited reaction


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External DiffusionExample

For NRE = 1000 for NRE = 10

Mass transfer factor Mass transfer factor

= 0.57 X (1000) = 0.84 (10)

= 0.03 = 0.25

When does NRE become small, < 50

NRE = 2R . G liner mass velocity

Increase particle size, NRE

Increase linear mass velocity NRE

To circumvent this in the LAB

1. Make catalyst chips2. Feed + diluent (ballast)

How to check for external diffusion

- Vary catalyst bed volume

-0.41 -0.51


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DETECTING A LIMITATION IN EXTERNAL DIFFUSION

Test 1

V 2V3V 4V

G = mass flow of reacting gas, vary

= constant catalyst pellet-diameter ( const. int. diffusion)

Limitaton by externaldiffusion

No limitation from

external diffusion

IF FLOW RATE IS INCREASED PROPORTIONATELY TO THE CATALYST OLUME, SO THAT

SPACE VELOCITY IS CONSTANT (LHSV = FO ) AS THE MASS FLOW INCREASES, THEN

CONSTANT CONVERSION = NO LIMITATION

Flow rateFo

Conv

ersion

C F1

G1

2F1

2G1

3F1

3G1

4F1

4G1

G


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1.8.2 Internal Pore Diffusion

The second step in reaction mechanism is diffusion ino the catalyst pores

leading to the reacting surface sites. Resistance to this diffusion isthrough collisions either with

1. Other molecules (bulk diffusion), DB or

2. The walls of the pore (Knudsen diffusion) DK

DB=T /PT Bulk Diffusion, DB Eqn 6

DK = T TP Knudsen Diffusion, DK Eqn 7

Where

T = temperature

PT = total pressure

TP = radius of the pore

Usually DB and DK are combined

Dave = DB DK

DB + DK Eqn 8

3/2

1/2


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And corrected for particle porosity, and tortuosiity of the pores

Eeff= Dave Eqn 9

Porosity is measurable but is difficult to characterize. As an approximation

= 1/0 Eqn 1

Is useful. If not known, sufficient accuracy is achieved by the approximation that =

0.5. thus it is good enough to assume

Deff = (0.25) D ave Eqn 11

For simple nth order irreversible reactions models for diffusion-reaction lead to

the relationship


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Diffusion n Adsorption

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