institut für chemie ringvorlesung methods in heterogeneous catalysis reaction engineering in...

Institut für Chemie

Ringvorlesung „Methods in Heterogeneous Catalysis“

Reaction Engineering in Heterogeneous Catalysis

- Reaction and mass transport in porous catalysts

- Up-Scaling of Reactors

Reinhard SchomäckerInstitut für Chemieder Technischen Universität Berlin



Schematic presentation of a chemical process

Reactant-purification

ReactionProduct-isolation

Main product

solvent, reactants, catalyst

BP

Heat

Procedure for reactor design1. Stoichiometry und Thermodynamics

2. Apparatus and Conditions

3. Calculation of Conversion and Reactor Size

4. Calculation of Material Flow



Steps of Heterogeneous Reaction

1. Diffusion of reactant to catalyst

2. Transport of reactant within catalyst pores

3. Adsorption of reactant on catalyst surface

4. Reaction

5. Desorption of products from catalyst surface

6. Transport of products out of catalyst pores

7. Diffusion of products away from catalyst



Langmuir Hinshelwood Mechanism

A B

AA

AAA pK

pK

1

21 BBAA

BBAABA

pKpK

pKpKkkr



Mass Transport and Heterogeneous Catalysis

Principles

Surface layer

catalyst

Concentration profile

fluid phase

Influence of mass transport on the temperature dependance of het. catalysis

Mass transport influence



Description of pore diffusion

cgradDj

A

j

cgrad

D wg 1

2

k T

p

wk T

m

B

B

2

8

2

Average free path length

Average molecular velocity

Dg ~ T1,5 und Dg ~ 1/p

1. Fick`s Law



a) Diffusion in pores dp >>

D Deff g

b) Knudsen – Diffusion dp =

D Dd

weff Kp

1

2 2

DK ~ T0.5

c) Intermediate range

D

D D

eff

g K

11 1

N2, X

N2, X =?

N2

Wicke-Kallenbach-Experiment

porousmaterial



Description of simultaneous reaction and pore diffusion

temporal change changes of material changes causedof materials within = amount by transport + by reactionsvolume element

dV

dc

dtdV j do r dVi

Vi i

V ( )

( )

j do div j dV

V

dc

dtdiv j ri

i i

one dimensional

Spherical geometry

div jd j

dzz

div jR

d

dRR jR

12

2( )



01

22

R

d

dRR j riR i( ) Mass balance of sperical particle

in steady state

Solution of mass balance and description of average reaction rate

Dd c

dR R

dc

dRk ceff

n( )2

2

2 with r= kcn and =-1

c R R c

dc

dR R

( )

0 0

0 0

0 00

1

Rkc

D

n

eff

renormalized parameter= Thiele-Modulus

c R cR

R

RR

( )sinh( )

sinh 0

0 00

0

radial concentration profilwithin sperical pellet



r V A Ddc

dRK K effR R

0

r = rhet

rR

Dc

Rhet effo

31

0 0

0

0

(tanh

)

r k chom 0 Reaction without mass transport limitation

r

rhet

hom

3 1 1

0 0 0 (tanh

) Effectiveness factor

Thiele-Modul

Porenwirkungsgrad

0

0,2

0,4

0,6

0,8

1

0 5 10 15 20

effe

ctiv

enes

s fa

ctor



3

0

r k cR

D

kk c k chet

effeff

3 3

00

00 0

k D keff eff E E Eeff D 1

2( )

Influence of pore diffusion on effective rate constant



Film diffusion und Reaction

ms

mol3

*

n S Dc c

Diff aW 0

n S c c mitD

Diff a W

.( ),

0

rV

dn

dti

i1 1

r

S

dn

dtSi a

i1 1

ms

mol2

*

r r a k k a mit aS

VS Sa , :



)()( 0

.

WSaWa crSccSn

Discussion of a first order reaction with rs=kscw

ß(c0-cw) = kscw

cc

kWS

0

Border cases:

ks << ß cw =c0 ( no layer formation)c0 cw

ks >> ß cw 0 c0

cw



0,0 ckck

kckr effS

S

SWSS

1 1 1

k kS eff S,

k a ka

k k a

eff S eff

s

, 1 11

1 1

Calculation of eff. volume related rate constant

1 1 1

k a keff

dspheredd

Particle volumea

6

6

3

2

Particle surface



Temperature dependance:



L

G

G

L

Packed Bubble Column

Column

Gas-Liquid-Reactors Gas-Solid-Reactors Three-Phase-Reactors

Fixed Bed Reactor

Katalysator

GL

L G

G

Trickle Bed Reactor

G

Tube Reactor

GK+L

K+L

Tank Reactor



Universal mass balance

VR

jA

r

c

tdiv j rA

A A

Akk.Transp.

Reaction

c c XA A 0 1( )

c

tc

X

tA

A 0

r kc r k c X XA A , , ( )0 0 1

r kc r k c X XA A 20 0

2 21, , ( ) ( )

r kc c r k c c X X X

mitc

c

A B A B

B A

A B

, , ( ) ( )( )0 0 0

0

0

1 1

r r T x 0 ( ) ( )

rjdivt

Xc AAA

0

.

V

V R Residence time



rjdivt

Xc AAA

0

X

t cdiv j

r

cX

AA

A

A

0

0

0

( )

Dar

cA

A

( ) 0

0

[-] Damköhler Number

X

t cdiv j Da X

AA

0

( )

reactorreaction

Solution of general mass balance with boundary conditions forDifferent reactions and reactor results in X = f(Da, reactor)



Ideal Tube Reactor (PFTR)

X

t cdiv j Da X

AA

0

( )

0 Lz

qnA

.

- steady state (X/t=0)- no back mixing (plug flow)- Volume of feed is constant- no radial concentration gradient (one dimensional system)- characteristic time is definied by: =VR/V

.



0 Lz

qnA

.

div jdj

dz q

dn

dz

V

q

dc

dz

c V

q

dX

dz

c V

q

dX

dz

c L dX

dzAA A A A A R A

1 0 0 0

(4-17)

c c XA A 0 1( )z

Xc

z

cA

A

0cn AAV

..

cnj AA

A q

V

q

..

.

V

V R

X

t cdiv j Da X

AA

0

( )



)(* 0

0

XDadz

dXLc

cA

A

)(X

dX

L

dzDa

Separation of variables: Integration

Z: 0 LX: 0 Xe

DadX

X

Xe

( )0



X eA

X

X

dXkDa

e

1

1ln

1)(

0

eXDa

e

1

0. Order reaction: r0=k (X)=1

X

dXDae

X e0

XX

XXc

e

e

eBA

X dXkDa

e

1

11

)(1)1(0

20

2. Order reaction: r0=kcA0cB0 (X)=(1-X)2

Da

DaX e

1

1. Order reaction: r0=kcA0 (X)=1-X



X

Xce

eBA

X

XX

dXkDa

e

1

1ln

1

1

)1)(1()(

00

2. Order reaction: r0=kcA0cB0 (X)=(1-X)(1-X)

eeX Da

Da

e )1(

)1(1

Conversion as function of Damköhler numberDa

00.10.20.30.40.50.60.70.80.9

1

0 2 4 6 8 10



Design of a reactor:

Demands: Xe, nP

(X); Xe Da

Residence time:

rcDa

A

A

0

0

)(

XcVnL RP

P0

Reactor capacity : Reactor volume:

A

PeAP Xcn V

0

..

Produced product

Xcn

rcDa

VeA

P

A

A

RV

0

.

0

0.

*)(



Fluidized bed reactor (CSTR)

M

CSTR

cAV

0

cAV

.

V

V RVR

Xc

V

ccV

V

nnjdiv A

R

AA

R

AA 000 )(

)(* 0

0

XDaXcc

A

A

1. Order reation: (X)=1-X

XDa

Dae 1

coordinate z

inlet outlet

cA



2. Order reaction: (X)=(1-X)(1-X)

DaX

X Xe

e e

( )( )1 1

2

2

1)1(

411

2

1)1(

Da

Da

Da

DaX e

Simple procedure for solution of mass balance: X/Da = (X)

Reactor design:

X

(X)

1

1

X/Da

Xe

(X) ; Xe Da ;

LP VR=V.

A

PeAP Xcn V

0

..

Xcn

rcDa

VeA

P

A

A

RV

0

.

0

0.

*)(



Comparison of ideal reactors CSTR and PFTR

Dependence of Conversion on Damköhler number for 1. order raction

eXDa

e

1

XDa

Dae 1



Heat balance of chemical reactors

universal heat balance VR

jA

r

q. [J/m2s]

constTmch p

constTcV

Tmc

V

hh p

pV

t

c T divq H rp( ) ( )

c

tdiv j rA

A A

universal mass balance

universal heat balance

V cdT

dtQ Q QR p kon W chem ... integral heat balance



( )Q V c T Tkon p a

( )Q k F T TW W W K

( )Q V H rchem R

2

1

1

11

d

k w

d1 2T

Tk

0 Q Q Qkon W chem

)()()()( TrVHTTFkTTcV RKWWap

The cooled CSTR



0

0 )()()(

A

A

c

TrTDa

)()()( 0 xTrTr

)(

)()( 0

0A

AcDar

TT

.

V

V R

rc V

VDa T XA

A R

0

( ) ( )

(4-46)

(4-47) ( ) ( )( )

( ) ( ) ( )V c T T k F T T

HVc Da T Xp a W W K

AA

0

)()( XTDaX

Stk F

V c

k F

V cund T

Hc

cW W

p

W W

R pad

A

A p

( )

( )

0

T T St T T T Xa K ad ( ) (4-48) Coupling Equation



XTTTStTT adKa )(

XTStTStTTT adKa

XTStTTStT adKa )1(

)1/()()1/( StStTTStXTT Kaad

Separation for T:

TT

StX T mit T

T St T

Stad a K

1 10 0

Stk F

V c

k F

V cund T

Hc

cW W

p

W W

R pad

A

A p

( )

( )

0

Design of cooling follows solution of MB: DaX

X

r

cA

( )

( ) 0

A0.LP VR=V Calculation of Ta or Tk from T0



Safty Scenario

4.4.3 Stability analysis

a) FW high, T-TK low: rightb) FW low , T-TK high : wrong

T TRT

EK 2

Quantitative calculation

Da T Da eE

RT( )

Da eX

X

ERT

( )

MB

( )( )1 0 St T T T Xad HB



Example: 1. Order reaction

Q

V c

ab

p

Q

V cp

Q

V c

chem

p

Q

V c

ab

p

Q

V c

chem

p

Q

V cp

dQ

dT

dQ

dTab chem

XDa T

Da T

Da e

Da e

mit Da k Mass balance

ERT

ERT

A

( )

( )

( ) ( )

11

( )( ) ( )1

1

0

St T T T

Da e

Da e

Coupling eqn.ad

E

RT

E

RT



4.4.4 Qualitative Description of other reactors

BR und PFTR

Adiabatic reactors

T T T Xa ad

dX

dtDa e X

E

RT X

( ) ( )BR:

PFTR: dX

dzDa e X

ERT X

( ) ( )

cooled reactors

BR:

PFTR:

dT

dtT Da e X St T Tad

ERT

K

( ) ( )

Zeit

Tem

pera

tur

adiabatischer Reaktor

gekühlter Reaktor

TT

aK



r

TK

Radial temperature profile with tube reactor

rtube< rcrit.

rtube> rcrit.

institut für chemie ringvorlesung methods in heterogeneous catalysis reaction engineering in...

Documents

heterogeneous catalysis

x slide

catalyst slide

b slide

tank reactor slide

particle surface slide

reaction residence time

s law slide