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Course Review Non -Ideal Reactors

Hetero geneous Reaction Systems

Consultation Time:2-3 pm (22-26 April)E5-03-18

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What We Have Covered

Isothermal, Ideal Reactor (Homogeneous SingleReaction) Design

Mole Balance

In Out + Gen = Acc

=+ V A A A A dt dN dV r F F 0

Design Algorithm

1.GMBE, 2.Rate Law3. Stoich , 4.Combine

Rate Law

n A A kC r =

Analysis of Rate LawKinetics: k and n

Output

Time (t)

Space time()

Conversion(X)

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Non-Ideal Reactors

Isothermal, Non-Ideal Reactors (Single reaction)

RTD (macromixing)

1. Pulse injection

2. Step injection

Rate Law

n

A AkC r =

Output

Conversion(X)

Models (micromixing)1.SEG2.TIS3.Dispersion4.Compartment

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RTD for Chemical Reactors (Unit 7) Outline the concept of residence time distribution (RTD) as well as the

reasons for using this concept in connection with non-ideal reactors. Define the residence time distribution function, E(t), and the cumulative

residence time distribution function, F(t), and use the relation betweenthem.

Outline and understand the measurement methods for obtaining the

residence time distribution. Use experimental results from pulse and step experiments to calculate

the mean residence time and the variance.

Derive the residence time distribution functions, E(t) and F(t), for idealreactors (PFR and CSTR).

Define the concept of mean residence time, t m, and, for a CSTR as anexample, show that this time equals the space-time, .

Define the concept of variance about mean residence time, 2, and showthat this variance for a CSTR equals the space time squared, 2.

Use the information of RTD to diagnose the ills of real reactor systems.P-4

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Calculate E(t), F(t), t m , and 2

=

0 )(

)()(

dt t C

t C t E

= t dt t E t F 0 )()(

= 0 )( dt t tE t m

=0

22 )()( dt t E t t m

RTD functions for an ideal reactor

)()( = t t E Plug flow:

CSTR:

/

)(

t e

t E

=P-5

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Models (Unit 8)

Outline the concept of macromixing and micromixing.

Outline the concept of macrofluid and microfluid.

Outline the basic assumptions of the segregation model as well as thecases when this model may be applied.

Use the segregation model for calculations on non-ideal reactors.

Outline the basic idea of the tanks-in-series model and the dispersionmodel.

Use the TIS model and the dispersion model to solve reactorperformance problems with experimental results from tracer experiments.

Outline the concept of compartment model, and use this model to predict

the performance of non-ideal reactors.

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Models for PredictingConversion from RTD Data

SegregationModel

E(t)

t

=0

)()( dt t E t X X

1 2 n1C 1nC

nV

V i = ni

=

nC

Tanks-in-Series

2

2

=n

Plug Flow DispersionDispersionModel

)1(2 22 r PeePe

Pe r r

+=

P-7

Mixing of globules of different ages occurs here

ni k

X )1(

11

+=

1st order

DULPek D

Pe Dq

qPeq

qPeq

Peq

X

r ar

a

r r

r

==+=

+=

; ;41

)2

exp()1()2

exp()1(

)2

exp(41

22

1st order

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Models for Predicting Conversionfrom RTD Data (Complicated RTD)

rateflowFractional

volumeFractional

t ModelCompartmen

==

P-8

)(t F

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Heterogeneous Catalytic Reactor Design

Isothermal, Heterogeneous Catalytic Reactor (PBR,Single Reaction) Design

Design Algorithm

1.GMBE, 2.Rate Law3. Stoich , 4.Combine

Synthesize the Rate Law

Output

Conversion(X)

Catalyst

weight (W)Bed length

(L)

group)n(adsorptiogroup)force-ivingfactor)(dr (kinetic

rate =

Mole Balance

In Out + Gen = Acc

0' =+ b A Ab r dzdC

U z z z +0= z L z =

c A

External mass transfer Internal mass transfer Intrinsic reaction rate

Overall Rate Law Expression

)(' Ab A C f r =

AbC

r

Ar W AsC

)(r C A

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Overview of Packed Bed Reactor Design

,,,,,,

,

0

bca

Ab

c

S W U vC

L A

PBR

0' =+ b A Ab r dzdC

U

R

B A

A catalyst pellet Porous catalyst pellet

ABc Ar

c p

Dk W

ad R

,,

,,

AsC AbC

AC

,,

,,

n

A As Ab C C C

)'()'(' n Asn As A C k r r ==

)'()'(' n Abn Ab A C k r r ==

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The Steps to Consider

The overall rate of reaction isequal to the rate of the sloweststep in the mechanism rate-determining step.

1. Mass transfer through external boundary layer2. Diffusion into pores3. Adsorption4. Surface reaction5. Desorption6. Diffusion of products out of pores7. Mass transfer back to bulk fluid

9Unit

)(' A A C f r =

10Unit

)( Ab As C f C =

11Unit

)( As A C f C =

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Elements of Heterogeneous Catalysis (Unit 9)

Outline the steps in a catalytic reaction and use the concept of a rate-

limiting step to derive a rate law.

Develop a rate law and linearize it to determine the rate-law parametersfrom a set of gas-solid reaction rate data.

Derive the design equation for a catalytic reactor.

Calculate the conversion or catalyst weight for packed bed reactors.

Describe the different types of catalyst deactivation.

Outline the basic idea to design reactors to solve the catalyst deactivationproblems.

Calculate the conversion or catalyst weight for moving bed reactors.

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An Algorithm for Catalytic Reactor Design

Obtain data fromlaboratory reactors

Develop mechanism

and rate-limiting step

Synthesize rate

law from data

Estimate rate lawparameters

Reactor design

Adsorption

Surface reactionDesorption

More than 75% of allheterogeneous reactions aresurface-reaction-limited .

group)n(adsorptiogroup)force-ivingfactor)(dr (kinetic

rate =Irreversible Surface-Reaction-Limited Rate Laws

Single site S BS A B B A A

A A

PK PK

kPr

++=

1'

Dual site S S BS S A ++( )21

' B B A A

A A

PK PK

kPr

++=

S S C S BS A ++( )21

'C C B B A A

B A A

PK PK PK

PkPr

+++=

Eley-Rideal S C g BS A + )(C C A A

B A A PK PK PkP

r ++= 1'P-15

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Catalyst Deactivation

Catalyst deactivation)fresh,0('

)(')( =

=t r

t r t a

A

A

Rate of reaction)fresh(')(' A A r t ar =

Decay law

d r dt da =

Overcoming catalyst deactivationtemperature-time trajectorytransport reactors

To offset the decline in chemical reactivity of decaying catalysts:

Temperature - Time Traject ories

)(t f T =

Moving -BedReactor

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Use mass transfer in the context of reactor calculations.

Outline the concept of the film theory for the external mass transfer.

Evaluate the effects of fluid flow rate and particle size on theperformance of a mass transfer-limited reactor.

Derive the reaction rate expressions for slow and rapid reaction ona catalyst surface and outline the assumptions which this derivationis based on.

Outline how mass transfer-limited reactions respond to changes intemperature and flow conditions.

Design a reactor operating at conditions limited by external masstransfer.

External Mass Transfer Resistance (Unit 10)

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External Mass Transfer in a Packed-Bed Reactor

z z z +0= z L z =

c AA steady-state mole

balance on reactant A(ideal plug flow)

0'' =+ c A Ab ar dzdC

U

Diffusion across stagnant filmsurrounding a catalyst pellet

AsC

AbC Ar W

Boundarylayer

For reaction at steady state

Ar A W r =''

= zU

ak

C

C cc

Ab

Ab exp0

External-mass transfer limited

P-18

Abc A C k r =''

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Summary Scheme of surface reaction kinetics

sites

adsorption

rxn

desorption

internaldiffusion

externaltransport

fluid reactants products

solid

B A

0'' =+ c A Ab ar dzdC

U

Flow and reaction (ideal plug flow)

( ) As Abc Az C C k W = The film theory

Correlations of k c

1/31/2Sc0.6Re2Sh +=Flow around a spherical

particle (Frossling)

Flow through a packedbed (Thoenes-Kramers)1/31/2

)(Sc')(Re'Sh' =

External mass transfer-limited, PBR

LU ak

X cc=

11ln

P-19

Abc A C k r =''

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Derive the Thiele modulus.

Derive the effectiveness factor for porous catalyst particles with variousgeometries.

Use the concept of the effectiveness factor and outline how this factorcan be increased by various operation conditions.

Use the Thiele modulus for reactions with diffusion. Distinguish between internal and overall effectiveness factor.

Describe how the reaction rate is influenced by parameters such asvelocity, particle size and temperature.

Design PBR operating under pore-diffusion limited regime.

Internal/Pore Diffusion Resistance (Unit 11)

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Qualitative Analysis

porouscatalystpellet

Reactant concentration profiles around and within a porous pellet.

AC

x R +R

bAC sAC

reaction limited

pore diffusion limited

external masstransfer limited

(x)C A

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For 1 st order surface reaction in spherical porous catalysts

= As A C k r ''

rate without any

diffusion effects

with )1coth(3

1121

=

Effectiveness factor, a fudgefactor which varies between 0and 1, and which accounts for

the resistance to pore diffusion.

wheree

ac

DS k

R

''1

1= Thiele modulus, useful for

predicting reactor behaviorfrom known kinetic information,thus known k.

Effective diffusion coefficientin porous solids.

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For first -order reaction

U zS k Ab Ab

abeC C /)''(01 =

Porouscatalystpellet AbC AsC AC

Externalresistance

Internalresistance

z z z +0= z L z =

c A

0 AbC AbLC

U LS k abe X /)''( 11 =

P-23

ccba ak S k /''1 1

+=

ee

ac

Dk

R D

S k R 111112

1

'' );1coth(

3 ===

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P-24

Dependence of Reaction Rate on d P, U, and T(1 st order reaction )

12/112/1

2/1

2/1

6/1

3/2

T U k

d U D

k

c

p

ABc

Ase A

C k D R

r 13=

External diffusion Internal diffusion

Ab A C k r 1=

Reaction-limited

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Summary Scheme of surface reaction kinetics

B A

sites

adsorption

rxn

desorption

Internaldiffusion

externaltransport

fluid reactants products

solid

The Thiele modulus for porous spheres

The effectiveness factors

ratediffusionratereaction

]/)0[(

12

2n ===

RC DC k R

DC Rk

Ase

n

Asn

e

n

Asn

AsC toexposed surfaceentireif occur d that woulreaction

reactionof rateoverallactual=

Abtoexposed surfaceentireif occur d that woulreactionreactionof rateoverallactual=

For large values of Thiele modulus

nn 3

12

2/1

+=