8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
1/12
CHINA PARTICUOLOGY Vol. 3, Nos. 1-2, 113-124, 2005
SIMULATION OF PARTICLE COATING
IN THE SUPERCRITICAL FLUIDIZED BED
Carsten Vogt, Ernst-Ulrich Hartge*, Joachim Werther and Gerd Brunner
Technical University Hamburg-Harburg, D21071 Hamburg, GermanyAuthor to whom correspondence should be addressed. E-mail: [email protected]
Abstract Fluidized bed technology using supercritical carbon dioxide both as a fluidizing gas and as a solvent for thecoating material makes possible the production of thin, uniform and solvent-free coatings. But operation at low fluidizing
velocities, which is favorable to facilitate gas cleaning under the high pressure conditions, may lead to uneven distribution
of the coating in the fluidized bed and to unstable operation due to agglomeration. Therefore a model has been devel-
oped which describes local fluid dynamics within the high pressure fluidized bed. Based on this model, the coating
process is described and the distribution of the coating inside the fluidized bed is calculated. Furthermore a submodel for
the calculation of local concentrations of liquid paraffin has been set up, which may be used as a basis for the prediction
of agglomeration and thus stability of operation.
Keywords particle coating, fluidized bed, supercritical fluid, fluid mechanics
1. Introduction
Coating of particles finds application in, amongst others,
the protection of high-value products, the encapsulation of
hygroscopic or toxic substances, and in the selective or
controlled release of drugs in the pharmaceutical industry
(Kleinbach & Riede, 1995).
Fluidized bed technology using supercritical carbon di-
oxide both as a fluidizing gas and as a solvent for the
coating material makes possible the production of thin,
uniform and solvent-free coatings. Solubility in supercritical
carbon dioxide can be varied easily by changing pressure
and/or temperature, down to practically zero at ambientconditions. Besides, the reduction of surface tension at
high pressures makes the production of thin and smooth
coatings possible. Because of the comparatively low criti-
cal temperature of carbon dioxide of 304 K, coating can be
realized at relatively low temperatures, thus enabling the
coating of temperature-sensitive substances. Therefore,
the combination of the advantages of the fluidized bed
(good solids mixing, reduced risk of agglomerate formation)
with the potentials of a supercritical fluid constitutes a very
promising process for the production of coatings.
The process described in this work follows the RESS
(Rapid Expansion of Supercritical Solutions) process
(Tsutsumi et al., 1995) with the modification that a super-critical solution is expanded into supercritical carbon diox-
ide. Previous work (Schreiber et al., 2002a) showed that
very thin and uniform coatings could be produced using
this method, though often the coatings were incomplete
and agglomerates tended to build up, primarily because of
insufficient mixing in the fluidized bed due to the low gas
velocities used. Gas velocities had to be as low as possible
in order to prevent solids entrainment and thus to minimize
the requirements on expensive gas cleaning under the
high pressure conditions.
To acquire more insight into the coating process, the
fluid mechanics of the fluidized bed and the governing
parameters for uniform coating, a mathematical model of
the process was formulated and validated with experi-
mental results. The model was adapted to the process
operated by Schreiber et al. (2002a). They studied as an
example the coating of glass beads with paraffin. A sche-
matic diagram of their experimental setup is shown in Fig.1.
Into a fluidized bed of glass beads operated with CO 2 un-
der supercritical conditions (8 MPa, 313 K) CO2 is injected
which is saturated with paraffin at a pressure of 24 MPa
and a temperature of 343 K. The injection nozzle is posi-
tioned about 15 mm above the gas distributor on the cen-
terline of the fluidized bed.
Fig. 1 Sketch of the experimental setup used by Schreiber et al.
(2002b).
For modelling of fluid mechanics of fluidized beds dif-
ferent approaches are widely used. Semi empirical ap-
proaches like the two-phase models (e.g. Werther & Wein,
1994) offer the advantage of low requirements for compu-
tational resources and good accuracy for standard ge-
ometries and conditions. A disadvantage of these models
is that they usually assume uniform flow patterns across
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
2/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005114
the bed. Thus the influence of a strong jet on the solids
flow inside a fluid bed cannot be simulated. On the other
hand, there are other models using methods of computa-
tional fluid dynamics (CFD). Here Euler-Euler-approaches
or two-fluid models (TFM) have to be distinguished from
Euler-Lagrange approaches and from the special case ofthe discrete particle modelling (DPM).
The Euler-Euler approach treats the solids as a pseudo
continuous phase. To model particle-particle interactions in
this pseudo-continuous phase, generally the granular the-
ory (e.g. Gidaspow, 1994) is used. Up to now the use of
TFM is restricted to Geldart group B particles, while the
fluidized bed under supercritical conditions behaves more
like a Geldart group A system. The classical
Euler-Langrange approach can not be used for dense
fluidized beds, since for the simulation of the movement of
individual particles within a given gas flow field only the
interactions between particles and gas are considered
while direct particle-particle interactions are neglected.While this approach is valuable for systems with low solids
volume concentrations, direct particle-particle interactions
dominate the flow in dense fluidized beds.
The most fundamental approach among the above men-
tioned models is the DPM approach. Here all individual
particles are tracked simultaneously and collisions be-
tween particles are calculated (e.g. Li & Kuipers, 2003; Ye
et al., 2004). The major drawback of this approach is the
very high requirement for computing resources and the
limitation in the maximum number of particles which can be
treated, e.g., about 105~10
6particles, while the actual
number of 100 m particles in a fluidized bed, 10 cm in
diameter and 10 cm in height, is in the order of 109
.Therefore this approach is yet not suited for reactor mod-
elling.
Some kind of compromise is a model suggested by
Kobayashi et al. (2000), which computes the movement of
bubbles in a fluidized bed on the basis of empirical corre-
lations for their rise velocity, for their coalescence, and for
the interaction between neighbouring bubbles. In contrast,
the surrounding dense suspension (emulsion) phase is
modelled as a pseudo fluid with CFD-methods. A modified
model has been used by Bruhns and Werther (2005) for
the 3D-simulation of the injection of liquids into a fluidized
bed. The model used in the present paper will follow the
same approach, since it allows describing the gross circu-lation of the solids induced by a locally injected jet.
To simulate the coating process itself a model for the
wetting and for the solidification of the paraffin used by
Schreiber et al. (2002a) as coating is added.
2. Theory
2.1 Fluid mechanics of the fluidized bed
The model approach used here assumes the existence
of two phases, a bubble phase and a suspension phase,
respectively. The bubble phase consists of voids free of
solids and the adjacent bubble wake (Fig.2). This bubble
rises in a surrounding suspension phase, which is kept in
the fluidized state by the percolating gas. The suspension
phase is treated as a continuous fluid. Thus the flow of this
fluid can be modelled by means of the Navier-Stokes
equations and mass balance.
bubble phase
suspension phase
Fig. 2 Two-phase model of fluidized bed: the bubble phase consists
of a solids-free void and the wake adjacent to the void.
Since the reactor to be modelled is cylindrical and ra-
dially symmetrical, radial symmetry was assumed and the
model was formulated in polar coordinates. The original
model by Kobayashi et al. (2000) has been extended by
the consideration of solids transport by the bubble wake.
Suspension phase
The density of the suspension or emulsion phase e
can be calculated by
( )e e f e s1 = + , (1)
from the gas density ( )f ,f p T = and the solids density s ,
when the porosity within the emulsion phase e is known.
The porosity of the suspension phase e was found ex-
perimentally in a former work (Vogt et al., 2005) to be in-dependent of pressure. For the glass beads with a mean
surface diameter p,s 169 md = , which are used for the
model validation, the measured suspension porosity was
found to be e 0.525 = .
Fig.3 depicts the flow of the suspension phase into and
out of a single volume element. The mass balance can
accordingly be formulated as the change of mass within
the volume element with time minus the sum of in- and
out-flowing mass flows:
bubble-volume fractionb
rdrvbze
21
( ) rdrdzz
vv
b
ze
ze
21
+
rdzvbre
21
( ) rdzdrrr
vrvb
re
re 21
+
Fig. 3 Flows into and out of the suspension phase in a volume element.
( )e b1 2zv r r d
( )e b1 2rv z r d
b
( )ee d
z
z
vv z
z
+
( )b1 2r r d
( ) ( )ee bd 1 2r
rr vv r z r r r
+ d
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
3/12
Vogt, Hartge, Werther & Brunner: Simulation of Particle Coating in the Supercritical Fluidized Bed 115
( )( )( )( ) ( )( )
e b
e b e b e
1 11 1 .r zr v v m
t r r z
+ + =
(2)
Here the velocity of the suspension phase is denoted by
r
v in radial direction andz
v in vertical direction;e
m denotes
sources and sinks within the emulsion phase and b is
the volume fraction of the bubble phase.
Also the Navier-Stokes equation is written in cylindrical
coordinates. Kobayashi et al. (2000) neglected the con-
vective momentum transport in their model in order to re-
duce computational requirements and to improve the
convergence of the solution. This simplification is possible
when the fluid has high viscosity and only small velocity
gradients. Since in the present case of jet injection high
velocity gradients occur in the vicinity of the jet, this simpli-
fication was not possible. Thus the momentum transport in
radial direction is described by
( )( ) ( )( ) ( )( )
( )( ) ( )( ) ( )
e b e b e b
b b b
e
1 1 1
1 1 11,
r r r
z r
rz rr
r r
v v vv v
t z r
rpF m v
r z r r r
+ + =
+ + +
(3)
and in vertical direction by
( )( ) ( )( ) ( )( )
( )( ) ( )( )( )
e b e b e b
b b
e b e
1 1 1
1 111 .
z z z
z r
zz zr
z z z
v v vv v
t z r
rpg F m v
z z r r
+ + =
+ + +
(4)
Here rF and zF are external forces in the radial and
vertical directions and p denotes the local pressure. For
Newtonian fluids in a radially symmetric system the tension
terms in normal directions are given by
( )
( )
( )
= +
= +
= +
e e
e e
e e
2 12
3
2 12
3
2 12
3
rz zzz
rr zrr
rr z
r vv v
z r r z
r vv v
r r r z
r vv v
r r r z
, (5)
and in tangential direction by
er z
rz zr v vz r
= = + , (6)
where e is the dynamic viscosity of the emulsion. The
viscosity of the suspension has a significant influence on
the simulation results. It may be determined either by fitting
the model to experimental data or it can be taken from
independent measurements which can be found in the
literature. Although no such measurements are available
for fluidized beds under supercritical conditions, meas-
urements at ambient conditions may be used as an ap-
proximation since the viscosity of the fluidizing gas at su-
percritical conditions is close to that under ambient condi-
tions (CO2 at 40 C and 1 bar:41.6 10 = kg(m-1s-1);
CO2 at 40 C and 80 bar:42.2 10 = kg(m-1s-1)), and the
influence of solids properties dominates the viscosity of the
emulsion phase. Therefore measurements by Grace (1970)
under ambient conditions (cf. Table 1) have been used to
determine, by interpolation, the dynamic viscosity.
Table 1 Viscosities of suspension phase measured with air as fluid-
izing gas at ambient conditions (Grace, 1970)
Type of solidsDensity
-3
s (kg m )
Particle size
p,s md
Viscosity
e Pa s
Quartz sand 2650 72 0.7
Quartz sand 2650 140 0.9
Quartz sand 2650 330 1.3
To solve the system of differential equations, boundary
conditions for pressure and for velocities of the suspension
phase have to be given. For the pressure boundary, condi-
tions of the Neumann type can be formulated for the outer,
inner, upper and lower boundaries of the calculation do-
main, that is, the component of the suspension velocity in
normal direction to the boundary is zero, and thus the
pressure gradient normal to the boundary has to be zero:
max
max
0
0
0 0
0 0
z z z
r r r
p p
z z
p p
r z
= =
= =
= =
= =
. (7)
At the upper bound additionally a Dirichlet boundary
condition can be given with
( )max absp z p= . (8)To set the boundary conditions for the velocities, it is
assumed that there is no friction in the suspension phase
at the inner (center) and the upper (bed surface) bounda-
ries. Thus the velocity gradients parallel to these bounda-
ries are set to zero:
max 0
0 0r z
z z r
v v
z r= =
= =
. (9)
At the walls friction between suspension phase and wall
is assumed according to Ding et al. (1992):
max 0
z rz rr r z
v vv v
r z
= =
= =
. (10)
Furthermore the velocities normal to the boundaries areset to zero for all boundaries, i.e. no suspension flows out
of the calculation domain:
= =
= =
= =
= =max max
0 00 0
0 0
r zr z
r zr r z z
v v
v v. (11)
Bubble phase
The mass balance for the bubble phase with volume
fraction b is given by
( ) ( ) ( )bub b bub b bub bbub
1 r zru u mt r r z
+ + =
, (12)
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
4/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005116
where the velocity of the bubble phase is denoted as u,
andbubm is a source or sink within the bubble phase. The
density of the bubble phase bub is the mean density
averaged over the solids-free void and the wake. Assum-
ing that the fraction of the bubble volume taken by thewake is constant for all bubbles, the mass balance can be
simplified to
( ) ( )b bb bubbub
1 r zru u m
t r r z
+ + =
. (13)
The absolute velocity of the bubble phase in the (vertical)
z-direction is defined as
( )0 e bz zu u u u v = + + , (14)
where 0u is the superficial gas velocity and eu is the
superficial velocity (related to the empty tube) of the gas
which percolates through the emulsion. The velocity bu is
the rise velocity of a single bubble calculated according to
Davidson and Harrison (1963) by
b b0.71u gD= . (15)
The superficial gas velocity in the emulsion phase is
calculated following the approach of Hilligardt and Werther
(1986):
e mb
0 mb
1
3
u u
u u
=
, (16)
where mbu is the minimum bubbling velocity, i.e. the low-
est velocity at which bubbles occur.
Closely neighboring bubbles (cf. Fig. 4) will attract each
other (e.g. Clift & Grace, 1984), giving rise to a radial drift
velocity d,ru which increases with decreasing distance.
The intensity of the drift between bubble A and bubble Bis,
according to Clift and Grace (1984), determined by the
distance sa between the centers of the two bubbles
normalized with the bubble diameter bD .
Fig. 4 Radial interaction between two neighboring bubbles.
For the determination of the radial drift velocityd,ru
Kobayashi et al. (2000) and also Bruhns and Werther
(2005) used a number balance for the bubbles in each
volume element and accumulated the interaction between
all individual pairs of bubbles. This approach is hard to use
for a 2-dimensional model as in this work, since the num-
ber of the bubbles over the whole cross-section of the
fluidized bed is needed to calculate the interactions.
Therefore the correlation by Bruhns and Werther (2005)
has been modified such that the bubble volume fraction
instead of the number of bubbles in a volume element isused. With this modification the correlation for the radial
drift velocity is given by
max max 2
sd, b 2 2
b b0 0
1 1 1exp d d
2 22
r
r r z
au s u r r
D D
= , (17)
where sa is the distance between the centers of the two
bubbles (cf. Fig.4) and rs is the distance in radial direc-
tion. These values can be calculated from
( ) ( ) = + 2 22
scos cos sin sina r r r r , (18)
and
cos cosrs r r = . (19)
To get the absolute radial velocity of the bubble phase,
the drift velocity has to be added to the local radial velocity
of the suspension phase, that is,
d,r r ru u v= + . (20)
The bubble diameterbD can be determined by a bub-
ble growth model such as that by Hilligardt and Werther
(1986) for the case of fluidized beds under ambient condi-
tions. In the case of fluidization under supercritical condi-
tions experimental data were used for the determination of
the bubble diameter. According to previous experiments
(Vogt et al., 2005) in supercritical fluidized beds, a constant
bubble size results from a balance between bubble splitting
and bubble coalescence after a very short distance above
the gas distributor. Therefore a constant bubble size of
b7.5 mmD = has been adopted throughout the whole flu-
idized bed.
In the models of Kobayashi et al. (2000) and Bruhns and
Werther (2005) solids are transported only by the flow of
the suspension phase. But measurements of many authors
showed that especially vertical mixing of solids is mainly
due to the transport of solids within the wake of the bub-
bles, that is, solids are taken by the wake from the bottom
region and transported without significant exchange to the
surface of the fluidized bed, where they are released by the
exploding bubbles. Since bubble volume flow is not con-
stant across the bed surface, some radial mixing is also
induced by the solids transport in the wake. This mecha-
nism has been simulated within the model by relating the
sources of bubble gas at the distributor and at the jet with
corresponding sinks for the solids inside the suspension
phase. At the surface of the fluidized bed the sinks for
bubble gas are related to source terms in the suspension
phase balance. The strength of the suspension sinks or
sources is given by the strength of the corresponding gas
sources or sinks and the fraction wf of the bubble volume
which is taken by the wake. According to Werther (1976),
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
5/12
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
6/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005118
sity and viscosity of the fluid and may thus be extrapolated
to the present supercritical conditions:
0.470.6540.5852
f injs p,s 0
f
814.2o
o o o
d ud uL
d d gd
=
. (29)
For modeling the precipitation of the paraffin on the par-
ticles it is assumed that the probability that a paraffin
droplet hits a particle decreases linearly with the distance
from the jet orifice. With this assumption it holds for the
local wetting mass flowspar,inj
( , )m r z :
( )
( )
spray inj( )
par,inj inj
0
inj inj
2 ( , ) d ,
,
r z z
rm r z r c z z
z z z L
=
+
(30)
where cis a proportionality constant, zinj is the height of the
nozzle and rspray(zzinj) is the height dependent radius ofthe spray cone. With the assumption that the entire mass
of injected paraffin per unit time is deposited on the bed
particles within the spray cone with the length L, the con-
stant ccan be determined byinj spray inj
inj
( )
par,inj par,tot
0
2 ( , ) d d
z L r z z
z
rm r z r z m
+
= . (31)
Assuming furthermore that the local wetting mass flows
par,inj( , )m r z is independent of the radial distance from the
jet center for any given distance from the jet orifice, the
local wetting mass flows par,inj( , )m r z can be calculated by
( )
( ) ( )( )
par,inj
inj injinjpar,tot
2 22
injinj
( , )
forsin .tan
0 else
m r zz z z LL z zm
L r L z z z z
=< < +
<
(32)
Solidification of the deposited paraffin
If only the distribution of coating thickness under stable
operating conditions has to be calculated, it suffices just to
model the deposition of paraffin on the particles as de-
scribed in the previous section. Under stable conditions
solidification only takes time, but will not change the dis-
tribution of paraffin on the particles. If the simulation aimsalso at the prediction of stable and unstable operation
conditions, i.e. conditions under which severe agglomera-
tion occurs, the solidification process has to be taken into
consideration. To form agglomerates wet particles have to
come into contact. If the amount of un-solidified paraffin in
a volume element becomes too high, the formation of ag-
glomerates will dominate the destruction of agglomerates
by mechanical stress. On the other hand, the solidified
paraffin will not cause any agglomeration.
The mass of paraffin solidified per unit timepar,sol
m in a
volume element can be estimated by a heat balance: the
heat of solidification has to be balanced by the heat trans-
ferred from the paraffin to the solids plus the heat trans-
ferred to the fluid
( ) ( )par,f f par par par,s s par par sol par,solk T T A k T T A h m + = , (33)
where fT and sT are the temperatures of the fluid andthe solids, respectively;
parT is the temperature of the par-
affin, assumed to be its melting point;solh is the heat of
crystallization, which is released during the solidification;
par,fk and par,sk denote the heat transfer coefficients be-
tween paraffin and fluid and between paraffin and particle,
respectively. The heat transfer coefficient between paraffin
and fluidpar,fk is calculated according to the procedure
given in the VDI-Heat Atlas (1997). For a typical fluidizing
velocity -10.024 m su= and for the heat capacity
4.946pc = kJ(kg-1K-1) and the heat conductivity
0.042 57 = W(m-1K-1) of the supercritical CO2, this
procedure gives the high value ofpar,f
2 800k = W(m-2K-1).
This high value ofpar,f
k implies that the heat transfer be-
tween the paraffin and the fluid will be the dominating
process and the heat transfer between the paraffin and the
particle is negligible. By neglecting this latter process,
Eq.(33) is simplified to
( )par,f f par par sol par,solk T T A h m = . (34)
This simplification allows the calculation of the mass of
solidified paraffin per unit time par,solm without solving a
unsteady-state heat balance around a single particle. The
particle surface parA coated with a layer of liquid paraffin
depends on the mass of liquid paraffinparm in the volume
element and the thickness of the liquid layer s:
par par
par
par
particle
for not completely covered particles
for completely covered particles
V m
s sA
A
=
=
.
(35)
Finally, the mass of liquid paraffin in a volume element is
calculated with the help of Eq.(27), where C is now
defined as the mass of liquid paraffin per unit volume parm
and the source and sink term Cm is given by the mass
flow of injected paraffin as the source and the mass of
solidified paraffin per unit time par,solm as the sink term.
3. Results
3.1 Validation of the fluid-dynamic model
Due to the lack of experimental data obtained under high
pressure, validation of the fluid-dynamic model has been
carried out using data measured in fluidized beds under
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
7/12
Vogt, Hartge, Werther & Brunner: Simulation of Particle Coating in the Supercritical Fluidized Bed 119
ambient conditions. A detailed investigation of the local
flow in fluidized beds was carried out by Werther (1976),
who used capacitance probes to measure local flow prop-
erties at various radial positions in fluidized beds with di-
ameters varying from 0.2m to 1.0m. The experimental
conditions of his experiments are given in Table 2 togetherwith the model parameters used for simulation.
Table 2 Operational conditions used in Werther s experiments
(1976) and model parameters for simulation
Operational conditions (Werther, 1976)
Solids Quartz sand
Solids density s 2 650 kgm-3
Surface-volume mean diameter p,sd 83 m
Gas Air
Gas densityf
1.2 kgm-3
Minimum fluidization velocity mfu 1.810-2 ms-1
Superficial fluidizing velocity 0u 0.09 ms-1Model parameters
Suspension viscositye
(after Grace, 1970) 0.8 Pas
Fraction of visible bubble flow
(Hilligardt & Werther, 1986)0.61
Wake fractionwf (Werther, 1976) 0.18
Figure 6 shows Werthers measurements (1976) of visi-
ble bubble flow. For comparison, the visible bubble flow
has been calculated from the simulation results by
( )b b w1 zv f u= . (36)
-100 -50 0 50 1000.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14 H=30 cm
H=15 cm
H=5 cm
vb
/(ms
-1)
r/mm Fig. 6 Comparison of measured and simulated radial profiles of the
visible bubble flowbv . (bed diameter 0.2 m, bed height 0.5 m,
measurement data of Werther (1976)).
Basically there is satisfactory agreement between the
simulated and the measured profiles. The tendency for the
bubbles to move towards the center with increasing height
is well described, and even the positions of the maxima are
predicted with good accuracy. Only the absolute values for
the visible bubble flow are higher than experimental in the
lower region and lower than experimental in the upper part
of the fluidized bed. This divergence has been observed
also in the simulation by Bruhns and Werther (2005) and
may result from simplifications in the description of the gas
flow through the suspension.
A gross circulation of the suspension, depicted in Fig.7,
is induced by the uneven distribution of the bubble flow as
shown in Fig.6, that is, there is a downward movement ofthe suspension in the vicinity of the walls, and a corre-
sponding upward flow in the center region in addition to
horizontal compensation flows at the top and near the
bottom of the bed. This kind of gross circulation is typical
for fluidized beds with small diameters (Kunii & Levenspiel,
1991).
-0.10 -0.05 0.00 0.05 0.100.0
0.1
0.2
0.3
0.4
0.5
heighth/m
distance from centerline r/m
Fig.7 Calculated suspension flow in a fluidized bed 0.2 m in diameter
and 0.5 m in height.
3.2 Fluid dynamics in the high pressure fluidized
bed
In a second step the fluid-dynamic model has been ap-
plied to the fluidized bed operated under supercritical con-
ditions with the injection of a paraffin-laden CO2-jet. The
dimensions, operating parameters, and gas and solids
properties have been taken from Vogt et al. (2005), as
listed in detail in Table 3. The geometry of the fluidized bed
(cf. Fig.1) has been simplified for the simulation by as-
suming that the gas distributor is in the same plane as the
injection nozzle (Fig.8).
Fig.8 Simplified geometry of the high pressure fluidized bed for
simulation.
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
8/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005120
Table 3 Operational parameters, gas and solids properties and mod-
eling parameters for the simulation of the fluidized bed under
supercritical conditions
Fluidized bed geometry
Diameter 39.4 mm
Bed height 140 mm
Operating conditions
Pressure p 8 MPa
Temperature T 313 K
Fluidizing gas CO2
Fluid density f 277 kgm-3
Fluid viscosity f 2.2310-5
Pas
Bed material Glass beads
Surface-volume mean diameterp,sd 169 m
Solids density 2 485 kgm-3
Minimum fluidization velocitymfu at
operating conditions0.016 ms-1
Minimum bubbling velocitymbu at
operating conditions0.023 ms-1
Fluidizing velocity 0u 0.027 ms-1
Mass flow of injection gas injm 0.46 gs-1
Model parameters
Suspension viscositye 1.3 Pas
Fraction of visible bubble flow 0.61
Wake fraction wf 0.18
Compared to the simulation for ambient conditions a
slightly increased suspension viscosity was used;
e 1.3 Pa s = , due to the higher viscosity of the super-
critical CO2 as compared to that of air under ambient con-
ditions. To study the sensitivity of the simulation againstthis parameter an additional simulation run has been car-
ried out with a lower viscosity.
The results of the simulation are shown in Fig.9 to Fig.11.
Fig.9 shows the visible bubble flow in the high pressure
fluidized bed which is highly dominated by the influence of
the jet. The influence of bubble drift as seen for the at-
mospheric fluidized bed is negligible as compared to the jet.
Only about 5% of the total CO2 mass flow are contributed
by the jet; this highly concentrated flow in a small area is
mostly transported as bubbles through the fluidized bed,
causing a high local bubble flow in the center. Fig.10
shows the corresponding plot of the bubble volume fraction,
high in the center and decreasing towards the walls.Intense circulation of suspension is expected from the
pronounced profiles of bubble flow and bubble fraction, as
can be seen in Fig.11 for the suspension. In the plot on the
left hand side the direction of flow is plotted, in the plot on
the right hand side the velocity, shown in logarithmic scale.
The velocities near the jet are about two orders of magni-
tude higher than those in the upper part. As expected,
circulation with up flowing suspension in the center and
down flowing suspension near the wall exists. But besides
this gross circulation, a second swirl in the bottom part can
be seen, which results from the jet at the centerline. This
lower swirl can not be explained by bubble flow alone
(Fig.9) as it results from the momentum of the jet. The
suspension is accelerated upward by the jet issuing from
the nozzle, where the suspension attains its highest veloc-
ity. For continuity reasons fresh suspension has to flow
along the bottom from the walls towards the center. With
increasing height the momentum disperses and the sus-pension decelerates, thus making the suspension flow
radially away from the center. From the velocity plot it can
be seen that the velocities within this local swirl at the jet
are much higher than those within the gross circulation,
causing intense mixing in the bottom region.
In order to estimate the influence of the suspension
viscosity on the gross flow pattern, another simulation run
was performed with the same parameters as before (cf.
Table 3), except for the suspension viscosity e which has
been changed from e=1.3Pas to e=0.7Pas. This lattervalue is the lower limit of the range of suspension viscosi-
ties experimentally determined by Grace (1970). The re-
sults for the suspension flow calculated with this lowersuspension viscosity are shown in Fig.12. The flow pattern
is very similar to that with the higher suspension viscosity;
except for the slight difference that the jet region is ex-
tended upward. Due to the lower viscosity the high vertical
suspension velocity just above the jet needs greater dis-
tance to be damped out, and thus the high velocity region
is slightly elongated in the vertical direction.
0.000 0.005 0.010 0.015 0.0200.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
h= 0.05 m
h= 0.13 m
visiblebu
bleflow
vb
/ms
-1
r/m
Fig.9 Calculated profiles of visible bubble flow in the high pressure
fluidized bed with a jet (data cf. Table 3).
-0.01 0.00 0.01
0.00
0.02
0.04
0.06
0.08
0.10
0.12
r/m
heighth/m
0
0.0125
0.0250
0.1000
0.1500
0.2000
bubble
volume
fraction
b
Fig.10 Calculated two-dimensional profile of bubble volume fraction
in the high pressure fluidized bed with a jet (data cf. Table 3).
.
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
9/12
Vogt, Hartge, Werther & Brunner: Simulation of Particle Coating in the Supercritical Fluidized Bed 121
-0.01 0.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
r/m
heighth/m
1E-5
6.9E-5
4.8E-4
0.0033
0.023
0.16
1.1
-0.010.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
heighth/m
r/m Fig.11
Simulated flow of the suspension in the high pressure fluidized
bed. Left: direction of flow; right: velocity ( )2 2r zv v v= + of
the suspension phase.
-0.01 0.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
r, m
heighth,m
1E-5
6.922E-5
4.791E-4
0.003317
0.02296
0.1589
1.100
, m/sv
-0.01 0.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
heighth,m
r, m
Fig.12 Simulated flow of the suspension in the high pressure fluid-
ized bed, calculated with a lower suspension viscosity
e=0.7Pas, left: direction of flow; right: velocity
( )2 2r zv v v= + of the suspension phase.
3.3 Paraffin distribution in the fluidized bed
Knowing the fluid dynamics and especially the solids
movement and mixing it is possible to simulate the coating
process and the distribution of the paraffin in the fluidized
bed. This simulation has been carried out for the conditions
which have been experimentally investigated in previous
works (Vogt et al., 2004b; Vogt et al., 2004a), as shown in
Table 4 together with a comparison of measured and cal-
culated values of the paraffin loading of the particles. The
loading X is defined as the mass of paraffin in a sample
related to the mass of solids in that sample,
par solidsX m m= . (37)
Table 4 Comparison of calculated and measured paraffin loading of
particles at 8 MPa and 313 K (experimental values in pa-
rentheses)
Paraffin loading of particlesmass X/ %
u0 /(cms-1
) injm /(gs-1) par,inj/gm Upper region Lower region
2.7 0.46 11.9 4.5 (10.6) 2.6 (2.7)
2.4 0.70 7.7 2.6 (3.8) 1.9 (1.9)
2.5 0.93 8.0 2.8 (2.6) 2.0 (2.2)
2.4 1.49 8.2 3.5 (3.3) 2.9 (2.9)
During the experiments samples of the bed were with-
drawn after shutdown of the fluidized bed and after pres-
sure release. Several samples of about 2 g each were
taken from the top of the bed, The paraffin loading of these
samples were used to get an average value of the loading
in the upper part of the fluidized bed. To get the paraffin
loading in the lower section of the bed, the bed was emp-
tied down to the lower two to three centimeters of the set-
tled bed. Then one sample of about 2 g was taken from the
center just above the nozzle.
To get comparable values from the simulation, the cal-
culated loadings of the uppermost 3 cm of the fluidized bed
have been averaged and used as the value of the paraffin
loading of the upper section. For the lower region of the
bed the average loading in a cylindrical region with 1 cm
diameter and at a height of about 2 cm starting 1 cm above
the jet was used.
The values of the measured and the calculated paraffin
loadings are plotted in Fig. 13. The plot shows a good
agreement between calculated and measured values for
the loading in the upper region. Also in the lower region the
agreement is reasonable, only at low injection flows there
is some discrepancy which might be related to agglomera-
tion of particles observed during the experiments with low
injection flows. Such agglomeration increases the ten-
dency of segregation, particularly at the low fluidizing ve-
locities of about 2.5 cms-1, which is quite close to theminimum bubbling velocity umb=2.3 cms
-1. At this low ve-
locity solids mixing by the fluidizing gas is quite weak and
calls for the assistance of the jet.
0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.02
0.04
0.06
0.08
0.10
experiment simulation
lower region
upper region
paraffinloadingX
Fig.13 Calculated and measured paraffin loading Xversus injection
mass flow injm .
v/(ms-1)
v/(ms-1)
r/mr/m
he
ighth/m
heighth/m
Injection mass flow injm /(gs-1)
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
10/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005122
Figure 14 portrays the development of paraffin distribu-
tion in the fluidized bed with time for the run with a low
injection mass flow of -10.46 g sinjm = . Basically the same
pattern is to be observed in all the three plots consisting of
a zone with high paraffin loadings at the center and above
the jet, and dwindling paraffin loadings toward the wall.
Obviously vertical mixing is much more effective than
horizontal mixing. While the pattern of the distribution does
not change much with time, the absolute values do vary. In
order to better resolve the gradients in all the three plots,
their scales have been adjusted individually. The absolutevalues of the minimum and maximum concentrations in-
crease nearly linearly with time.
From the simulations it follows that it is difficult to
achieve uniform distribution of the paraffin coating with low
fluidizing velocities, even in a small apparatus as was used
for the present experiments. If such low velocities are
necessary, at least a high injection mass flow should be
used in order to enhance solids mixing.
All the calculations presented up to now deal only with
solid paraffin, while the solidification process is not taken
into account. Such calculations allow the prediction of the
homogeneity of the coating process, but they give no in-
formation as to the stability of the process. From experi-ments it is known that under certain conditions, such as
low fluidizing velocity, high paraffin concentration in the
injection gas and low mass flow of the jet, the system tends
to form large agglomerates, which may cause defluidiza-
tion of the bed. Such formation of agglomerates will occur if
too much liquid paraffin is present in a volume element. In
such a case the probability of collision of two wet particles
each with a layer of liquid paraffin will increase. Such a
collision of two wet particles may lead to the formation of a
liquid bridge between the particles, which will solidify to
become a stable bonding. To acquire more information
about the mass of liquid paraffin within the fluidized bed,
simulations have been carried out which include the injec-
tion and the solidification of the liquid paraffin. Results of
such simulation run with 0 2.4u = cms-1
and a quite high
injection mass flow of inj 1.49m = gs-1
are depicted in
Fig. 15. Due to fast solidification, liquid paraffin can be
observed only in the immediate vicinity of the jet, even
though the mass flow of the injected paraffin is quite. Al-
though, according to Bruhns and Werther (2005) it would
be expected that the spray angle in the fluidized bed is
nearly the same as outside in free air, the spreading of theliquid paraffin in the high pressure fluidized bed is wider,
possibly because of the swirl flow of the suspension near
the bottom.
0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
r/m
h
eighth/m
2.5E-7
2.9E-5
5.7E-5
8.6E-5
1.1E-4
1.4E-4
1.7E-4
2E-4spray angle = 20
o
Fig. 15 Paraffin loading on the solids, 30 seconds after injection
-1 -1
0 inj( 2.40 cm s , 1.49 g s )u m= = . The spray angle fol-
lows the measurement outside the fluidized bed (Schreiber
et al., 2002b).
-0.01 0.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
r/m
1.0
1.2
1.3
1.5
1.7
1.9
2.0
2.2
X/%
-0.01 0.00 0.010.00
0.02
0.04
0.06
0.08
0.10
0.12
r/m
heighth/m
0.50
0.59
0.67
0.76
0.84
0.93
1.0
1.1
X/%
-0 .01 0.00 0 .010.00
0.02
0.04
0.06
0.08
0.10
0.12 2.0
2.4
2.7
3.1
3.5
3.9
4.2
4.6
after 45 minafter 22 minafter 11 min
r/m
X/%
Fig. 14 Development of paraffin distribution in the fluidized bed with time
-1 -1
0 inj( 2.72 cm s , 0.46 g s )u m= = .
2.5E7
2.9E5
5.7E5
8.6E5
1.1E4
1.4E4
1.7E4
2E4
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
11/12
Vogt, Hartge, Werther & Brunner: Simulation of Particle Coating in the Supercritical Fluidized Bed 123
More investigations are needed to validate these latter
results and to formulate a stability condition, which will
allow the prediction of the range of stable operating condi-
tions.
4. ConclusionsFor the prediction of product quality and for deeper un-
derstanding of the coating process in a fluidized bed oper-
ated under supercritical conditions, a model has been de-
veloped, which combines CFD-methods with semi empiri-
cal models. This hybrid-model uses the full set of conser-
vation equations for the description of the suspension flow,
while for the description of the bubbles well proven
semi-empirical models are utilized. This approach allows
the simulation of the fluid dynamics within a high pressure
fluidized bed with quite low computing requirements. Fur-
thermore the distribution of the paraffin and the uniformity
of the paraffin loading on the particles can be described
with good accuracy. In combination with a model of the
solidification of the paraffin, the instantaneous loading of
the fluidized bed with liquid paraffin can also be predicted.
These latter simulations can be used as the basis for the
prediction of stable operating regimes.
The calculations show that the central jet dominates the
flow structure in the fluidized bed and that it significantly
enhances solids mixing. Therefore the homogeneity of the
paraffin distribution depends strongly on a sufficiently high
jet mass flow and thus a high jet momentum. First simula-
tions of the spreading and solidification of the liquid paraffin
show that only in the close vicinity of the jet, can liquid
paraffin be found. Provided the jet mass flow is sufficiently
high, the formation of stable agglomerates in this region
will be suppressed by the high shear forces, which result
from the jet.
Acknowledgement
This work was funded by the German Research Foundation
(Deutsche Forschungs Gemeinschaft, DFG) under grant No. WE
935 / 7-1. The authors gratefully acknowledge this support.
Nomenclature
A area, m2
C tracer concentration, kgm-3d0 diameter of jet outlet opening, m
Db bubble diameter, m
Dr, Dz dispersion coefficients in radial and vertical direc-
tion, ms-1
dp,s mean surface diameter of solids, m
fw fraction of the bubble volume taken by the wake
g gravity, ms-2h height above gas distributor, m
H height of fluidized bed, m
kw heat transfer coefficient, W(K-1m-2)L penetration depth of the jet, m
m mass, kg
m mass flow, kgs-1
p absolute pressure, Pa
r radial distance from the center line, m
Re Reynolds number
s thickness of layer, m
sr separation distance between two bubbles in radial
direction, m
t time, sT temperature, K
u0 superficial velocity of fluidizing gas, ms-1
uinj jet outlet velocity, ms-1ur, uz velocity of the bubble phase in radial and axial di-
rection, ms-1vr, vz velocity of the suspension phase in radial and axial
direction, ms-1V volume, m
3
z vertical distance from the distributor plate, m
Greek letters jet angle,
porosity of the fluidized bed
b,0 bubble volume fraction at the distributor plate
b bubble volume fraction
e porosity of the suspension phase
s sphericity of the particles
f dynamic viscosity of the fluid, Pas
e dynamic viscosity of the suspension phase, Pa s
coefficient of friction
b density of the bubble phase, kgm-3
e density of the suspension phase, kgm-3
f density of the fluid, kgm-3
paraffin density of paraffin, kgm-3
s solids density, kgm-3
viscous stress, Pa
Indicesb bubble, bubble phase
e suspension (emulsion) phase
max maximum value
mb conditions of onset of bubbling, minimum bubbling
point
mf minimum fluidization conditions
p particle
r radial direction
z axial (vertical) direction
ReferencesBasov, V. A., Markhevka, V. I., Melik-Akhnazarov, T. K. & Orochko,
D. I. (1969). Investigation of the structure of a nonuniform fluid-
ized bed. Int. Chem. Eng., 9, 263-266.
Bruhns, S., (2002). On the Mechanism of Liquid Injection into
Fluidized Bed Reactors. PhD thesis, Hamburg University of
Technology, Hamburg.
Bruhns, S. & Werther, J. (2005). 3-D modeling of liquid injection
into fluidized beds: flow structure, solids mixing, heat and mass
transfer. Chem. Eng. Sci., in press.
Clift, R. & Grace, J. R. (1984). Continuous bubbling and slugging.
In Harrison, D. (Ed.), Fluidization. London: Academic Press.
Davidson, J. F. & Harrison, D. (1963). Fluidized Particles. Cam-
8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed
12/12
CHINA PARTICUOLOGY Vol.3, Nos.1-2, 2005124
bridge: Cambridge University Press.
Ding, J., Lyczkowski, R. W., Burge, S. W. & Gidaspow, D. (1992).
Three-dimensional models of hydrodynamics and erosion in
fluidized bed combostors. AIChE Symp. Ser., 88(289), 85-98.
Gidaspow, D. (1994). Multiphase Flow and Fluidization. Boston:
Academic Press.
Grace, J. R. (1970). The viscosity of fluidized beds. Can. J. Chem.Eng., 48, 30-33.
Hilligardt, K. & Werther, J. (1986). Gas flow in and around bubbles
in gas fluidized beds local measurements and modellingconsiderations. World CongessIII of Chem. Eng. (p.429-432),
Tokyo, Japan.
Kleinbach, E. & Riede, T. (1995). Coating of solids. Chem. Eng.
Process., 34, 329-337.
Kobayashi, N., Yamazaki, R. & Mori, S. (2000). A study on the
behavior of bubbles and solids in bubbling fluidized beds.
Powder Technol., 113, 327-344.
Kunii, D. & Levenspiel, O. (1991). Fluidization Engineering. Bos-
ton: Butterworth-Heinemann.
Li, J. & Kuipers, J. A. M. (2003). Gas-particle interactions in dense
gas-fluidized beds.Chem. Eng. Sci.
, 58, 711-718.
Merry, J. M. D. (1975). Penetration of vertical jets into fluidized
beds. AIChE J., 21, 507-510.
Schreiber, R., Reincke, B., Vogt, C., Brunner, G. & Werther, J.
(2002a). Fluidized bed coating at supercritical fluid conditions. J.
Supercrit. Fluids, 24 (2), 137-151.
Schreiber, R., Reincke, B., Vogt, C., Werther, J. & Brunner, G.
(2002b). High pressure fluidized bed coating utilizing super-
critical carbon dioxide. Proc. World Congress Particle Tech-
nology 4, Sydney, Australia.
Tsutsumi, A., Nakamoto, S., Mineo, T. & Yoshida, K. (1995). A
novel fluidized-bed coating of fine particles by rapid expansion
of supercritical fluid solutions. Powder Technol., 85, 275-278.
VDI-Heat Atlas (1997). Duesseldorf: VDI Verlag.
Vogt, C., Hartge, E.-U., Werther, J., Schreiber, R. & Brunner, G.
(2004a). Simulation der Beschichtung von Partikeln in einer mit
berkritischem Fluid betriebenen Wirbelschicht. In Teipel, U.(Ed.), Produktgestaltung in der Partikeltechnologie (pp.245-
258). Stuttgart: Fraunhofer IRB Verlag.
Vogt, C., Schreiber, R., Werther, J. & Brunner, G. (2004b). Influ-
ence of hydrodynamics on fluidized bed coating at supercritical
fluid conditions. In Arena, U., Chirone, R., Micchio, M. &
Salatino, P. (Eds.), FluidizationXI (pp.51-58). Brooklyn: ECI.
Vogt, C., Schreiber, R., Brunner, G. & Werther, J. (2005). Fluid
dynamics of the supercritical fluidized bed. Powder Technol.,
accepted.
Werther, J. (1976). Convective solids transport in large diameter
gas fluidized beds. Powder Technol., 15, 155-167.
Werther, J. & Wein, J. (1994). Expansion behavior of gas fluidized
beds in the turbulent regime. AIChE Symp. Ser., 90(301),
31-44.
Yang, W.-C. & Keairns, D. L. (1979). Estimating the jet penetration
depth of multiple vertical grid jets. Ind. Eng. Chem. Fundam., 18,
317-320.
Ye, M., van der Hoef, M. A. & Kuipers, J. A. M. (2004). A numeri-
cal study of fluidization behavior of Geldart A particles using a
discrete particle model. Powder Technol., 139, 129-139.
Manuscript received March 7, 2005 and accepted March 24, 2005.
Top Related