Simulation of Particle Coating in the Super Critical Fluidized Bed

8/8/2019 Simulation of Particle Coating in the Super Critical Fluidized Bed

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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


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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


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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



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)


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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),


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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


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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.


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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).

.


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-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)


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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


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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-


12/12


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.

Simulation of Particle Coating in the Super Critical Fluidized Bed

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