Catalysts and Catalytic Reactors, Catalytic Reactor Models_ Fixed Bed Reactors

8/18/2019 Catalysts and Catalytic Reactors, Catalytic Reactor Models_ Fixed Bed Reactors

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Lecture 7

Catalysts and Catalytic Reactors

Catalytic reactor models: Fixed Bed reactors


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The choice of catalyst is very important

but still largely empirical.

• Most processes use a catalystCatalysts increase the rate of reaction but are unchanged in quantity

and chemical composition at the end of the reaction.

Catalysts for multiple reactions: the catalyst may have different effects

on the rates of the different reactions

Catalysts need to be developed that increase the rate of the desiredreactions relative to the undesired reactions

CATALYSTS


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• The reactions proceeds entirely in the vapour or liquid phase• The catalyst may modify the reaction mechanism by participation in the

reaction but is regenerated in a subsequent step. The catalyst is then free

to promote further reaction

E.g. Production of acetic anhydride

CH3COOH CH2=C=O + H2O acetic acid ketene water

Catalyst : triethyl phosphate

• The catalytic process can beHomogenous

Heterogenous

Biochemical

(i) Homogeneous Catalyst


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• The reaction rate of catalysed reactions is more complex than that

of uncatalysed ones.

• The overall rate of a heterogeneous gas-solid reaction is made up

of a series of physical steps as well as the chemical reaction.Mass transfer of reactant from the bulk gas phase to the external solid surface

Diffusion from the solid surface to the internal active sites Adsorption on solid surface

Activation of the adsorbed reactants

Chemical reaction

Desorption of products

Internal diffusion of products to the external solid surface

Mass transfer to the bulk gas phase

all these steps are rate processes and are temperature dependent rate controlling step : the step that is slower than the others

Heterogeneous Gas-Solid Reaction Rate


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• The optimal performance of the catlayst is obtained by locating the

Dirac Delta catalyst distrubtion so as to maximize the reaction rate by

taking advantage of both temperature and concentration gradients

within the pellet.

• Location of Dirac Delta Function to be optimsed.In practice, step function is used for Dirac Delta Function

the ratio of the observed rate to that which would beobtained if the whole of the internal surface of the pelletwere available to the reagents at the same concentrationsas they have at the external surface

Effectiveness Factor

• Effectiveness factor =

0 1

Less than 5 % of thecharacteristic dimensionof the pellet

(b) Step function.0 1

(a) Dirac delta function.

(Morbidelli, Gavriilidis and Varma (2001) Catalyst Design: Optimal Distributionof Catalyst in Pellets, Reactors and Membranes, Cambridge University Press).


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Solid-catalysed reactions

• Usually, multiple reactions

• The gross flow pattern of fluid through reactor should be

considered

• For parallel reactions

Maintaining the appropriate high or low concentration and temperature levelsof reactants at the catalyst surface

- Encourage the desired reaction

- Discourage the byproduct reaction

• For series reactions

Avoiding the mixing of fluids of different compositions


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Local non-homogeneity of catalyst

• Lowered reactant concentration or change in temperature within the catalyst

pelletsThe concentration and temperature in the interior of catalyst pellets may differ from the

main body of the gas

Different product distribution from that for homogenous system

• Two extremes for local non-homogeneitySurface reaction controls

concentrations of reactant inthe main gas stream

concentrations of reactantat the catalyst surface

Diffusion controls

concentrations of reactant inthe main gas streamconcentrations of reactantwithin the pellets

When the desired reaction is of lower order,operating under conditions of diffusion controlincreases selectivity

The gross flow pattern of f luid through the reactor would be considered

Lowered reactant concentrationfavours the reaction of lower order


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Selectivity for solid catalysed reactions

Optimum selectivity given by Dirac Delta Function

Step function can be used in practice

Need to optimize the location of the step function within the

catalyst pellet

(Morbidelli, Gavriilidis and Varma, (2001) Catalyst Design: Optimal Distribution of Catalyst in Pellets, Reactors and Membranes, Cambridge University Press)

Practical difficulties in producing catalyst pellets with preciselocation of catalyst step function

Deterioration of catalyst performance with time needs to beconsidered


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Temperature Control

• Adiabatic operation leads to the simplest and cheapest reactor

designTemperature control is required for

- Unacceptable temperature rise for exothermic reactions

- Unacceptable temperature fall for endothermic reactions

• Temperature control for adiabatic operationCold shot or hot shot : the injection of cold or hot fresh feed directly into the

reactor

- Temperature control by direct contact heat transfer

- Concentration control of feed material to adjust the rate of reaction

Indirect heat transfer with the reactor: indirect heating or cooling

- Heat transfer takes place inside the reactor or

- Material is taken outside of the reactor to a heat transfer device and returned to the

reactor.


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Example of Temperature Control (I)

• Temperature control for adiabatic operation (continued)

Heat carrier : An inert material can be introduced with the reactor feed- to increase the feed CP (mass flowrate multiplied by specific heat capacity)

- to reduce the temperature rise or fall for reactions

When possible, the existing process fluids should be used as heat carriers Product or byproduct recycling as a mean of temperature control should not have

a detrimental effect on the selectivity of the reaction.

Catalyst profiles- Change of the distribution of active material in the catalyst bed or

- Use a different catalyst in different parts of the reactor or

- Use a mixture of catalyst and inert solid to ‘dilute’ the catalyst

Easy to control the rate of reaction in different parts of the bed


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Example of Temperature Control (II)

Lowconcentration

Reactionproceeds

Highconcentration

REACTANTS

CoolingMedium

PRODUCTS

Reactionproceeds

Coolingmedium

Catalyst

Catalystarrangement

with gradient

Better temperaturecontrol

Feedconcentration

Cooling duty

Heat releasefrom the reaction

Reactor inlet Reactor outlet

Tubular Reactor

• Exothermic reaction with non-uniform catalyst performance


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Example of Temperature Control (III)

Tubular reactor

CO + 2H2 CH3OH

CO2 + H2 CO + H2O

REACTANTS

STEAM

CATALYST

BOILEDFEEDWATER

PRODUCTS

• Production of methanol

230 250 270 OC

Gas inlet temp

water temp

4OC

: Exothermic reaction

: Endothermic reaction

Temperature profile is relatively smooth

Cold shot reactor

REACTANTS

CATALYST

PRODUCTS230 250 270 O C

30OC

Significant temperature f luctuations Accidental catalyst overheating and

shortening of catalyst life


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Quenching of Reactor Effluent

• The reactor effluent may need to be cooled rapidly, or quenched , byIndirect heat transfer : conventional heat transfer equipment

Direct heat transfer : mixing with another fluid

e.g. Cooling of gaseous products mixed with a liquid.

The cooling is accomplished by mixing with a liquid that evaporates.

• Reasons to use quenching with direct heat transfer The reaction is very rapid and must be stopped quickly to prevent excessive byproduct formation.

The reactor product cooling would cause excessive fouling in a conventional exchanger.Special materials-of-construction or an expensive mechanical design is required because the

reactor products are so hot or corrosive.

• The liquid used for the direct heat transfer should be easy to separate from the

reactor product.

• Use of extraneous materials for the direct quenching may be used.

But it should not

Create additional separation problemsDegrade the specifications of product purity

Cause additional environmental problems


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Choosing Heat Transfer in the Reactor

HeatCarrier

HeatCarrier

Is AdiabaticOperation

Acceptable ?

Yes

No

Is IndirectHeat Transfer

Feasible ?

Yes

No

Is HighTemperatureor High FluxRequired ?

Yes

No


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• Catalytic degradation can cause a loss of performancePhysical loss

- Homogenous catalysts : generally important

- Heterogenous catalysts : particularly for catalytic fluidized bed reactors

Attrition of the particles causes the catalyst particles to be broken down

Surface deposits

- The formation of deposits on the surface of solid catalysts introduces a physical barrier to the reacting

species.

- Most often, the deposits are insoluble or non-volatile. e.g. Coke formation (carbon deposits) in hydrocarbon reactions

suppression by adjustment of feed composition or regeneration by air oxidation at elevated temperatures

Sintering : molecular re-arrangement below the melting point

- Sintering causes a reduction in the effective surface area of catalyst.

- Sintering results from high temperature reaction / poor heat transfer / poor mixing of reactants / catalyst

regeneration at high temperature

Poisoning- Usually impurities in the raw materials or products of corrosion chemically react with or form strong

chemical bonds with the catalyst

Chemical change

- some catalysts can slowly change chemically with a consequent reduction in activity

Catalyst Degradation


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Effects of Catalyst Degradation

• Catalyst degradation is important for :the choice of catalyst

reactor conditions

reactor configuration

• Deterioration in catalyst performance lowers the rate of reaction.

• Increasing the temperature of reactor gradually can be used to compensate for the deterioration in performance.

High temperature can decrease selectivity considerably and often accelerate the catalyst

degradation.

• The reactor configuration must make a provision if degradation is rapid.Use standby capacity or

Removal of catalyst from the bed on a continuous basis

The lost or degraded catalyst implies cost and environmental impacts.


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Types of catalytic reactors: Fixed-bed reactors

•

Major part of catalytic processes carried out in fixed-bed reactors

–

With the exception of catalytic cracking of gas-oil

• Carried out in fluidised beds

–

Typical fixed bed industrial processes include:

Chemical

industry

Petrochemical

Industry

Petroleum refining

Steam reforming Ethylene oxide Catalytic reforming

CO conversion Ethylene

dichloride

isomerization

Synthesis: Vinyl acetate polymerization

Sulfuric Acid butadiene hydrodesulfurisation

Methanol Maleic anhydride hydrocracking

Oxo cyclohexane

ammonia styrene

hydrodealkylation


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Technical innovations•

Fixed-bed reactors are large capacity units – To address high market demands – Made possible by progress in both technical and fundamental areas

•

Introduction of better materials of construction – E.g. centrifugal cast 25% Cr 20% Ni steel tubes to increase operating T’s and

throughput

• Better design of reactor internals to improve the rate of uniformity of heatremoval

– By molten salts

• Better design techniques allowing construction of multi-bar reactors withapprox 20,000 tubes of large diametre.

•

Modification of auxiliary equipment increase the capacity of establishedprocesses such as ammonia synthesis – Centrifugal compressors

• Flow pattern modifications – Use of radial flow reactors to reduce pressure drop and enhance recycle capacity

of compressor

• Use combinations of small catalyst particles to enhance heat transfer and oflarge catalyst particles to limit pressure drop

• Design of improved control scheme

•

Development of new catalysts and modifications of existing ones – Formulation of stable low P methanol synthesis catalyst

– Introduction of low T CO shift catalyst

• Availability of more reliable kinetic data and physicochemical data – Advanced experimental design techniques

– Improved methods in data analysis

• Improved reactor models


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Fixed-bed reactor models

• Principles of general models

–

Models of variable complexity –

Required degree of sophistication depends on specific process• Kinetic reaction scheme• Sensitivity to perturbing operating conditions

–

Both macroscale and microscale issues• Microscale deal with catalyst particles and sites• Macroscale mainly determined by hydrodynamics

–

Plug flow enough or more accurate?

• Model classification in two big categories: –

Pseudohomogeneous models:• Do not expliciltly account for the presence of catalyst

–

Heterogeneous models:• Separate conservation equations for fluid and catalyst

–

Models can be 1-D or 2-D• 2-D models account for variations in radial dimension

– Mixing in axial directions to account for non-ideal flow conditionscan be included


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1-D pseudo-homogeneous model

• Concentration and T gradients only occur in axial

direction• Overall transport mechanism: plug flow

• Conservation equations:

– S.S. and single rxn in tube:

•

I.Cs: at z=0, C A=C A0, T=T0, pt=pt0

•

dp is the equivalent particle diameter, us the superficialvelocity, !g the gas density, U the overall heat transfercoefficient, dt the internal tube diameter, Tr the ambient T, !B the catalyst bulk density and f the friction factor

p

s g t

r

t

B A P g s

B A A s

d

u f

dz

dp

T T d

U Hr

dz

dT cu

r

dz

C ud

2

)(4

)(

!

! !

!

="

""#"=

="


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1-D pseudo-homogeneous model (contd)Heat transfer coefficient

• Overall heat transfer coefficient

– ai =heat transfer coefficient on the bed side (kJ/m2soC)

–

au= heat transfer coefficient, transfer medum side (kJ/m2soC)

– Ab= heat exchanging surface, bed side (m2)

– ! = heat conductivity of the wall (kJ/m-hr oC)

– Au= heat exchanging surface, heat transfer medium

side (m2) – Am= log mean of Ab and Au (m

2)

u

b

um

b

i A

A

a A

Ad

aU

111++=

!


23/33

1-D pseudo-homogeneous model (contd)Pressure drop

•

Pressure drop equation for flow through packed beds: –

Ergun 1952

–

Bed of connecting parallel channels with hydraulic radius R h= " / # v• " = void fraction

•

# v = surface solid per m3 bed

–

Equivalent particle diameter, d p, diameter of sphere with the samesurface area per unit volume as actual particle, Sv = # v / (1- " )

–

So d p=6 (1- " ) / # v –

Ergun proposed:

• "=1.75 and b=150

• Handley and Heggs (1968) derived: "=1.24 and b=368

•

Hicks (1970) found that Ergun’s equation is limited to Re / (1- " ) < 500 – Handley and Heggs’ equation to 1000 < Re / (1- " ) < 5000

!"

#$%

& '++

'=

Re

)1(13

(

(

( ba f


24/33


with axial mixing

•

Mixing in the axial direction – Due to turbulence and presence of packing

– Accounted by superimposing an effectivetransport mechanism

•

On overall transport by plug flow

–

Flux due to this mechanism analogous toFick’s law for mass transfer, Fourier’s law forheat transfer

• Proportionality constants effective diffusivities,conductivities

• They implicitly contain the effect of the velocityprofile


25/33


with axial mixing (contd)

• Steady-state mass balance for component A:

• Energy equation:

• The b.c.s used in general are:

02

2

=!! B A

A

s

A

ea r

dz

dC u

dz

C d D " #

( ) 0)(42

2

=!!"!+! r t

B A P g sea T T d

U r H dz

dT cudz

T d # # $

L z for dz

dT

dz

dC

z for dz

dT T T cu

z for dz

dC DC C u

A

ea p s g

Aea A A s

===

=!=!

=!=!

0

0)(

0)(

0

0

" #

$


26/33


with axial mixing (contd)

•

Two-point boundary value problem•

Effect of axial dispersion for heat and mass onconversion – Negligible when bed depth > 50 particle diameters

–

More accurately, for monotonically decreasing rate:•

Axial dispersion negligible when:

–

Addition of axial mixing leads to the possibility of steadystate multiplicity for adiabatic case

ha

p g sw

p B A

ma

s

p B A

Pe

cuT T

d r H

PeC u

d r


27/33


•

1-D models neglect resistance to heat and mass transferin radial direction

–

Predict uniform temperatures, conversions in cross-section

–

Problem for rxns with high heat effects

• 2-D model here uses effective transport concept

–

In r-direction –

Effective diffusivity non-isotropic

• Radial component different from axial component

• Based on flow characteristics

–

Effective conductivity #e decreases strongly near the wall

• Can consider #e

constant away from wall and introduce newcoefficient for heat transfer near the wall

w

er W Rw

dr

dT T T a !

"

#$%

&'=' ( )(


28/33

2-D pseudo-homogeneous model (contd)

• Mass balance for single component A

• Energy balance

•

B.C.s

•

Note that (Der )s=$Der and #er based on superficial flow velocity

0)1

()(2

2

=!!+ B A

A

s

A A

ser r

dz

dC u

dr

dC

r dr

C d D "

( ) 01

2

2

=!"+"##$

%&&'

(+ B A P g ser r H

dz

dT cu

dr

dT

r dr

T d ) ) *

z Rr at T T a

dr

dT

z r at dr

dT

z Rr and r at dr

dC

Rr z at T T

Rr z at C C

W R

er

w

A A

!=""=

!==

!===

##==

##==

,)(

,00

,0,00

0,00,0

0

0

$


29/33

1-D heterogeneous model

accounts for interfacial gradients •

Very rapid rxns with high heat effects

– Need to distinguish between conditions in the fluid and

on catalyst surface

•

Even inside catalyst

–

Can have 1-D or 2-D models• Steady state mass and energy balances for single rxn:

–

For fluid:

–

For solid:

)(4)(

)(

r

t

s

sv f P g s

s

sv g A

s

T T d

U T T ah

dz

dT cu

C C ak dz

dC u

!!!=

!=!

"

)()(

)(

T T ahr H

C C ak r

s

sv f A B

s

sv g A B

!="!

!=

#

#


30/33

1-D heterogeneous model

accounts for interfacial gradients (contd)

•

B.Cs: at z=0, C=C0 and T=T0• k g =mass transfer coefficient from gas to solid interface

• # v =external particle surface area per unit volume

•

hf =heat transfer coefficient for film surrounding particle

• Most likely interfacial gradient to occur is

temperature gradient•

Compared to the corresponding pseudo-homogeneous 1-D model – Fluid/solid intrerface can lead to multiplicity of steady

states

•

Heat produced in the catalyst: sigmoidal curve•

Heat removed by the fluid through the film: straight line – 3 steady states arise from their intersections


31/33

1-D Heterogeneous model accounting for

interfacial and intraparticle gradients

• When resistance to mass and heat transfer inside particleis important

–

Rate or rxn not uniform throughout particle

–

Equations describing concentration and temperature gradients

inside particle are needed

–

Steady state mass and energy balances for single rxn become:

• Fluid:

•

Solid:

)(4)(

)(

r

t

s

sv f P g s

s

sv g A

s

T T d

U T T ah

dz

dT cu

C C ak dz

dC u

!!!=

!=!

"

0),()(

0),(

2

2

2

2

=!"+##$

%&&'

(

="##$%

&&'(

s s A s

se

s s A s

se

T C r H d

dT

d

d

T C r d

dC

d

d D

) *

* * *

+

) *

* * *


32/33


interfacial and intraparticle gradients

(contd)•

B.Cs: C=C0 T=T0 at z=0

• A single particle is considered not whole solid

•

The shape of particle also determines values for De and #e

•

Set ODEs describing intra-particle gradients need to be integrated at

each computational node of the fluid – Computationally tedious

•

Even with strongly exothermic rxns particle practically isothermal

– Main resistance inside the pellet to mass transfer

2)(

2)(

00

p se

s

s f

p se

s

s g

s s

d at

d

dT T T h

d at

d

dC DC C k

at d

dT

d

dC

=!=!

=!=!

===

" "

#

" "

" " "


33/33


interfacial and intra-particle gradients Effectiveness factor

•

When gradients occur inside particle use effectiveness factor %

–

Multiplies rxn rates at particle surface conditions

• To account for rate actually experienced when conditions insideparticle are different

•

System then becomes:

–

Fluid:

–

Solid:

•

Effectiveness factor depends on Thiele modulus f and needs to becomputed at each computational node

)(4)(

)(

r

t

s

sv f P g s

s

sv g A

s

T T d

U T T ah

dz

dT cu

C C ak dz

dC u

!!!=

!=!

"

)(),()(

)(),(

T T ahT C r H

C C ak T C r

s

sv f s s A B

s

sv g s s A B

!="!

!=

# $

$#

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Catalysts and Catalytic Reactors, Catalytic Reactor Models_ Fixed Bed Reactors

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