A Multiscale Approach for Modeling Oxygen Production by Adsorption
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publié dans la revue 951 >Editorial 977 >Molecular Simulation of Adsorption in Microporous Materials Modélisation moléculaire de l'adsorption dans les solides microporeux 1049 >A Multiscale Approach for Modeling Oxygen Production by Adsorption Modélisation de la production d'oxygène par adsorption par une approche multi-échelle D. Pavone and J. Roesler 1059 >Bubbles in Non-Newtonian Fluids: A Multiscale Modeling Bulles en fl uide non Newtonien : une approche multi-échelle 1073 >Multiscale Study of Reactive Dense Fluidized Bed for FCC Regenerator Étude multi-échelle d'un lit fl uidisé dense réactif de type régénérateur FCC 1093 >CO2 Capture Cost Reduction: Use of a Multiscale Simulations Strategy for a Multiscale Issue Réduction du coût du captage de CO2 : mise en oeuvre d'une stratégie de simulations multi-échelle pour un problème multi-échelles 1109 >International Conference on Multiscale Approaches for Process Innovation - MAPI - 25-27 January 2012 - Round Table Discussion Conférence internationale sur les approches multi-échelles pour l'innovation des procédés - MAPI - 25-27 janvier 2012 - Comptes-rendus des discussions de la table-ronde
995 >Sulfur Deactivation of NOx Storage Catalysts: A Multiscale Modeling
Empoisonnement des matériaux de stockage des NOx par le soufre :
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IFP Energies nouvelles International Conference
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MAPI 2012: Multiscale Approaches for Process Innovation
MAPI 2012 : Approches multi-échelles pour I'innovation des procédés
A Multiscale Approach for Modeling Oxygen
Production by Adsorption
D. Pavone* and J. Roesler
IFP Energies nouvelles, Rond-point de l'échangeur de Solaize, BP 3, 69360 Solaize - France
* Corresponding author
Re´ sume´ — Mode´ lisation de la production d’oxyge` ne par adsorption par une approche multi- e´chelle —
La production d’oxyge` ne par adsorption peut se re´ ve´ ler plus avantageuse que la cryoge´ nie
classique pour la capture et le stockage du CO2. Dans le cadre du projet europe´ en DECARBit,
nous avons de´ velopp e´ une approche a` trois e´chelles de longueur pour mode´ liser l’adsorption
d’oxyge` ne sur pe´ rovskites.
La plus grande e´ chelle est celle de l’adsorbeur du laboratoire, soit typiquement 0,2 m. A` cette
e´ chelle (10 1 m), l’adsorbeur est suppos e´ 1D homoge` ne. Les variables du mod e`le sont les
compositions (Cbk ðt; xÞ), la tempe´ rature (T ðt; xÞ) et la vitesse des gaz (vðt; xÞ) sachant que les gaz
conside´ re´ s sont N2, O2, CO2 et H2O.
La seconde e´ chelle correspond a` la taille des pellets suppos e´s sphe´ riques qui remplissent
l’adsorbeur. Chaque pellet a un rayon d’environ 5 mm, soit une e´ chelle de 10 3 m. Si rp est la
variable inde´ pendante d’un pellet, et si ce pellet est a` une hauteur (x) dans l’adsorbeur, les
concentrations en gaz dans le pellet d e´pendent de (t, x, rp) soit Cpk t; x; rp . Ceci conduit a` une
dimension de plus que pre´ c e´demment et le mode` le du pellet est donc 2D dynamique, couple´ au
mode` le de l’adsorbeur, lui-meˆ me 1D dynamique.
La troisie` me e´ chelle permet de d e´crire plus finement la structure cristalline des pe´ rovskites. Les
cristaux sont suppos e´s sphe´ riques de rayon 0,5 lm (e´ chelle 10 7 m). Seul l’oxyg e`ne s’adsorbe
dans les cristaux de pe´ rovskite. La concentration en oxyge` ne adsorbe´ de´ pend de sa position
dans le cristal (note´ e rc), de la position du cristal dans le pellet (rp) et de la position du pellet
dans l’adsorbeur (x). D’ou` : Cc2 t; x; rp; rc , ce qui ajoute une troisie` me dimension au mode` le.
Les couplages entre les e´ chelles se font par bilans matie` res, compte´ s comme des termes sources a`
l’e´ chelle supe´ rieure et comme des flux de surface a` l’e´ chelle infe´ rieure.
Pour re´ soudre ce mod e`le impliquant trois sous-mode` les couple´ s de diffe´ rentes dimensions et de
diffe´ rentes e´ chelles, nous avons choisi Comsol Multiphysics. Le simulateur ainsi re´ alis e´ a e´te´
cale´ sur des expe´ riences de laboratoire et ensuite utilise´ pour simuler un proc e´d e´ de taille
industrielle afin de juger de son efficacite´ .
Abstract — A Multiscale Approach for Modeling Oxygen Production by Adsorption — Oxygen
production processes using adsorbents for application to CCS technologies (Carbon Capture and
Storage) offer potential cost benefits over classical cryogenics. In order to model adsorption
processes an approach using three size scales has been developed. This work is being conducted in the
framework of the DECARBit European research project. The first scale is at the size of the oxygen
adsorption bed to be modelled as a vertical cylinder filled with pellets. Its length is 0.2 m
(scale 10 1 m). The bed is homogeneous in the transversal direction so that the problem is 1D
(independent variables t, x). The physics in the process include gas species (Cbk (t, x)) convection
and dispersion, thermal convection and conduction (T(t, x)) and hydrodynamics (v(t, x)). The
gas constituents involved are N2, O2, CO2 and H2O.
The second scale is at the size of the pellets that fill the adsorber and which are assumed to be of
spherical shape with a typical radius of 5 mm (scale 10 3 m). The independent variable for the pellets
is the radius “rp”. At a certain height (x) down in the adsorber all the pellets are the same and are
surrounded by the same gas composition but inside the pellets the concentrations may vary. The state
variables for the inner part of the pellets are the gas concentrations Cpk(t, x, rp). The pellets are so
small that they are assumed to have a uniform temperature. This leads to a 2D transient model for
the pellets linked to the 1D transient model for the bulk.
The third scale looks into the detailed structure of the pellets that are made of perovskite crystallites.
The latter are assumed to be spherical. Oxygen adsorption occurs in the crystallites which have a
radius of about 0.5 lm (scale 10 7 m). All the crystallites at the same radius in a pellet are supposed
to behave the same and because they are spherical, the only independent variable for a crystallite
located at (x, rp) is its radius “rc”. The state variables for the crystallites are then the adsorbed
oxygen concentration Cc2 (t, x, rp, rc). The crystallites are so small that they are assumed to have a
uniform temperature. This leads to a third transient model that is 3D for the crystallite and is linked to
the 2D transient model for the pellets which is itself linked to the 1D transient models for the bulk.
From the larger to the lower scales, the links between the three models are the following: the bulk
concentration and temperature give the boundary conditions surrounding the pellets. The pellet
concentration gives the boundary conditions for the crystallites.
We chose to solve this multiscale approach that requires the coupling of models of different
dimensions in Comsol Multiphysics. The simulator was built to gain knowledge from laboratory
experiments in order to estimate whether oxygen separation from air is realistic or not.
Bulk concentration (mol/m3)
Crystallite oxygen concentration (oxygen #2
Maximum adsorbed oxygen concentration at
equilibrium at PO2 (mol/m3)
Maximum adsorbed oxygen concentration at
infinite oxygen pressure (mol/m3)
Gas thermal capacity (J/mol/K)
Pellet concentration (mol/m3)
Pellet thermal capacity (J/mol/K)
Diffusion coefficient for the adsorbed oxygen
in the crystallites (m2/s)
Dispersion of species (k) (m2/s)
Bulk thermal conductivity (J/m/s)
Bulk porosity (m3/m3)
Volume fraction that can be occupied by the
adsorbed oxygen (m3/m3)
Pellet porosity (m3/m3)
Adsorption flux towards crystallite (mol/m2/s)
Molar flux between bulk and pellets
Desorption flux from crystallite (mol/m2/s)
Component index (-)
Oxygen adsorption constant (m)
Medium permeability (m2)
Gas viscosity (Pa.s)
Number of pellets per cubic meter (1/m3)
Number of crystals per cubic meter of pellets
Adsorbed flux concentration order (-)
Oxygen adsorption order (-)
Desorbed flux concentration order (-)
Oxygen partial pressure at equilibrium with
oxygen concentration (Pa)
Mol flux of species (k) injected in the adsorber
Crystallite radius 2 [0, Rc] (m)
Crystallite external radius (m)
Processes generally involve porous media. They are
natural in the case of reservoir characterization or
can be artificial when heterogeneous catalysts are
involved. Porous media are decimetric to metric in size
for industrial and lab process but knowledge deals with
millimetric or nanometric length scale for pore sizes,
wettability or even more specific in our case,
adsorption ability and diffusibility in perovskite [
Numerical simulators are of course representative of the
highest scale [
To use low level information at the highest scale, some
authors condensate lower level knowledge in some kind
of overall parameters that could be calculated (Thiele
modulus) or estimated on experiments or given by
known correlations [
The Thiele modulus is a calculated parameter. It
consists in an analytical solution of the diffusion from the
bulk to the catalyst pellets. Assumptions make possible
to solve analytically the diffusion and to derive a global
parameter (the Thiele modulus) that takes diffusionnal
limitation into account as a global parameter used at
the reactor level.
Artificial millimetric networks [
] or structured
catalytic reactors [
] are also designed to be representative
of actual porous media. The main advantage is that their
geometrics are simple and fully controlled and large scale
parameters can be derived from these networks through
numerical simulations. Another way to control the
geometrics is to finely measure the solid matrix structure
in order to reconstruct the porous media. Solid matrix
can be described by series of images [
] or by high
resolution computed micro tomography [
]. Large scale
characteristics such as capillary pressure and relative
permeabilities can then be calculated [
geometrics were very popular in the 90’s to describe porous
media geometry [
]. The difficulty with fractals was to
link the large scale parameter to the fractal
decimal dimension that characterizes the pattern.
Barthe´ le´ my et al. [
] mixed fractal and statistical
descriptions of fractured geological layers to derive hydraulic
Another way to integrate multiscales in porous media
is to perform homogenisation techniques on real
equations and variables at the pore scale. Marle [
developed a complete theory to derive generalized
twophase flow in porous media based on the
homogenisation of the Navier-Stocks equations and variables.
] worked on Marle’s equations towards
two-phase Darcy law in porous media while
] completed Marle’s equations by the
derivation of a macroscopic capillary pressure equation for
porous media based on wettability and on solid-liquid
areas. Similar researches were performed by Quintard
and Whitaker [
] by the same time.
The paper presented hereafter is different in the sense
that it solves different length scales simultaneously in a
1D + 2D + 3D numerical simulator. A 2D approach
involving Knudsen diffusion in fuel cells is also described
]. In this case multiscale is solved by a 2D model for
which one dimension is 1.0 9 10 3 m and the other is
4.0 9 10 1 m. Following the same idea, Ingram et al. [
solve a catalytic packed bed reactor using a discretisation
scheme of N pellets exchanging with a bulk solved in
N meshes. Discretisation allows to keep 1D models for
the pellets whereas we solve a 3D model in a continuous
The approach is applied to an oxygen production
process using solid sorbents for application to CCS
technologies (Carbon Capture and Storage). These processes
can offer potential cost benefits over classical cryogenics.
The Ceramic Autothermal Recovery (CAR) process is
one such oxygen production system investigated by
BOC that uses pressure swing adsorption principles.
Here an alternate technology is being researched that
implements the sorbents in a rotating bed and uses the
oxygen partial pressure differences between air and a
sweep gas for collecting the oxygen.
1 MODEL GEOMETRY
One can have knowledge on adsorption and desorption
at deferent size levels. Of course the adsorber can be
described at its own level with its length, injection area,
flow rates, etc.
At a lower scale, the pellet one, other information can
be added like the pellet size, their porosity, internal
diffusion coefficient, etc.
And finally, because a pellet is made of a huge
amount of perovskite crystallites aggregated together,
information like the mean crystal size can be useful. If
it occurs that additional information are available for
the perovskite crystallites such as the oxygen diffusion
parameters and/or the oxygen adsorption isotherm,
these should be integrated at this level.
This is the reason why we need to describe the
adsorber at three different scales, from the bulk to the crystal
going through the pellet one as an intermediate scale.
1.1 The Bulk Sorbent Bed
The fixed bed adsorber is a vertical cylinder filled with
pellets (Fig. 1). On the absorber scale, the bed is
considered globally homogeneous at all axial (vertical)
positions such that the radial (horizontal) gradients are
zero. The state variables for the bulk gas at the sorbent
bed length scale are the gas concentrations Cbk ðt; xÞ,
the pressure Pðt; xÞ, the temperature T ðt; xÞ and the gas
velocity vðt; xÞ. State variables depend on the time “t”
and on the axial position “x”. This leads to a 1D
transient model for the bulk.
1.2 The Pellets
The pellets are actually cylindrical but will be assumed to
be spherical so as to model them with a 1D spherical
symmetry approach. The independent variable for the
pellets is their radius “rp”. The state variables for the
pellets are the concentrations Cpk t; x; rp in the pellets and
the temperature T p t; x; rp . Because the pellets are
relatively small compared to the adsorber size, the
temperature in the pellet is assumed to be homogeneous and
equal to the bulk temperature (T p t; x; rp ¼ T ðt; xÞ).
Pellet state variable Cpk depends on the time “t”, on the
vertical position “x” and on the position inside the pellet
“rp”. This leads to a 2D transient model for pellets.
There is no adsorption or gas reaction at the pellet
scale, only gas transport occurs within the porosity of
1.3 The Crystallites
As presented in Figure 2, a pellet is made of
crystallites that are assumed to be spherical as well. The
independent variable for the crystallites is their radius
“rc”. The state variables for the crystallites are the
absorbed oxygen concentrations Cc2 t; x; rp; rc and
the temperature T c t; x; rp; rc . The “#2” in Cc2 stands
for oxygen that is referred as #2. Because the
crystallites are very small compared to the adsorber size,
the temperature in the crystallites is assumed to be
homogeneous and equal to the bulk temperature
(T c t; x; rp; rc ¼ T ðt; xÞ). The state variable Cc2 depends
on the time “t”, on the axial position “x”, on the
crystallite position inside the pellet “rp” and on the
position inside the crystallite itself “rc”. This leads to a 3D
transient model for crystallites.
Cbk (t, x))
From the sorbent bed to the pellet geometry.
From pellet geometry to crystal geometry.
2 MATHEMATICAL MODEL
2.1 State Variables
The absorber is perfectly characterized by its state
variables which are time (t) and space (x, rp, rc) dependent.
These state variables are:
– species (#k) concentration in the bulk: Cbk ðt; xÞ
– species (#k) concentration in the pellet pores:
Cpk t; x; rp (mol/m3),
– adsorbed O2 (#2) concentration in the crystallites:
Cc2 t; x; rp; rc (mol/m3),
– temperature in the catalyst: T ðt; xÞ(K),
– superficial gas velocity in the bulk: vðt; xÞ(m/s),
– gas pressure: Pðt; xÞ(Pa).
The components are the air components (mainly N2 and
O2) plus a gas for desorption that can be condensed to be
separated from oxygen with two possibilities: CO2 and
2.3 Mass Balance Equations for the 1D Bulk
The bulk gas transport in the bed is convective and
diffusive with a source term (Sbk) that derives from the
gas transfer between the bulk and the pellets:
¼ Sbk with 0
where Cbk (t, x) is the (k) species concentration in the
bulk gas, eb is the bulk porosity and Dbk is the dispersion
of species (k). The molar sources in the bulk flow (Sbk)
occur at the external surface of the pellets and is due to
adsorption/desorption processes within the pellets. The
model assumes that the molar flux is proportional to
the difference between the concentration of a species in
the bulk phase (Cbk (t, x)) and at the surface of the pellets
(Cpk (t, x, Rp)):
Fpk ¼ kpk Cbk ðt; xÞ
where Rp is the radius of the pellet and kpk is the
proportionality factor. The bulk source term can be derived and
calculated as the flux summed over the surface of the
n#c ¼ 4
where np (in #/m3) is the number of pellets per cubic
meter and is derived from the bulk porosity:
Here Vp (in m3/m3) is the volume occupied by the pellets
in one cubic meter of the porous media. By substitution
the source term becomes:
The boundary conditions are standard
DirichletNeumann conditions driven by the flux at the entrance
and convective flux at the exit:
v Cbk þ
where Qin,k is the injected mol flux of species (k):
2.4 Mass Balance Equations for the 2D Pellets
At a distance “x” from the absorber entrance, it is
assumed that the perovskite pellets are spherical and
surrounded by an homogeneous bulk gas mixture. Inside
the pellets, the species transport is only diffusive. The
mass balance equations for the gas phase species are:
where Cpk is the (k) species concentration in the pellet, ep
is the pellet porosity and Dpk is the dispersion of species
(k). Spk is the source terms of species (k) that derives
from the oxygen adsorption and desorption in the
crystallites. As oxygen is #2, Spk ¼ 0 for k #2:
Sp2 ¼ n#cðFa
where n#c (in #/m3) is the number of crystals per cubic
meter of pellets, Fa is the adsorption flux, Fd is the
desorption flux and Rc is the crystallite radius:
The adsorption flux (Fa) is positive in the case of
adsorption and null in the case of desorption. The adsorption
flux tends towards zero when equilibrium is reached.
Inversely, the desorption flux (Fd) is positive in the case
of desorption and null in the case of adsorption. The
desorption flux tends towards zero when the equilibrium
is set as well:
Fa ¼ kaðCc2m
Cc2Þ na if Cc2m
Fa ¼ 0 if Cc2m < Cc2
where ka and na are constant, Cc2 is the adsorbed oxygen
concentration and Cc2m is the adsorbed oxygen
concentration that would be at equilibrium with the oxygen
partial pressure in the pellet (PO2 ).
Cc2m ¼ Cc2M 1 þ KcmPO2 nc
Cc2M is the maximum adsorbed concentration that the
medium can hold under an infinite oxygen partial
pressure and Kcm is a constant together with nc. For the
Fd ¼ kdðPc2m
PO2 Þnd if Pc2m
Fd ¼ 0 if Pc2m < PO2
where Kd and nd are constant, Pc2m is the oxygen partial
pressure that would be in equilibrium with the oxygen
adsorbed concentration in the pellet:
2.5 Mass Balance Equations for the 3D Crystallites
It is assumed that a perovskite crystallite within a pellet
is spherical and surrounded by a homogeneous gas
where Sreac is the adsorber surface.
mixture. Inside the crystallites, adsorbed oxygen can
transfer by some kind of ionic diffusion here described
with a standard Fick’s law. Ionic diffusion between
crystallites is not considered. The mass balance equation is
where ec is a volume fraction that can be occupied by the
adsorbed oxygen and Dc2 is the diffusion coefficient for
the adsorbed oxygen in the crystallites.
The boundary conditions are standard where it is
assumed that there are two oxygen fluxes at the
crystallite boundary, one for adsorption and one for
2.5.1 Molar Balance in the Bulk, Pellets and Crystallites
The molar balance Qk can be calculated with:
Qk ¼ Z heb Cbk þ n#p Qpki Sreac dx
where Qpk is the accumulated mol in one pellet:
ep Cpk þ n#c Qck
4p rp2 drp
where Qck is the accumulated mol in one crystallite:
The boundary condition at the surface of the pellets
simulates the conservation of gas flux from the bulk to the
pellets. Because the length scales of the bulk and the
pellets are not the same, the gas concentration can not be
taken as continuous from one scale to the other. To
account for that the model introduces a jump in the
concentrations and a mol flux proportional to it that
corresponds to the source term of the bulk phase.
¼ kpk Cbkðt; xÞ
2.6 Thermal Equation
As pellets are small, the simulator assumes that the
pellets are homogeneous in temperature and that this
temperature is the same as for the bulk at the same spacial
position. As a result the temperature just depends on
two independent variables (x,t):
ebCpg þ ð1
where Cpg is the bulk gas thermal capacity, Cs is the
pellet thermal capacity and DT is the bulk averaged thermal
conductivity. Qb is the energy source derived from
adsorption and desorption fluxes and the heat of
adsorption or reaction.
The boundary conditions are:
Gas mol fraction at the inlet (O2 and CO2 are equal).
injected (Fig. 3). As a result, oxygen is desorbed and
released from the medium (blue curve in Fig. 4). Then
for a new time period of 45 s, oxygen is injected at the
same amount of 0.21 mol/mol. Normally 0.79 mol/
mol N2 should be injected as well but to give a reference,
CO2 is “numerically” injected as a non adsorbed gas, like
a tracer, to show what would be the oxygen level in the
case of no adsorption. Hence injection is 0.21 O2,
0.21 CO2 (acting as N2) and 0.58 N2.
In Figure 4, we can see the adsorption and desorption
effects looking at the difference between the blue curve
(O2) and the green curve (CO2 acting as a inactive gas).
Looking at the oxygen amount remaining in the
perovskite can give interesting insight into the process.
Figure 5 presents the amount of oxygen still trapped in
T bjx¼0 ¼ T inj
The hydrodynamics just concern the bulk flow. The
model uses the Darcy equation that links the flow
velocity with the pressure head:
Kd is the medium permeability and lg is the gas viscosity.
3 SIMULATIONS AND RESULTS
3.1 Transient Results
Material is a LSCF (Lanthanum Strontium Cobalt
Ferrite) perovskite investigated experimentally in the
framework of the European funded DECARBit project.
The experiments allowed to estimate the model
parameters for the simulations presented here. The calculations
that are presented correspond to cyclic adsorption and
desorption phases lasting 45 s each.
The presented simulation lasts 45 s for desorption and
the same for adsorption. The results are presented in
Figure 3 and Figure 4. At first, the medium is saturated
with air then at time zero and during 45 s, steam is
am tse 0.95
the perovskite compared to the total amount at the
beginning of the desorption. In this example, the figure
shows that the process deals with less than 15% of the
3.2 Instantaneous Results
It is interesting to look at three instantaneous snap shots.
The first one gives the oxygen content in the bulk gas in
the adsorber and is 1D according to the model
construction (Sect. 2.3). The second one gives the oxygen content
in the gas in the pellets and is 2D according to the model
construction (Sect. 2.4). Finally the third one presents
the amount of oxygen adsorbed in the crystallites and
is 3D (Sect. 2.5). This last is a little more complex to
analyze than the two others.
3.2.1 1D Oxygen Mol Fraction in the Bulk at the Adsorber Scale
At the highest scale, the bulk concentrations are quite
easy to understand because they are 1D. Figure 6
presents oxygen concentrations versus adsorber length at
three different times: one at the end of air injection
and the two others just after the switching from air to
steam. The first curve, the upper one, shows that injected
oxygen mol fraction is 0.21 and decreases in the adsorber
due to oxygen adsorption. The two lower curves show
that no more oxygen is injected but due to oxygen
release, the bulk still contains oxygen with a decreasing
amount with the time.
3.2.2 Oxygen in the Gas at the Pellet Scale
Figure 7 gives the oxygen mol fraction in a pellet in the
adsorber (2D map at bottom). The horizontal axis gives
the position of the pellet in the adsorber, from the inlet
(x = 0 at left) to the outlet (x = 0.2 at right). The vertical
axis gives the oxygen mol fraction inside the pellet
located a` x. In the example, the 1D graph gives the
oxygen mol fraction in the gas for a pellet located at
(x = 0.01) from the centre of the pellet to the boundary.
3.2.3 Adsorbed Oxygen at the Crystallite Scale
The 3D graph presented in Figure 8 is complex.
Surprisingly, the adsorber is cylindrical but the graph is
Actually, this graph gives the adsorbed oxygen (in
– in the crystallites located,
– in the pellets,
– in the adsorber.
The vertical dimension is the adsorber length, going
from the inlet (x = 0 m) at the bottom to the outlet
(x = 0.2 m) at the top. The location of the crystallite
in the pellet is given by the horizontal green axis (from
Rp = 0 to Rp = 5 9 10 3 m). The crystallites located
on the pellet surface are presented on the vertical side
at the right of the cube. The ones at the centre of the
pellets are on the opposite hidden surface. And finally the
graph gives also the concentration in the crystallite (from
Rc = 0 to Rc = 0.5 9 10 6 m) along the blue horizontal
The figure presents the adsorbed oxygen just after the
beginning of a new air injection phase. Air is injected
Oxygen profile in a pellet close to the adsorber entrance.
Adsorbed oxygen at the crystallite scale.
upwards at the visible angle (dark red angle in Fig. 8).
We can see on the figure the diffusion of the adsorbed
oxygen in the three directions.
A multi-scale simulator is presented that allows to
account for a metric adsorber (2 9 10 1 m) filled with
millimetric pellets (5 9 10 3 m), each pellet being an
agglomerate of micrometric crystallites (5 9 10 7 m).
The simulator meshes and solves these three length scales
at a time in a 1D model plus a 2D model plus a 3D
model, all linked and coupled together.
This simulator has been adapted to match lab
experiments and can be used as a tool to test the effects of
microscopic parameters such as the crystallite size and
diffusivity on oxygen adsorption and desorption.
This research has received funding from the European
Union’s Seventh Framework Program (FP7/2007-2011)
under grant agreement No. 211971 (the DECARBit
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Manuscript accepted in November 2012 Published online in October 2013