07 - modelling of membrane reactors

Modelling of membrane reactors

Martin van Sint Annaland & Fausto Gallucci

Chemical Process Intensification

DEMCAMER/CARENA Workshop

January 30th, 2013 @ Eindhoven TU/e

Overview lecture

• Modelling membrane permeation

– Porous membranes

– Dense (supported) membranes for H2

– Dense membranes for O2

• Different reactor concepts

• Packed bed membrane reactors

– Detailed particle model for heterogeneous catalysts

– Coupling of SDMs with particle models

• Fluidized bed membrane reactors

– Phenomenological two-phase model

– CFD-based models: discrete particle models

Page 1 11-2-2013 Multiphase Reactors Group, SPI

Modelling of membrane permeation

• Porous membranes

0 0

,

1 4 8

3

ln

i

g

i m

i mi m

i

pRTN K B

RT M

p

rr

r

Membrane flux:

(Dusty-Gas-Model):

Page 2 11-2-2013

Parameters K0 and B0

depend on the pore

size/structure distributions

Multiphase Reactors Group, SPI



Fick model: only diffusion

Page 3 11-2-2013

eff ii i

p xN D

RT r

1

, ,

1 1eff

i eff eff

i m i K

DD D

Bosanquet:

Blanck’s law:

(harmonic averaging of

molecular and Knudsen diffusion )

, ,

1

1

1

neff eff

i m i j j

jij i

D D xx

(Bosanquet + Blanck laws

strictly only valid for dilute mixtures)

, ,

eff

i j i jD D

, 0

4 8

3

eff

i K

i

RTD K

M

Effective molecular diffusion:

Effective Knudsen diffusion:

( = porosity)

( = tortuosity)


Fick’s law: What is wrong?

• Fick’s law (applied to film model):

Page 4 11-2-2013

ii i

dcJ D

dz

,0 ,i i iN k c c

Flux with respect

to the mixture:

Flux with respect

to the interface:

[mol/m2s]

[mol/m2s]

Diffusivity

[m2/s]

Mass transfer

coefficient [m/s]

Film model: D

k

,0ic

,ic

z0z

Film model:



• Binary equimolar diffusion

Page 5 11-2-2013

11 1

dcJ D

dz

22 2

dcJ D

dz

Constant total concentration

(i.e. isobaric & isothermal) 1 2 constanttotc c c

Flux of component 1

with respect to the mixture:

Flux of component 2

with respect to the mixture:

Total net flux: 2

1 2 1 2

1

0tot i

i

dJ J J J D c c

dz

provided that there is only 1 binary diffusivity D,

independent of composition

Life is nice

and simple?



• Consider two ideal gasses separated by

a porous membrane

Page 6 11-2-2013

He Ar

pure Ar

high flow rate

298 K

105 Pa

298 K

105 Pa

pure He

high flow rate

Is the He flux equal to the Ar flux

(i.e. NHe = –NAr)?



• Consider two ideal gasses separated by

a porous membrane

Page 7 11-2-2013

He Ar pure Ar

high flow rate

298 K

105 Pa

298 K

105 Pa

pure He

high flow rate

NHe –3 NAr

Much higher He flux despite identical concentration gradients!

Explanation:

– Movement of mixture with respect to membrane!

– Friction He-membrane < Friction Ar-membrane pressure gradient

– Resulting in viscous flow from right to left: retarding He, accelerating Ar

Observation:

Interaction with

membrane




Extended Fick model: diffusion + d’Arcy

Page 8 11-2-2013

eff ii i i tot

p xN D x N

RT r

0 0tot tot

B p B p pN c

r RT rd’Arcy:

Extended Fick model:

accounts for net total molar flow rate

01 eff i ii i

x B x p pN D p

RT r r

Extended

Fick:

“viscous flow”




constantirN c

Extended Fick model for tubular membrane:

Page 9 11-2-2013

10i

drN

r dr

Steady state component continuity equation for cylindrical membrane:

r

Membrane tube

R1

R2 dr

pA(r=R1) = pA,1 pA(r=R2) = pA,2

L

2 ,2iR N cPermeation flux = flux at r = R2:

m

1 mR r

2 1 mR R

,2

2

i

m m

c cN

R r





Page 10 11-2-2013

Substitution of extended Fick model:

01 eff i ii i

x B x p pN D p

RT r r

i

cN

rComponent continuity:

01 eff i ii i

x B x p p cN D p

RT r r r

2 2 2

1 1 1

0

R R R

eff i ii

R R R

dx B x p dp cRTD p dr dr dr

dr dr r

Integration over the tube thickness:





Page 11 11-2-2013

diffusion

2 2 2

1 1 1

0

R R R

eff i ii

R R R

dx B x p dp cRTD p dr dr dr

dr dr r

viscous flow

important when

pressure drop

is negligible

p p

important when

concentration gradient

is negligible

i ix x

,2 2 2

,1 1 1

0

i

i

x p R

ieff

i i

x p R

B x drD p dx pdp cRT

r

0 2 2 21,2 ,1 2 12

1

lnieff

i i i

B x RD p x x p p cRT

R





Page 12 11-2-2013

0 2 2 21,2 ,1 2 12

1

lnieff

i i i

B x RD p x x p p cRT

R

2 21 12 1 2 1 2 1 ,2 ,12 2i i i ix p p x p p p p p p pNote:

0 2,2 ,1

1

lneff

i i i

B p RD p p cRT

R

,2

2

i

cN

R

,0

,2

1

ln

i meff

i i

i mi m

m

pB pN D

RT rr



• Consider three inert ideal gases in two-bulb system

Page 13 11-2-2013

A B

N2, CO2 N2, H2

2

0

, 0.50N Ax

2

0

, 0.50CO Ax

2

0

, 0H Ax

2

0

, 0.50N Bx

2

0

, 0.50H Bx

2

0

, 0CO Bx

Does N2 flow: a) from A to B?

b) from B to A?

c) not at all?

d) or does it do a), b) and c)?

(isobaric &

isothermal) at t=0 connected

by narrow capillary




Page 14 11-2-2013

A B

N2, CO2 N2, H2

Reverse

diffusion

at t=0 connected by

narrow capillary

(isobaric &

isothermal)

Taylor & Krishna (1993)

Fig. 5.4, p. 109




Page 15 11-2-2013

A B

N2, CO2 N2, H2

(isobaric &

isothermal) at t=0 connected by

narrow capillary

Reverse

diffusion

– H2 and CO2 change monotonically to equilibrium

concentrations as expected

– N2 initially diffuses first without concentration gradient and

later even against its concentration gradient from A to B,

only later bulbs go gradually back to equal compositions

Explanation:

H2 moves from B to A, and CO2 from A to B

N2 molecules more friction with CO2 than H2

and CO2 seems to drag N2 along from A to B

cannot be explained

with Fick’s law!

Observation:



• Generalized Maxwell-Stefan equations:

id

,

1

n

tot i i T P i i i i i i j j

j

c RTd c p c F c F

1

ni j j i

i

j tot ij

x N x Nd

c Đ

In terms of fluxes with

respect to interface Ni:

Generalized driving forces:

= driving force for

component i

Derivation by considering binary interactions between

molecules of different type:

2

2

1

2

2

2

2

u1

u2

1

,

1, ,

lnnii

T P i ij i j

j j T P

xx x

RT xwith:

id

1 1 2 1 2F x x u u



Rewriting in (n-1) matrix notation using

Page 17 11-2-2013

1

nji

ii

jin ijj i

xxB

Đ Đ

1 1ij i

ij in

B xĐ Đ

1

totJ c B d

In n-1 matrix notation:

totc d B J (v) = vector with n-1 components

[M] = square matrix of rank n-1

1

2

1

...

n

d

dd

d

11 12 1, 1

21 22 2, 1

1,1 1,2 1, 1

...

...[ ]

... ... ... ...

...

n

n

n n n n

B B B

B B BB

B B B

• Generalized Maxwell-Stefan equations:

1

0n

i

i

Ji i i totJ N x N( )




Dusty Gas Model (DGM):

Page 18 11-2-2013

Based on the generalized Stefan-Maxwell equations for diffusion

in multi-component mixtures

0

1 , , ,

11

ni j j i i i i

eff eff effj i j i K i Kj i

x N x N N x x B p p

pD pD RT r pRT D r

Consider membrane as one of the components in the mixture

see e.g. Veldsink et al., Chemical Engineering Journal 57 (1995) 115-125



• Dense Pd-membranes for H2

(Pd, Pd/Ag, Pd/Au based membranes)

2 2 2H H H

n nret permm

m

KN p p

(0.5 < n < 1)

(n = 0.5: Sieverts’ law)

H2 H2O CO2

1 2

3

4

5

Pd-membrane

High pressure Low pressure Mechanism involves

a series of steps:

1) adsorption

2) dissociation

3) diffusion

4) re-association

5) desorption



2

H,H H,Pdmole

dcD

dx

Pd

H H

H H

H

H

H H

H

H

H H

Bulk diffusion control:

For ideal (dilute) systems:

H,PdD is constant

2 2 2

0.5 0.5H,Pd H,Pd H,Pd

H H H H H

ret perm ret perm

m m

D D KN c c p p

Dissociation and association

at equilibrium:

2H ( ) H( )g adsHK

2

0.5

H HC HK p

and

HK




Bulk diffusion control:

Pure H2 streams

at permeate and retentate

(i.e. no sweep gas)

Page 21 11-2-2013

(ΔP(support) ≤ 0.1 bar)

QH = 1.54 · 10-4 mol m-2 s-1 Pa-n

n = 0.730

Jurriaan Boon et al. (ECN)

2 2 2

HH H H

n nret perm

m

QN p p


Modelling membrane permeation

Pd

H H

H

H

H

H

H H

H

H

H

H

• Supported Pd-membranes for H2

Without sweep (i.e. only H2 is present)

http://www.hysep.com

Bulk diffusion Pd-layer:

DGM support:




With sweep

Pd

H H

H

H

H

H H

H

H

H

concentration polarisation

Pd permeation

resistance in support concentration polarisation




With sweep: Dusty Gas Model (DGM):

Pressure drop H2-support:

Diffusion resistance H2-stagnant N2:

Page 24 11-2-2013





Page 25 11-2-2013


low sweep gas flow rate high sweep gas flow rate

With sweep: Comparison of different mass transfer resistances:



• Dense membranes for O2

O2 permeation flux through dense perovskites

MIEC = Mixed Ion and Electron Conducting

Page 26 11-2-2013

O2- 2e-

CO, CO2, H

2, H

2OCH

4, CO, H

2

O2

O2 2O2- + 4e-

O2

O2/O2- + ? ?

N2

air

O2

2 2

O2

ln

vO O

ln

( ) ln4

perm

ret

p

m m p

DN d p

V

Wagner equation:

( ) = non-stoichiometry: 20 O

np

2 2 2

v 0O O O

4

n nret perm

m m

DN p p

V n

Note n is typically small (and <0)!!

Compressing air not very effective!

Partial pressure at permeate side

important!




O2 permeation flux through dense perovskites

(LaCa)(CoFe)O3- : Flux studied experimentally for reducing atmospheres

Greatly enhanced in presence of CO and H2 (left)

Highly dependent on thickness (right), indicating bulk diffusion

(T = 1223 K, Φv = 200 ml/min (STP), dilution with N2)




CO2 inhibits permeation rate (left)

Rate determined by local equilibrium of CO combustion,

proportional to CO/CO2 ratio and thus xO2 (right)

(T = 1223 K, Φv = 200 ml/min (STP), dilution with N2)

O2 permeation flux through dense perovskite (LaCa)(CoFe)O3-



2 2 2O O Oexpn n

ret permact

m

C EN p p

RT

Zhang et al., J. Membrane Science 291 (2007) 19-32


Permeation expressions derived to describe results

2

2

CO

O

CO eq

xx

x K

n = -0.153

Eact = 260 kJ/mol,

C = 2.01·108 (cm4/cm2/min, STP)

Page 29 11-2-2013





Model can also accurately predict O2 permeation rate for H2 as

reducing gas assuming local equilibrium of H2 combustion

Page 30 11-2-2013


Zhang et al., J. Membrane Science 291 (2007) 19-32


11-2-2013

Different reactor concepts

• Basic classification

Packed bed membrane reactors:

Immobilized catalyst

Fluidized bed membrane reactors:

Particles kept in suspension by fluidum


11-2-2013


• Packed bed reactors:

used for reactions

with small heat effect

Single adiabatic bed used for reactions

with a large heat effect

Multi-tubular reactor


• Packed bed membrane reactor configurations


Reactants in

Sweep gas out

Catalyst inside

tubular membranes

Example:

multi-tubular module

with sweep gas

Products out

Sweep gas in

Page 33 11-2-2013

• Gas addition/gas extraction

• Flat vs. tubular membranes

• Dead end membranes vs. sweep

• Co-current/countercurrent sweeping

• Catalyst as particles inside/outside

membrane tubes

• Catalytically active membranes

• Supported/unsupported

• etc. etc.

Many different possible configurations:

A A+B C+D

B

Catalytic membrane

A A+B C+D

B

Catalytic membrane

AB

Reaction Zone

Gas PhaseGas Phase

Catalytic Membrane

(a)

(b)

(c)

(d)

A+B C +B D +E

A, B

A+B C

Catalytic membrane

C +D E

Catalytic packed be

A,B

D

(e)

A A+B C+D

B

Catalytic membrane

A A+B C+D

B

Catalytic membrane

AB

Reaction Zone

Gas PhaseGas Phase

Catalytic Membrane

(a)

(b)

(c)

(d)

A+B C +B D +E

A, B

A+B C

Catalytic membrane

C +D E

Catalytic packed be

A,B

D

(e)


11-2-2013

• Phenomenon of fluidization



11-2-2013

• Phenomenon of fluidization


Bubbles (= voids) are formed,

which create excellent mixing

in the fluidized bed

Particles suspended

in a gas stream

behaves as a “fluidum”


11-2-2013

• Fluidization at large scale: Granulation and coating



11-2-2013

• Fluidization at large scale: FCC and olefin polymerization


FCC (Fluid Catalytic Cracking)

Ethylene/propylene

polymerization



• Fluidized bed membrane reactor configurations

Flat membranes

integrated in the walls

Immersed

membrane tubes

Permeate Retentate

Sweep in

500z

Feed

Sweep out

Feed

Retentate

Permeate

Page 38 11-2-2013

Zona de

Reacción

Zona de

Regeneración

Reaction

zone

Regene-

ration zone


11-2-2013

• Packed bed and fluidized bed membrane reactors:

Packed bed

membrane reactor

Fluidized bed

membrane reactor


11-2-2013

Membrane tubes

Heat exchange

surface

Gas inlet

Gas outlet Product gas outlet

Cyclone

P, W

O2 O2

A

W H2 H2

A

Selective

O2 dozing Selective

H2 extraction

• Simple reactor construction

• Possibly large temperature and

concentration gradients (in case of

fast & strongly exothermic reactions)

• Reactor instability

• Isothermal reaction conditions

• Catalyst attrition

• Gas back-mixing / gas by-passing


Packed bed membrane reactors

• Modelling of packed bed membrane reactors

– First steps:

– Determine what is rate limiting

– Determine the key performance quantities

– Determine required model accuracy in relation to available data:

e.g. 1D/2D model? Isothermal/adiabatic? Phenomenological vs. CFD?

– Modelling membrane permeation:

– Flux constant? Permeation equation?

Extended multi-component DGM?

– Modelling catalyst:

– Internal/external mass transfer limitations?

– Simplify with effectiveness factors?

– Pseudo-homogeneous models?

– Heterogeneous models with detailed particle models?

Page 40 11-2-2013

simplify

whenever

possible!!!


• Detailed particle model

Page 41 11-2-2013

2

2

1g

g rr n St r r

2

, ,2

11 g s p s eff s h

T TC r S

t r r r

Component mass balances (n-1) using

Maxwell-Stefan description for molar diffusion fluxes:

Homogeneous energy balance:

eff iD D Effect of particle

porosity/tortuosity via:

, ,

1

1reactn

r i i g s i j j

j

S M r

,

1

1reactn

h g s j r j

j

S r h

1

tot g totn j n B n with:



• Detailed particle model

Page 42 11-2-2013

0r

Boundary conditions:

+ constitutive equations for the flux correction factors etc.

Yields local production rates (source terms)

To be coupled with reactor model

pr r

0i

r

0T

r

1 10

, , , ,

1 1

c cn n

ig eff i k i tot g s ik g k bulk k

k k

d n kr

,eff s g s bulk

TT T

r



• Heterogeneous reactor model:

,

g i g g i i

g g ax i s m i m

uD n a a

t z z z

, 2 2

0

4 with =

g g g ig m tot m m

i

u da a

t z d d

Total continuity equation gas phase:

Component continuity equations gas phase (i = 1..nc-1):

Catalyst in

annular space! Superficial velocity!


, ,

1

,

1

c

c

n

g g p g p g g g g i s i

i

n

m i m i b w w w

i

T T TC C u n a H

t z z z

a H a T T

Gas phase energy balance:

ni computed from

particle model

+ boundary conditions (Danckwert’s type) Page 43 11-2-2013 Multiphase Reactors Group, SPI


Page 44 11-2-2013

• Constitutive equations:

22

2 3 3

1 1150 1.75

g gg g g g

p g p g

u up

z d d

2 2

2

O ,

, 0 0

4 8

3ln

O m

m O

g i mi m

i

M ppRTK B

RT M rr

r

Pressure drop (differential Ergun equation):

Membrane flux equation(s),

e.g. in case of O2 addition via porous membranes:

+ Reaction kinetics, transport parameters, physical properties


C H

H H

C H

H H

O O C

H

H

C H

H

O H

H O

H H

C H

H H

C H

H H

C O C O

H H

H H H

H

H H

H H

H H

Outer shell of particle

• Heat generation

• Ethylene production

Inner core of particle

• Heat consumption

energy integration

• Synthesis gas production

Catalyst particle


Page 45 11-2-2013

• Combining OCM + SMR in a single dual-function

catalyst particle


• Novel reactor concept: PBMR for OCM/SRM

with dual function catalyst

O2

CH4 + H2O CO, CO2, C2H6, C2H4

porous membrane

inert

impermeable

O2

O2 O2

dual function catalyst

Distributive O2 feeding & autothermal operation!

OCM

SRM

mole

r [m]

O2 c

on

cen

trati

on

0 R

Use strong internal

diffusion limitations to

avoid O2 to the SRM

Ensure that C2 flux out of particle is much

larger than C2 flux toward particle core

(minimize C2 losses)

Tune CH4 conversion in OCM and SRM

(autothermal operation)



• Extension to 2D: Determination of extent & effect of concentration polarization

Continuity + Navier-Stokes eqns.

Note: membrane permeation is implemented

via (Danckwert’s) boundary conditions

Fluidized bed membrane reactors

• Modelling of fluidized bed membrane reactors

– First steps (same as before!):

– Determine what is rate limiting

– Determine the key performance quantities

– Determine required model accuracy in relation to available data:

e.g. Phenomenological vs. CFD?

– Phenomenological model:

– Phenomenological = two-phase model (bubble-emulsion phase)

– Use semi-empirical correlations for bubble and solids behaviour

– Bubble size (and thus all other key quantities) function of axial position

– Extent of gas phase mixing in emulsion phase via number of CSTR’s

in series

– CFD model:

– At what scale: particle scale vs. industrial scale?

– Computational resources? Patience?

simplify

whenever

possible!!!

• Phenomenological two-phase model:


• Two phases: emulsion and bubble phase

• Axial dispersion in emulsion and bubble

phases via number of CSTRs in series

(to be determined from experiments)

(typically: emulsion phase = 1 CSTR;

bubble phase large nr of CSTRs)

• Emulsion phase remains at incipient

fluidization conditions despite reaction or

membrane permeation instantaneous

transfer with bubble phase

• Only reaction in emulsion phase

(relatively low reaction rates)

• Isothermal and isobaric conditions


SF(x) = Heaviside function: x<0: SF(x) = 0, else SF(x) = x

• Model equations

Ratio of membrane addition/extraction to/from

bubble and emulsion phases according to bubble hold-up

Transfer Q is required to maintain emulsion phase

at incipient conditions


• Constitutive equations

Page 52 11-2-2013

Effect of internals not accounted for

(correlations not available)!



• CFD: Multi-scale modelling strategy

DNS Continuum

Discrete Bubble

Larger geometry, larger scale phenomena

Fluid-particle

interaction

Particle-particle

interaction;

Bubble behavior

Large scale

motion

Industrial size

Discrete

Particle

Particle-

particle

interaction

Page 54 11-2-2013

Phenome-

nological

“Black box”

Industrial size



• Discrete Particle Model

gas flow

drag

gravity

,contact aF

• Intermediate-level model

• Eulerian grid size is larger than the particle size

• Incorporation of detailed particle interaction models

• Computation limitation: 104~106




Gas phase conservation equations (3D-DPM model)

0g g g g gut

v1

S1

uag a a

a cellcell g

p

Vr r

V

Volume-averaged Navier-Stokes equations

+ continuity equation

+ momentum equation

inter-phase momentum transfer

Sg g g g g g g g g g gp gu u u p gt

2

3

T

g g g gg gu u u I




Taa a

dI

dt

+ translational momentum

+ rotational momentum

,g1

paa a g a a c a

g

Vdvm V p u v m F

dt(Cundall & Strack (1979))

Particle motion equations (DPM model)

Npart: 104~106

Computation resource

32 1 0.343

3 0.5 22 2 2

1 1.5 Re [ 3 8.4Re ]180 18 0.31

1 10 Res s

g g s sg s g s s g g s s

p g p g p sd d d

(Beetstra et al., 2007)


• Flat membrane walls experiments:

Effect of gas addition/extraction

on bubble phase

Gas extraction results in increase of equivalent bubble size

Gas addition results in decrease of equivalent bubble size


extraction

addition addition

extraction


• Flat membrane walls: Effect of gas addition/extraction

40 % 0 % +40 %


Correlation bubble

behaviour and

emulsion phase

circulation patterns!

• Flat membrane walls: Effect of gas addition/extraction

40 % 0 % +40 %



• Flat membrane walls: DPM simulations


DPM predicts same results as experiments!


• Submerged membranes


Multiphase Reactors Group, SPI Page 62 11-2-2013

Development of DPM/IBM

(Immersed Boundary Model)

Concluding remarks

• Detailed reactor and particle models (and combinations thereof)

may be required to adequately account for all relevant effects

• Make models as simple as possible … but not simpler!

• Use models to enhance understanding, but experimentation

remains a critical component to validate the models!


07 - modelling of membrane reactors

Documents

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spi ficks law

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icz0zfilm model

effi j i jd d

diffusion darcy page

high flow rate nhe