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CHAPTER 1 (Lecture Note Part 1) CATALYTIC REACTION AND MASS TRANSFER

Chapter 1 Lecture Note Part 1

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Page 1: Chapter 1 Lecture Note Part 1

CHAPTER 1(Lecture Note Part 1)

CATALYTIC REACTION AND

MASS TRANSFER

Page 2: Chapter 1 Lecture Note Part 1

Subtopic covered in Chapter 1… Catalytic Reactions and Reactors

Surface and Enzyme Reaction Rates

Introduction of Porous Catalyst

Transport and Reaction

External Mass Transfer

Pore Diffusion

Catalytic Wall Reaction

Langmuir-Hinshelwood Kinetic Mechanism

Temperature Dependence of Catalytic Reaction Rates

Application of Reaction Engineering in MicroelectronicFabrication

Catalyst Deactivation

Page 3: Chapter 1 Lecture Note Part 1

CATALYST-DEFINITION

• A catalyst is a substance that affects the rate of a reaction but emerges from the process unchanged.

• A catalyst usually changes a reaction rate by promoting a different molecular path ("mechanism") for the reaction.

• Catalyst affect yield and selectivity• Changes only the rate of reaction; it does not

affect the equlibrium.

Page 4: Chapter 1 Lecture Note Part 1

CATALYST-EXAMPLE

• Example- H2 and O2 to form water; with Platinum as catalyst

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Basis of Catalysis

WITHOUT A CATALYST WITH A CATALYST

A catalyst lower the activation barrier for a transformation, by

introducing a new reaction pathway

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Three key aspects of catalyst action

taking part in the reaction

• it will change itself during the process by interacting withother reactant/product molecules

altering the rates of reactions

• in most cases the rates of reactions are increased by theaction of catalysts; however, in some situations the rates ofundesired reactions are selectively suppressed

Returning to its original form

•After reaction cycles a catalyst with exactly the samenature is ‘reborn’

• In practice a catalyst has its lifespan - it deactivatesgradually during use

CH4003 Lecture Notes 11 (Erzeng Xue)

Page 7: Chapter 1 Lecture Note Part 1

Catalysis is the increase in the rate of achemical reaction due to the participationof an additional substance called acatalyst.

also….

Catalysis is the occurrence, study, and use of catalystsand catalytic processes.

What is Catalysis

CH4003 Lecture Notes 11 (Erzeng Xue)

Page 8: Chapter 1 Lecture Note Part 1

• The types of catalysts

– Classification based on the its physical state, a catalyst can be

• gas

• liquid

• solid

– Classification based on the substances from which a catalyst is made

• Inorganic (gases, metals, metal oxides, inorganic acids, bases etc.)

• Organic (organic acids, enzymes etc.)

– Classification based on the ways catalysts work

• Homogeneous - both catalyst and all reactants/products are in the same phase (gas or liq)

• Heterogeneous - reaction system involves multi-phase (catalysts + reactants/products)

– Classification based on the catalysts’ action

• Acid-base catalysts

• Enzymatic

• Photocatalysis

• Electrocatalysis, etc.

Types of Catalysts & Catalytic Reactions

CH4003 Lecture Notes 11 (Erzeng Xue)

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Role of Catalysis in a National Economy

• 24% of GDP from Products made using catalysts(Food, Fuels, Clothes, Polymers, Drug, Agro-chemicals)

• > 90 % of petro refining & petrochemicals processesuse catalysts

• 90 % of processes & 60 % of products in the chemicalindustry

• > 95% of pollution control technologies

• Catalysis in the production/use of alternate fuels(NG,DME, H2, Fuel Cells, biofuels…)

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Advantages of catalytic processes...

– Achieving better process economics and productivity

• Increase reaction rates - fast

• Simplify the reaction steps - low investment cost

• Carry out reaction under mild conditions (e.g. low T, P) - low energy consumption

– Reducing wastes

• Improving selectivity toward desired products - less raw materials required, less unwanted wastes

• Replacing harmful/toxic materials with readily available ones

– Producing certain products that may not be possible without catalysts

– Having better control of process (safety, flexible etc.)

– Encouraging application and advancement of new technologies and materials

– And many more …

CH4003 Lecture Notes 11 (Erzeng Xue)

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11

• Research in catalysis involve a multi-discipline approach

– Reaction kinetics and mechanism

• Reaction paths, intermediate formation & action, interpretation of results obtained under various conditions, generalising reaction types & schemes, predict catalyst performance…

– Catalyst development

• Material synthesis, structure properties, catalyst stability, compatibility…

– Analysis techniques

• Detection limits in terms of dimension of time & size and under extreme conditions (T, P) and accuracy of measurements, microscopic techniques, sample preparation techniques…

– Reaction modelling

• Elementary reactions and rates, quantum mechanics/chemistry, physical chemistry …

– Reactor modelling

• Mathematical interpretation and representation, the numerical method, micro-kinetics, structure and efficiency of heat and mass transfer in relation to reactor design …

– Catalytic process

• Heat and mass transfers, energy balance and efficiency of process …

Research in CatalysisCatalysis & Catalysts

CH4003 Lecture Notes 11 (Erzeng Xue)

Page 12: Chapter 1 Lecture Note Part 1

Some Developments in Industrial catalysis-11900- 1920s

Industrial Process Catalyst

1900s: CO + 3H2 CH4 + H2O Ni

Vegetable Oil + H2 butter/margarine Ni

1910s: Coal Liquefaction Ni

N2 + 3H2 2NH3 Fe/K

NH3 NO NO2 HNO3 Pt

1920s: CO + 2H2 CH3OH (HP) (ZnCr)oxide

Fischer-Tropsch synthesis Co,Fe

SO2 SO3 H2SO4 V2O5

Page 13: Chapter 1 Lecture Note Part 1

Industrial catalysis-3 1950s

C2H4 Polyethylene(Z-N) Ti

C2H4 Polyethylene(Phillips) Cr-SiO2

Polyprop &Polybutadiene(Z-N) Ti

Steam reforming Ni-K- Al2O3

HDS, HDT of naphtha (Co-Mo)/Al2O3

C10H8 Phthalic anhydride (V,Mo)oxide

C6H6 C6H12 (Ni)

C6H11OH C6H10O (Cu)

C7H8+ H2 C6H6 +CH4 (Ni-SiAl)

Page 14: Chapter 1 Lecture Note Part 1

Xylene Isom( for p-xylene) H-ZSM-5

Methanol (low press) Cu-Zn/Al2O3

Toluene to benzene and xylenes H-ZSM-5

Catalytic dewaxing H-ZSM-5

Autoexhaust catalyst Pt-Pd-Rh on oxide

Hydroisomerisation Pt-zeolite

SCR of NO(NH3) V/ Ti

MTBE acidic ion exchange resin

C7H8+C9H12 C6H6 +C8H10 Pt-Mordenite

Industrial catalysis-5 1970s

Page 15: Chapter 1 Lecture Note Part 1

Industrial catalysis-8 2000+

• Solid catalysts for biodiesel

- solid acids, Hydroisom catalysts

• Catalysts for carbon nanotubes

- Fe (Ni)-Mo-SiO2

For Developed Catalysts MAINLY IMPROVEMENT IN PERFORMANCE by New Synthesis Methods & use of PROMOTERS

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Promoters

• Substances which themselves are not catalysts, but whenmixed in small quantities with the catalysts increase theirefficiency are called as promoters or activators.

• (i) For example, in Haber’s process for the synthesis ofammonia, traces of molybdenum increases the activity offinely divided iron which acts as a catalyst.

• (ii) In the manufacture of methyl alcohol from water gas ,chromic oxide is used as a promoter with the catalyst zincoxide .

http://www.emedicalprep.com

Page 18: Chapter 1 Lecture Note Part 1

Explanation of Promotion Action

1. Change of Lattice Space: The lattice spacing of the

catalyst is changed thus enhancing the spacing

between the catalyst particles. The adsorbed

molecules of the reactant are further weakened and

cleaved. This makes the reaction go faster.

2. Increase in peaks and cracks: Promoters increase the

peaks and cracks on the surface of the catalyst

thereby increasing the concentration of reactant

molecules and hence the rate of reaction.

Page 19: Chapter 1 Lecture Note Part 1

Catalytic Poisons

A substance which destroys the activity of the catalyst to

accelerate a reaction, is called a poison and the process is

called Catalytic Poisoning.

(i) For example, the presence of traces of arsenious oxide in the reacting gases

reduces the activity of platinized asbestos which is used as catalyst in

contact process for the manufacture of sulphuric acid.

(ii) The activity of iron catalyst is destroyed by the presence of H2S or CO in

the synthesis of ammonia by Haber’s process.

(iii) The platinum catalyst used in the oxidation of hydrogen is poisoned

by CO.

Page 20: Chapter 1 Lecture Note Part 1

Explanation of Catalytic Poisoning

1. The poison is adsorbed on the catalyst surface in

preference to the reactants.

2. The catalyst may combine chemically with the

impurity.

Fe + H2S FeS + H2

Page 21: Chapter 1 Lecture Note Part 1

Auto CatalysisWhen one of the products of a reaction itself acts as a

catalyst for that reaction the phenomenon is calledautocatalysis.

Examples of autocatalysis: -

(a) Hydrolysis of an ester

CH3COC2H5 + H2O CH3COOH + C2H5OH

Here CH3COOH is acting as a catalyst.

Page 22: Chapter 1 Lecture Note Part 1

Negative Catalysis/ INHIBITORS

• When a catalyst reduces the rate of reaction, it iscalled a Negative catalyst or Inhibitor.

• A negative catalyst is used to slow down or stopaltogether an unwanted reaction.

• Inhibition should be distinguished from catalystpoisoning. An inhibitor only hinders the working ofa catalyst without changing it, whilst in catalystpoisoning the catalyst undergoes a chemicalreaction that is irreversible in the environment inquestion (the active catalyst may only be regained bya separate process).

Page 23: Chapter 1 Lecture Note Part 1

Classification of catalytic processes

There are two types of catalytic processes: -

1. Homogeneous catalysis

2. Heterogeneous catalysis

These two processes have industrial importance.

There is another mechanism involving catalysis i.e.

enzyme catalysis which possess biological

importance.

Page 24: Chapter 1 Lecture Note Part 1

In solution with at least one of the reactants

Example;

0xo process for manufacturing

normal isobutylaldehyde

more than one phase – typical solid catalyst in liquid/gaseous reactants

Example;

The dehydrogenation of cyclohexane

CATALYST-TYPECATALYST-TYPE

HOMOGENEOUS HETEROGENEOUS

Page 25: Chapter 1 Lecture Note Part 1

Homogeneous CatalysisHomogeneous Catalysis

Action • catalyst and reactants are in the same phase

• the catalyst is evenly distributed throughout.

• reaction proceeds through an intermediate species of lower energy

• there is usually more than one reaction step

• transition metal ions are often involved - oxidation state changes

Example

Acids Esterificaton

Conc. H2SO4 catalyses the reaction between acids and alcohols

CH3COOH + C2H5OH CH3COOC2H5 + H2O

Page 26: Chapter 1 Lecture Note Part 1

Heterogeneous Catalysis

• Catalyst is in different physical phase from the

reactants.

• It is also called Contact catalysis.

• It possesses great industrial importance.

Page 27: Chapter 1 Lecture Note Part 1
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Theory of Heterogeneous Catalysis

X + C → XC (1)Y + XC → XYC (2)XYC → CZ (3)CZ → C + Z (4)

Activated complex formation theory: Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process regenerating the catalyst. The following is a typical reaction scheme, where Crepresents the catalyst, X and Y are reactants, and Z is the product of the reaction of X and Y:

X + Y → Z

Page 29: Chapter 1 Lecture Note Part 1

Theory of Heterogeneous Catalysis (cont.)

Adsorption theory (Old): The reactants in gaseous state or insolutions, are adsorbed on the surface of the solid catalyst. The increase inconcentration of the reactants on the surface increases the rate of reaction.Adsorption being an exothermic process, the heat of adsorption is utilised inenhancing the rate of the reaction.

Adsorption theory (Modern): The modern adsorption theory is the combination of intermediate compound formation theory and the old adsorption theory. The mechanism involves five steps:

(1) Diffusion of reactants to the surface of the catalyst. (2) Adsorption of reactant molecules on the surface of the catalyst. (3) Occurrence of chemical reaction on the catalyst’s surface through formation of an intermediate (Figure depicted below). (4) Desorption of reaction products from the catalyst surface, and thereby, making the surface available again for more reaction to occur. (5) Diffusion of reaction products away from the catalyst’s surface.

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HH

Pt Pt Pt

H H

OO

O O

Pt Pt Pt Pt Pt Pt Pt Pt Pt Pt

H

OH

Adsorption theory

Page 34: Chapter 1 Lecture Note Part 1

Steps in Catalytic Reaction

External diffusion

Internal diffusion

Adsorption

Surface reaction

Desorption

Internal diffusion

External diffusion

Page 35: Chapter 1 Lecture Note Part 1

Example Heterogeneous Catalytic Reaction Process

• The long journey for reactant molecules to

j. travel within gas phase

k. cross gas-liquid phase boundary

l. travel within liquid phase/stagnant layer

m. cross liquid-solid phase boundary

n. reach outer surface of solid

o. diffuse within pore

p. arrive at reaction site

q. be adsorbed on the site and activated

r. react with other reactant molecules, either being adsorbed on the same/neighbour sites or approaching from surface above

• Product molecules must follow the same track in the reverse direction to return to gas phase

• Heat transfer follows similar track

j

r

gas phase

poreporous solid

liquid phase /stagnant layer

k

l

mn

o

pq

gas phasereactant molecule

Catalysis & Catalysts

CH4003 Lecture Notes 12 (Erzeng Xue)

Page 36: Chapter 1 Lecture Note Part 1

reactants

products

reactor

catalyst support

active

site

substrate

adsorption

reactiondesorption

bed of

catalyst

particles

porous

carrier

(catalyst

support)

product

Page 37: Chapter 1 Lecture Note Part 1

CATALYST-PROPERTIES Porous-Catalyst – a catalyst that has a very large area

resulting from pores

Molecular sieve – Materials with small pores (admit small molecule but prevent large ones from entering

Monolithic- can be either porous or nonporous, encountered in processes where pressure drop and heat removal are major consideration.

Supported-consists of minute particles of an active material dispersed over a less active substance.

Unsupported- mainly promoters that increase activity

Page 38: Chapter 1 Lecture Note Part 1

• catalyst that has a large area

• small pore that will admit small molecule

• can be either porous or non-porous

Page 39: Chapter 1 Lecture Note Part 1

4.Supported catalyst 4.Supported catalyst

•• consist of particles of an active consist of particles of an active material dispersed over a less material dispersed over a less active substanceactive substance

5.Unsupported catalyst5.Unsupported catalyst

•• Promoters Promoters –– small amount of small amount of active ingredientsactive ingredients

Page 40: Chapter 1 Lecture Note Part 1

40

• Catalyst composition

– Active phase• Where the reaction occurs (mostly metal/metal oxide)

– Promoter • Textual promoter (e.g. Al - Fe for NH3 production)

• Electric or Structural modifier

• Poison resistant promoters

– Support / carrier• Increase mechanical strength

• Increase surface area (98% surface area is supplied within the porous structure)

• may or may not be catalytically active

Solid CatalystsCatalysis & Catalysts

Catalyst

Support

CH4003 Lecture Notes 12 (Erzeng Xue)

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41

• Some common solid support / carrier materials

– Alumina• Inexpensive• Surface area: 1 ~ 700 m2/g• Acidic

– Silica• Inexpensive• Surface area: 100 ~ 800 m2/g• Acidic

– Zeolite• mixture of alumina and silica, • often exchanged metal ion present• shape selective• acidic

Solid CatalystsCatalysis & Catalysts

Other supports

Active carbon (S.A. up to 1000 m2/g)

Titania (S.A. 10 ~ 50 m2/g)

Zirconia (S.A. 10 ~ 100 m2/g)

Magnesia (S.A. 10 m2/g)

Lanthana (S.A. 10 m2/g)

poreporous solid

Active site

CH4003 Lecture Notes 12 (Erzeng Xue)

Page 42: Chapter 1 Lecture Note Part 1

Adsorption is a physical or chemical phenomenon by which the moleculespresent in a liquid or a gas attach to the surface of a solid.

The substance on which surface adsorption occurs is termed as the adsorbent, and the substance which adsorbed from the bulk phase is known as the adsorbate.

Depending on the force of attraction, adsorption is mainly two types: (1) Physical adsorption (Physisorption) and (2) Chemical adsorption (Chemisorption).

Surface means both external and internal surface.

Page 43: Chapter 1 Lecture Note Part 1

Physical adsorption is a phenomenon which takes place purely due to thevan der Waals forces of attraction.

- It can be compared with the condensation of vapour of liquids.

- It is a reversible phenomenon.

- Because of very week force of attraction, the physical adsorption cannot bring to any change of chemical structure of the adsorbent andadsorbate.

Page 44: Chapter 1 Lecture Note Part 1

Chemical adsorption is adsorption which results from chemical bondformation (strong interaction) between the adsorbent and the adsorbate in a monolayer on the surface.

Example: Organic compound get adsorbed on the solid surface with chemical bond formation.

Page 45: Chapter 1 Lecture Note Part 1

The adsorption phenomenon comes from the

existence of non-compensated forces of a

physical nature on the surface of the solid.

All the bonding requirements of the

constituent atoms of the material are filled

by other atoms in the material.

However, atoms on the surface of the

adsorbent are not wholly surrounded by

other adsorbent atoms and therefore can

attract adsorbates.

Adsorbate

Adsorbent

Adsorbate

Page 46: Chapter 1 Lecture Note Part 1

The following criteria define a good quality catalyst for a reaction:

Only small quantity is needed for a reaction

They are specific. One catalyst is needed for

specific

reaction only

Physical properties may change during a reaction

but it

does not take part in the reaction

No catalyst can change an equilibrium state of a

reaction

Page 47: Chapter 1 Lecture Note Part 1

47

• General requirements for a good catalyst– Activity - being able to promote the rate of desired reactions

– Selective - being to promote only the rate of desired reaction and also retard the undesired reactions

Note: The selectivity is sometime considered to be more important than the activity and sometime it is more difficult to achieve

(e.g. selective oxidation of NO to NO2 in the presence of SO2)

– Stability - a good catalyst should resist to deactivation, caused by– the presence of impurities in feed (e.g. lead in petrol poison TWC.

– thermal deterioration, volatility and hydrolysis of active components

– attrition due to mechanical movement or pressure shock

– A solid catalyst should have reasonably large surface area needed for reaction (active sites). This is usually achieved by making the solid into a porous structure.

Catalytic Reaction ProcessesCatalysis & Catalysts

CH4003 Lecture Notes 12 (Erzeng Xue)

Page 48: Chapter 1 Lecture Note Part 1

END OF CLASS QUESTION:

EXPLAIN EACH PROCESS INVOLVE IN CATALYSIS STEPS REACTIONS. ILLUSTRATE EACH STEP IN A CATALYTIC REACTION BY DIAGRAMS.

Page 49: Chapter 1 Lecture Note Part 1

Subtopic covered in Chapter 1… Catalytic Reactions and Reactors

Surface and Enzyme Reaction Rates

Introduction of Porous Catalyst

Transport and Reaction

External Mass Transfer

Pore Diffusion

Catalytic Wall Reaction

Langmuir-Hinshelwood Kinetic Mechanism

Temperature Dependence of Catalytic Reaction Rates

Application of Reaction Engineering in MicroelectronicFabrication

Catalyst Deactivation

Page 50: Chapter 1 Lecture Note Part 1

• Reactor volume, V = Volume of fluid plus volume of catalyst

V = V fluid + V catalyst

• Void fraction or the fraction of the reactor volume occupied by fluid

V

V fluid

reactor of Volume

fluid of Volume

Page 51: Chapter 1 Lecture Note Part 1

• Homogeneous Reactors:

• Heterogeneous Reactors

V fluid = εV

reactor the through passes rate flow volumetric

reactor ain fluid of volume=τ

rate flow metricinlet volu

reactor of volume

0

V

0

V

Page 52: Chapter 1 Lecture Note Part 1

• Packed bed Reactor

– Assume no mixing

– Mass balance:

rdz

dCu j

j

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 53: Chapter 1 Lecture Note Part 1

• Slurry and Fluidized Bed Reactor- Reactants are well mixed as CSTR

– Mass Balance:

– Reactor Residence Time

= =

rCC AA 0

v

V fluid

v

VR

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 54: Chapter 1 Lecture Note Part 1

• Riser Reactor

In riser reactor, no mixing at all, PFTR

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 55: Chapter 1 Lecture Note Part 1

• Assumption to be made: catalyst in solid phase

• All reaction on the surface of the catalyst(there is no reaction in the fluid phase).

• Surface reaction has unit of moles per unit areaof catalyst per unit time, r”

Surface and Enzyme Reaction Rates

Homogeneous reaction rate:

Heterogeneous (surface) reaction rate:

timevolume

moles

r

timearea

moles''

r

Page 56: Chapter 1 Lecture Note Part 1

• Surface area of catalyst

catalyst of mass

catalyst of area surfacegs

")1( rsr cg

Page 57: Chapter 1 Lecture Note Part 1

Summary of Reaction Rates

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 58: Chapter 1 Lecture Note Part 1

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Answer: 2x105

Page 59: Chapter 1 Lecture Note Part 1

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 60: Chapter 1 Lecture Note Part 1

Topic 1Catalytic Reaction and Mass Transfer

Catalytic reactions and reactorsSurface and Enzyme Reaction RatesIntroduction of Porous CatalystTransport and ReactionExternal Mass TransferPore DiffusionCatalytic wall reactionLangmuir-Hinshelwood Kinetic MechanismTemperature dependence of catalytic reaction ratesApplication of reaction engineering in microelectronic

fabricationCatalyst deactivation

Page 61: Chapter 1 Lecture Note Part 1

Why we need porous catalyst???

A few major catalyst support and catalysts:

Silica gels have surface areas up to ~ 500 m2/g, and they are widely used as supports for catalysts.

The surface area is up to ~ 200 m2/g in crystalline form.

Zeolites are microporous crystalline solids with well-defined structures. Generally they contain silicon, aluminium and oxygen in their framework

The activated carbon is a highly porous with high surface area (usually > 500 m2/g) carbon materials.

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Depositing noble metals on high-surface area oxide support (Al2O3, SiO2, Zeolites) disperses the metal over the surface so that nearly every metal atom is on the surface.

Page 63: Chapter 1 Lecture Note Part 1

Transport and Reaction

Different size scales in a catalytic reactor...

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 64: Chapter 1 Lecture Note Part 1

Steps in Heterogeneous Catalytic Reaction

CPE624 FACULTY OF CHEMICAL ENGINEERING

i. External mass transfer

(diffusion) of the reactants

(e.g., species A) from the bulk

fluid to the external surface of

the catalyst pellet.

ii. Pore diffusion of the reactant

from the pore mouth through

the catalyst pores to the

immediate vicinity of the

internal catalytic surface.

iii. Adsorption of reactant A onto

the active site of catalyst

surface

iv. Reaction on the surface of the

catalyst (A B)

v. Desorption of the products

(e.g., B) from the surface.

vi. Pore diffusion of the products

from the interior of the pellet

to the pore mouth at the

external surface

vii. External mass transfer of the

products from the external

pellet surface to the bulk fluid

Page 65: Chapter 1 Lecture Note Part 1

Concentration Gradient in Catalytic Reactor

CAb = ??

CAs = ??

CA(x) = ??

Copyright 1998 by Oxford University Press, Inc.

Page 66: Chapter 1 Lecture Note Part 1

Concentration Gradient in Catalytic Reactor (cont.)

Copyright 1998 by Oxford University Press, Inc.

Page 67: Chapter 1 Lecture Note Part 1

How do we know whether the reaction rate is reaction limited (reaction

control) or external mass transfer limited (external mass transfer

control)??

First, let’s recall on mass transfer coefficient…

Page 68: Chapter 1 Lecture Note Part 1

Mass Transfer Coefficients (for gasses)

If there is a concentration difference of A between two locations 1 and 2, then

JA = kmA (CA1 – CA2)

JA is the mass transfer flux, [mol/s.m2]

km is the mass transfer coefficient,

[mol/(s·m2)/(mol/m3), or m/s]

)2AC1AC(

AJ=mAk

-

CA1-CA2, concentration difference [mol/m3].

Mass transfer coefficient (kmA) can be defined through the Sherwood number:

AD

mAk=

l[convective mass transfer rate]

[diffusive mass transfer rate]Shl =

where l is length and DA is the diffusion coefficient of A

l

DShk Al

mA

Then KmA can be defined as:

Page 69: Chapter 1 Lecture Note Part 1

Mass Transfer Coefficients : Sherwood Numbers (Shl) ...

3) Flow through a tube For laminar flow (ReD < 2100):

For turbulent flow:

3

8DSh

318.0Re023.0 ScSh DD

2) Flow over a sphere:

4.032

21

Re06.0Re4.00.2 ScSh DDD

1) Flow over flat plate (of length L):For laminar flow (ReL < 105):

31

21

Re66.0 ScSh LL

For turbulent flow (ReL > 105):

318.0Re036.0 ScSh LL

Sherwood Numbers (Shl) several simple geometries..

4) Flow over a cylinder:

For ReD <4 :

31

DRe98.0=DSh

Page 70: Chapter 1 Lecture Note Part 1

External Mass Transfer

At steady state:[rate of transport to surface] = [rate of reaction at surface]

For first order reaction;

AsAsAbmA CkRrRCCkR "4"4)(4 222

mA

AbAs

kk

CC

"1

Abeff

mA

Ab Ck

kk

Ckr "

"1

""

nonporou

s catalyst

pellet

CAb

CA

CAs

(d)

x

Reaction limited

k″ << kmA

Mass transfer limited

k″=kmA

k″ >> kmA

By rearranging

Eliminating CAs

Copyright 1998 by Oxford University Press, Inc.

Page 71: Chapter 1 Lecture Note Part 1

External Mass Transfer

We now examine the limiting cases:

If kmA << k" then, r" kmA CAb

Reaction limited (reaction control)If k" << kmA then, r" k" CAb

External mass transfer limited (external

mass transfer control)

Page 72: Chapter 1 Lecture Note Part 1

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Page 73: Chapter 1 Lecture Note Part 1

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press