07 - Modelling of Membrane Reactors
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Transcript of 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
Modelling of membrane permeation
• Porous membranes
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)
Multiphase Reactors Group, SPI
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:
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• 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?
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• 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)?
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• 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
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
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”
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
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
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
Extended Fick model for tubular membrane:
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:
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
Extended Fick model for tubular membrane:
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
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
Extended Fick model for tubular membrane:
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
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• 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
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• Consider three inert ideal gases in two-bulb system
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
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• Consider three inert ideal gases in two-bulb system
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:
Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
• 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
Page 16 11-2-2013 Multiphase Reactors Group, SPI
Fick’s law: What is wrong?
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( )
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Porous membranes
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
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• 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
Modelling of membrane permeation
• Dense Pd-membranes for H2
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
Page 20 11-2-2013 Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Dense Pd-membranes for H2
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
Multiphase Reactors Group, SPI
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:
Page 22 11-2-2013 Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Supported Pd-membranes for H2
With sweep
Pd
H H
H
H
H
H H
H
H
H
concentration polarisation
Pd permeation
resistance in support concentration polarisation
Page 23 11-2-2013 Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Supported Pd-membranes for H2
With sweep: Dusty Gas Model (DGM):
Pressure drop H2-support:
Diffusion resistance H2-stagnant N2:
Page 24 11-2-2013
Jurriaan Boon et al. (ECN)
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Supported Pd-membranes for H2
Page 25 11-2-2013
Jurriaan Boon et al. (ECN)
low sweep gas flow rate high sweep gas flow rate
With sweep: Comparison of different mass transfer resistances:
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• 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!
Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Dense membranes for O2
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)
Page 27 11-2-2013 Multiphase Reactors Group, SPI
Modelling of membrane permeation
• Dense membranes for O2
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-
Page 28 11-2-2013 Multiphase Reactors Group, SPI
Modelling of membrane permeation
2 2 2O O Oexpn n
ret permact
m
C EN p p
RT
Zhang et al., J. Membrane Science 291 (2007) 19-32
O2 permeation flux through dense perovskite (LaCa)(CoFe)O3-
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
• Dense membranes for O2
Multiphase Reactors Group, SPI
Modelling of membrane permeation
O2 permeation flux through dense perovskite (LaCa)(CoFe)O3-
Model can also accurately predict O2 permeation rate for H2 as
reducing gas assuming local equilibrium of H2 combustion
Page 30 11-2-2013
• Dense membranes for O2
Zhang et al., J. Membrane Science 291 (2007) 19-32
Multiphase Reactors Group, SPI
Page 31 11-2-2013
Different reactor concepts
• Basic classification
Packed bed membrane reactors:
Immobilized catalyst
Fluidized bed membrane reactors:
Particles kept in suspension by fluidum
Multiphase Reactors Group, SPI
Page 32 11-2-2013
Different reactor concepts
• Packed bed reactors:
used for reactions
with small heat effect
Single adiabatic bed used for reactions
with a large heat effect
Multi-tubular reactor
Multiphase Reactors Group, SPI
• Packed bed membrane reactor configurations
Different reactor concepts
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)
Multiphase Reactors Group, SPI
Page 34 11-2-2013
• Phenomenon of fluidization
Different reactor concepts
Multiphase Reactors Group, SPI
Page 35 11-2-2013
• Phenomenon of fluidization
Different reactor concepts
Bubbles (= voids) are formed,
which create excellent mixing
in the fluidized bed
Particles suspended
in a gas stream
behaves as a “fluidum”
Multiphase Reactors Group, SPI
Page 36 11-2-2013
• Fluidization at large scale: Granulation and coating
Different reactor concepts
Multiphase Reactors Group, SPI
Page 37 11-2-2013
• Fluidization at large scale: FCC and olefin polymerization
Different reactor concepts
FCC (Fluid Catalytic Cracking)
Ethylene/propylene
polymerization
Multiphase Reactors Group, SPI
Different reactor concepts
• 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
Multiphase Reactors Group, SPI
Page 39 11-2-2013
• Packed bed and fluidized bed membrane reactors:
Packed bed
membrane reactor
Fluidized bed
membrane reactor
Different reactor concepts
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
Multiphase Reactors Group, SPI
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!!!
Multiphase Reactors Group, SPI
• 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:
Packed bed membrane reactors
Multiphase Reactors Group, SPI
• 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
Packed bed membrane reactors
Multiphase Reactors Group, SPI
• 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!
Packed bed membrane reactors
, ,
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
Packed bed membrane reactors
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
Multiphase Reactors Group, SPI
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
Packed bed membrane reactors
Page 45 11-2-2013
• Combining OCM + SMR in a single dual-function
catalyst particle
Multiphase Reactors Group, SPI
• 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)
Packed bed membrane reactors
Packed bed membrane reactors
• 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:
Fluidized bed membrane reactors
• 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
Fluidized bed membrane reactors
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
Fluidized bed membrane reactors
• Constitutive equations
Page 52 11-2-2013
Effect of internals not accounted for
(correlations not available)!
Multiphase Reactors Group, SPI
Fluidized bed membrane reactors
• 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
Multiphase Reactors Group, SPI
Fluidized bed membrane reactors
• 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
Page 55 11-2-2013 Multiphase Reactors Group, SPI
Fluidized bed membrane reactors
• Discrete Particle Model
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
Page 56 11-2-2013 Multiphase Reactors Group, SPI
Fluidized bed membrane reactors
• Discrete Particle Model
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)
Page 57 11-2-2013 Multiphase Reactors Group, SPI
• 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
Fluidized bed membrane reactors
extraction
addition addition
extraction
Page 58 11-2-2013 Multiphase Reactors Group, SPI
• Flat membrane walls: Effect of gas addition/extraction
40 % 0 % +40 %
Fluidized bed membrane reactors
Correlation bubble
behaviour and
emulsion phase
circulation patterns!
• Flat membrane walls: Effect of gas addition/extraction
40 % 0 % +40 %
Fluidized bed membrane reactors
Page 60 11-2-2013 Multiphase Reactors Group, SPI
• Flat membrane walls: DPM simulations
Fluidized bed membrane reactors
DPM predicts same results as experiments!
Page 61 11-2-2013 Multiphase Reactors Group, SPI
• Submerged membranes
Fluidized bed membrane reactors
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!
Page 63 11-2-2013 Multiphase Reactors Group, SPI