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• Catalyst:definition,effect on activity and selectivity,classification (homogeneous, heterogeneous, bio-catalysis)

• Heterogeneous catalysis:introduction steps, macrokineticsrate determining step (regimes)mass transport by convection – diffusion (Fick’s law)external diffusioninternal diffusionsimultaneous internal and external diffusion

Catalysis and macrokineticsCatalysis and macrokinetics

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CatalysisCatalysis

• Importance: approximately 85-90% of the products of chemical industry are made in catalytic processes.

• Definition: catalysis is a process in which the rate of a reaction is enhanced by a relatively small amount of a different substance (catalyst) that does not undergo any permanent change itself.

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How catalysts act ?How catalysts act ?A catalyst accelerates a chemical reaction by forming bonds with the reactants, allowing them to form the products, which detach from the catalyst, and leave it unaltered.

catalyst

catalystA

catalystP

bonding reaction

separationA P

Thus, the catalytic reaction is a cyclic event in which the catalyst participates and is recovered, in its original form, at the end of the cycle.

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1. The catalyst offers an alternative path for the reaction, which is energetically more favorable(higher reaction rate implies lower reactor capacity).

A P (elementary reaction)

E t

thermal reaction

ΔH react. P

A

pote

ntia

l ene

rgy

E t

thermal reaction

ΔH react.

catalytic reaction

E c

reaction

catalystA

catalystP

Pcatalyst

separationcatalyst

A

bonding

reaction coordinate

pote

ntia

l ene

rgy E c < E t

Catalysis and activityCatalysis and activity

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2. The catalysts change the kinetics, not the thermodynamics.

3. The catalysts accelerate both the forward and the reverse reaction to the same extent.

There are also cases in which the combination of catalyst with reactant or product is not successful:

• Bond with the reactant too weak• Bond with the reactant (or product) too strong (catalyst

poisoning)

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Catalysis and selectivityCatalysis and selectivity

In the presence of multiple reactions (consecutive and parallel reactions), a catalyst can accelerate selectively one reaction, thus increasing the process selectivity.

Higher selectivity implies reduction of the separation costs andwaste of reactants.

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Types of catalysisTypes of catalysis

• Homogeneous catalysis:reactants and catalyst are in the same phase (liquid or gas)

• Heterogeneous catalysis:reactants and catalyst are in different phasesCatalyst: solid, liquidReactant: liquid, gas

• Biocatalysis:enzymes are natural catalysts composed primarily of proteins (many aminoacids coupled by peptide bonds).Enzymes are the most efficient catalysts: highly active (108―1011-fold rate increase) and extremely selective.They work under mild conditions of temperature and pH.

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Properties of catalystsProperties of catalysts

easydifficultCatalyst separation

highlimitedVariety of application

drasticmildReaction conditions

lowhighSelectivity

varyingvaryingActivity

Heterogeneouscatalyst

Homogeneouscatalyst

Properties

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Heterogeneous catalystsHeterogeneous catalysts

Heterogeneous catalysts are solid materials which can be single or mixture of substances.

Often, the active component is supported on another, generally inert substance, called support.

As the reaction occurs on the surface, in general it is important to have high surface area per unit of weight.

High surface area can be obtained by using porous materials.

The catalytic activity is associated to localized points of the surface, called active centers. The decrease of the catalyst activity with the time is referred to as catalyst deactivation and it can be associated to various phenomena (fouling, sintering, poisoning etc.).

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Heterogeneous catalyst can have different shapes (powder, granules, gauzes, pellets, extrudate, rings etc.) and different dimensions depending on the reactor type.

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Steps in a heterogeneouslySteps in a heterogeneously--catalyzed reactionscatalyzed reactions• Heterogeneous catalytic reactions take place on the catalyst surface .

As the reactant have to be transported from the bulk fluid to the solid/fluid interface, the overall reaction includes also physical transport processes, beside chemical steps.

• Seven different steps :1. External diffusion: transfer of the reactants from the fluid phase

surrounding the catalyst particle (bulk fluid phase) to the external surface of the catalyst

2. Internal diffusion: transport of the reactants from the external surface of the particle through the pores to the active sites on the interior surface

3. Adsorption of the reactant on the active site4. Surface reaction5. Desorption of the product from the active site.6. Internal counter-diffusion: transport of the product through the pores

to the external surface7. External counter-diffusion: transport of the product from the external

surface to the bulk fluid phase

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Steps in a heterogeneouslySteps in a heterogeneously--catalyzed reactionscatalyzed reactions

Steps 3,4,5 are purely chemical phenomena:

Step 1,2,6,7 are strictly physical steps

(transport phenomena)

mac

roki

netic

s

microkinetics

The transfer steps 1 and 7 depend upon the flowdynamics of the system.The transport steps 2 and 5 are present only with porous catalysts and depend on the geometry of catalyst particles.

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Rate Rate determingdeterming stepstepSteps 1 and 7 (external diff.) are in series with steps 3-5 (chemical steps):the external transfer occurs separately from the chemical reaction.

Steps 2 and 6 (internal diff.) occur simultaneously with the chemical reaction.

As the heterogeneously catalyzed reaction involves sequential steps, at steady state the rate of these steps must be the same.If the rate constant of one of these steps is markedly smaller than the other, the overall rate is determined by this step, which is called the rate determining step.The reaction is said to be under the regime corresponding to the rate determining step.

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RegimesRegimes

• Kinetic regime: rds = chemical reaction(synonym: chemical regime)

• External diffusion regime: rds = external diffusion(synonyms: film diffusion, external mass transfer limitation)

• Internal diffusion regime: rds = internal diffusion(synonyms: pore diffusion, internal mass transfer limitation).

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Convective and diffusive transportConvective and diffusive transport

• Convection = transport by bulk motion of the fluid

initial condition

As the time passes …

… mixing occurs

• Diffusion = transport due to gradients(concentration gradients if the transported property is the mass, temperature gradients if the transported property is the thermal energy)

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Mass transport by diffusion: the FickMass transport by diffusion: the Fick’’s laws law

The diffusive mass transport transfer can be described by the Fick’s law:

J is the mass flux, i.e. the moles transported per unit of time and per unit of surface perpendicular to the diffusive movement

C is the concentration of the diffusing substance, D is the diffusion coefficient.

The negative sign indicates that the diffusion occurs in the opposite direction of the concentration gradient.

dxdCDJ −= ⎥⎦

⎤⎢⎣⎡

∗ smmol

2

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External diffusion: film modelExternal diffusion: film model

Film model:Existence of a stagnant layer (film), of thickness δ, surrounding the external surface of the catalyst, where is located the concentration gradient.In the bulk fluid phase the concentration is constant.

δ

film bulk

existing conc. profileconc. profile according the film model

conc

solid

0 distance xfrom the interface

Cb

Cs

fluid

If the supply of reactant from the bulk fluid to the external surface of the catalyst is slower than the rate of the surface chemical reaction, the reactant concentration on the catalyst surface Cs will be lower than that in the bulk fluid phase Cb.

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External diffusion: FickExternal diffusion: Fick’’s laws law

⎥⎦⎤

⎢⎣⎡

∗ smmol

2

The rate of mass transfer is expressed by the Fick’s law:

δ = thickness of the external film

∫∫ −=b

s

C

C

dCDdxJδ

0

By integration: )( sb CCDJ −−=δ

As the determination of the thickness δ of the external film is difficult, normally δis included in the constant giving the mass transfer coefficient β

)( sb CCJ −−= β ⎥⎦⎤

⎢⎣⎡

∗ smmol

2

At steady state, the rate r of mass transfer must be equal to the rate of the surface reaction, expressed per unit external surface area:

NB. k is the kinetic constant referred to the unit of volume catalyst

( ) nssb kCCCar =−⋅⋅= β

volumecatalystofunitpersurfaceexternalcatalysta ⋅⋅⋅⋅⋅⋅⋅=

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External diffusion: 1External diffusion: 1stst order reactionorder reaction

For 1st order reaction (n=1): ( ) ssb kCCCar =−⋅⋅= β

• Only the known bulk concentration Cb appears.• At the denominator there is the sum of resistances for sequential processes:

1/k = chemical resistance1/β = external mass transfer resistance

By expressing the unknown surface concentration Cs in function of the known bulk concentration Cb:

bC

ak

r

β⋅+

= 111

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External diffusion: limit cases External diffusion: limit cases

for 1st order reaction:

δ

film bulk

conc

solid

0 x

Cb

fluid

1

4

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1. No limitation by film diffusion2.,3 film diffusion and reaction4. maximum limitation by film diff.

bC

ak

r

β⋅+

= 111

Strong limitation by film diffusion(external diffusion regime)steep gradient concentration

bCar β⋅=β⋅>> ak

bkCr =

No limitation by film diffusion(kinetic regime)No gradient concentration

β⋅<< ak

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External diffusion:External diffusion:external effectiveness factor external effectiveness factor ηηee

conditionsfluidbulkatratereactionratereactionobserved

e ⋅⋅⋅⋅⋅⋅⋅

=η nb

obs

kCr

=

If the supply of reactant from the bulk fluid to the external surface of the catalyst will be not sufficiently fast to keep place with the potential intrinsic rate of the chemical reaction, the concentration of the reactant on the catalyst surface will be lower than that in the bulk fluid phase.For positive reaction orders, the observed reaction rate is lower than

that corresponding to the bulk concentration (ηe <1)

The degree of the external diffusion limitation is given by the external effectiveness factor:

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Internal diffusionInternal diffusion• For most catalysts the fraction of active sites located at the

external surface can be neglected. The reactant have to be transported through the pores to reach the active sites.

• The driving force for this transport (internal diffusion) is the concentration gradient inside the catalyst particle due to the chemical reaction.

• The resistance for this transport originates from collisions of the molecules, either with each other or with the pore walls.

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Internal diffusionInternal diffusion

dxdCDJ e−=

The diffusive mass transport inside the catalyst particle can be formally described by the Fick’s law:

x = perpendicular distance from the center of the particleDe = effective diffusion coefficient (instead of D).

⎥⎦⎤

⎢⎣⎡

∗ smmol

2

De takes into account that:

1. εp = porosity of the catalyst particle (characteristic values: 0,2<εp<0,7)(the diffusion does not occur in all the particle volume but only through the pores)

2. τ =tortuosity of the pores (characteristic values: 3<τ<7)(the pores neither are straight nor have the same cross-section: they have irregular structure)

3. the resistance towards transport originates from collision of the moleculeseither which each other (Dm = molecular diffusivity) or with the pore walls(Dk= Knudsen diffusivity)

τε p

km

e

DD

D 111

+=

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Internal diffusion:Internal diffusion:internal effectiveness factor internal effectiveness factor ηηii

conditionssurfaceexternalatratereactionratereactionobserved

i ⋅⋅⋅⋅⋅⋅⋅

=η

A degree of the internal diffusion limitation is given by

If the diffusion of the reactant from the external surface inside the particle is not fast enough to compensate for its disappearance by reaction, a decreasing concentration profile is established in the particle. For positive reaction orders, this leads to lower reaction rates at positions away from the external surface and, hence, to a lower

reaction rate when averaged over the complete particle volume (ηi <1).

ns

obs

kCr

=

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Thiele modulus Thiele modulus φφIt is possible to demonstrate that the internal effectiveness ηi

depends on a dimensionless number Φ, called Thiele modulus

Small φ: reaction rate is small; reaction limits the overall rate (kinetic regime)Large φ: diffusion rate is small: internal diff. the overall rate (int. diff. regime)

se

ns

p

p

CDkC

AV

∝φ

φ

1=η( )3.0⋅<⋅⋅ φφ small

se

ns

p

p

CDkC

AV

∝φ

maximum rate of pore diff.

rate of chem. reac. without pore diff.

kinetic regime Int. diff.

regimetransition

φη /3=( )3⋅>⋅⋅ φφ large

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Simultaneous external and internal diffusionAt steady state, the rate of external mass transfer must be equal to the rate of the surface reaction with internal diffusion.

( )sbexdiff CCar −⋅⋅=⋅ β ⎥⎦⎤

⎢⎣⎡

∗ smmol

3

volumecatalystofunitpersurfaceexternalcatalysta ⋅⋅⋅⋅⋅⋅⋅=

⎥⎦⎤

⎢⎣⎡

∗ smmol

3 (for 1st order reaction)

.. diffint.reactexdiffobs rrr ⋅+⋅ ==At steady state:

By substitution: general formula (for 1st order reaction from this formula all the limited cases can be obtained)

sidiffint.react Ckr ⋅⋅=⋅+ η..

ak

Ckri

biobs

⋅⋅

+

⋅⋅=

βη

η

1

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rds: surface reactiongeneral formula (for 1st order reaction)

1. At low reaction temperatures, the rate constant is small relative to the mass transfer coeffient βAdditionally, the Thiele modulus is small (since k is small relative to De) and thus η is unity. In this case the surface reaction is controlling and the concentration profile across the film and inside the pore is flat. The activation energy derived from the reaction rate correspond to the true activation energy of the chemical reaction without mass transport limitations

ak

Ckri

biobs

⋅⋅

+

⋅⋅=

βη

η

1

bkCr = attapp EE =

)/exp(ln 0 RTEkk att−=

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general formula (for 1st order reaction)

1. At intermediate reaction temperatures, the combination of pore diffusion and surface reaction is slowest: pore diffusion is controlling and there is a concentration gradient inside the pore. The activation energy derived from the observed reaction rate constant corresponds to approximately the half of the true activation energy

ak

Ckri

biobs

⋅⋅

+

⋅⋅=

βη

η

1

bappbep

pb

s

se

p

pb CkCkD

VA

kCkC

CDVA

kC ==∝∝φ1

bikCr η=

rds: internal pore diffusion

attapp EE 5.0=

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general formula (for 1st order reaction)

1. At high reaction temperatures, external diffusion is controlling and there is a concentration gradient across the film. The activation energy derived from the observed reaction rate constant is generally below 5kJ/mol

ak

Ckri

biobs

⋅⋅

+

⋅⋅=

βη

η

1

baCr β=

rds: external pore diffusion

molkJEapp /105−≈

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Arrhenius diagram

ln k

1 / T

Eeff = 5 kJ/molEeff = 0,5*Ea

Eeff =Ea

ln k

1 / T

ln k

1 / T

Eeff = 5 kJ/molEeff = 0,5*Ea

Eeff =Ea

Film Diffusion

Pore Diffusion

Surface Reaction

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•Van Santen, van Leeuwen, Moulijn, AverillCatalysis: An Integrated Approach

• Octave LevenspielChemical Reaction Engineering, third edition, Wiley (1999).

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Vocabulary Active centreActive componentActivitAdsorptionBiocatalysisChemical regimeConvectionDeactivationDesorptionDiffusionEffective diffusion coefficientEffectivenessExternal mass transport regimeGradientHeat and mass transport processes

Homogeneous catalysiInternal diffusionKnudsen diffusionMacrokineticsMass transferMass transfer coefficientMicrokineticMolecular diffusionPorosityPorosity factor

Rate determining stepRegimeSelectivityStagnant layerSupportSurface areaSurface reactionThiele ModulusTortuosity

Heterogeneous catalysis

Porous material