1. The document studies the effect of operating pressure on particle motion near the wall in a fluidized bed. Luminescent pigment was used to illuminate particle clusters and their movement was analyzed using digital imaging. 2. Preliminary experiments showed particle residence time at the wall decreases with increasing fluidization velocity. Further experiments analyzed particle motion at similar fluidization velocities but varying operating pressure. 3. The results indicate operating pressure has some influence on particle motion for Geldart A particles near the wall, with higher pressures resulting in faster particle exchange and shorter residence times, as seen through the decay and shifting of illuminated particle clusters along the wall over time.

1. Particle Motion near the Wall of a Fluidized Bed at Elevated
Pressure
Igor Sidorenko, Art Yew Looi, and Martin Rhodes*
CRC for Clean Power from Lignite, Department of Chemical Engineering, Monash University,
Victoria 3800, Australia
The influence of operating pressure on the motion of particles near the fluidized-bed wall surface
was studied for Geldart group A and B particles using luminescent pigment as bed solids in a
vessel of diameter 146 mm. A pulse of bright light transmitted from outside the pressure vessel
via fiber optics was used to illuminate a 7-mm-diameter region of the bed particles adjacent to
a transparent vessel wall. Digital image analysis of the motion of the illuminated region of bed
particles and its decay in luminosity permitted the determination of the influence of pressure
on a particle exchange frequency in the direction perpendicular to the wall surface, the mean
particle residence time at the wall, and the velocity of bed solids adjacent to the wall. These
findings are related to the observations of the effect of pressure on bed-to-surface heat transfer
in fluidized beds reported by other workers.
1. Introduction
One of the attractive features of bubbling fluidized
beds from a design viewpoint is their excellent heat-transfer
properties. Gas-to-particle heat transfer is
normally very efficient because of the high surface area
of the particulate phase. More interesting is heat
transfer between the bed material and solid surfaces
such as walls or immersed surfaces. Since the 1970s,
considerable attention has been given to research in the
field of fluidized-bed combustion and gasification of solid
fuels at elevated pressure. The operating conditions of
combustion boilers and reaction chambers of gasifiers
involve high bed temperatures (1023-1173 K) and
increased fluidizing gas pressures (up to 2 MPa). Under
these conditions, heat transfer between a surface and
a fluidized bed has a rather complex conductive-convective-
radiative character1 and is presented as a
sum of three independent components: particle convec-tive,
gas convective, and radiative.2 The main factors
in the heat transfer between a surface and a fluidized
bed are the movement of particles close to the surface
and their residence time at the surface.
According to Botterill,2 the good heat-transfer proper-ties
of fluidized beds are the result of the high heat
capacity of bed particles and their mobility. At temper-atures
below 873 K, when the radiative heat-transfer
component is negligible, the particles in the bulk of the
fluidized bed exchange heat by gas-phase conduction
and stay in the bulk of the bed long enough to reach
the same temperature as their neighboring particles.
When some of the particles are swept into close
proximity with the heat-transfer surface, there is a high
local temperature gradient between the surface and the
particles. The longer the particles stay at the surface,
the more their temperature approaches the surface
temperature, which leads to a reduction in the local
temperature gradient and the effective rate of heat
transfer. The highest rates of heat transfer between a
surface and a fluidized bed are obtained, therefore, when
there is rapid exchange of material between the heat-transfer
region and the bulk of the bed, i.e., when
particle residence times at the surface are very short.
However, it is common for vertical surfaces to become
covered by the downward return flow of solids. In 1953,
Toomey and Johnstone (in ref 2) described the now well-known
appearance of particle motion close to the wall,
in which there is upward flow of particles through the
center of the column induced by bubbles and compara-tively
slow downward flow at the wall. In general,
material adjacent to the wall is only occasionally
disturbed by rising bubbles and slugs that penetrate to
the wall.
According to Borodulya et al.,1 one of the most well-known
empirical correlations for calculating the maxi-mum
bed-to-surface heat-transfer coefficient h was
proposed by Baskakov and Panov,3 and it predicts a
strong dependence of the conductive component on
pressure. However, this fact was not confirmed by
extensive experimental studies.4
Several researchers studied the influence of pressure
on convective heat transfer between fluidized beds and
surfaces (e.g., refs 5-12). Convective heat transfer in
fluidized beds of fine particles is not expected to change
much with pressure, as was, in fact, observed by Xavier
et al.11 and Barreto et al.5
Convective heat transfer can be characterized by a
dimensionless parameter, the Nusselt number. To de-scribe
heat-transfer experiments under different condi-tions,
Borodulya et al.1 analyzed the results available
in the literature and proposed a relation that combines
the Nusselt number at maximum conductive-convec-tive
heat transfer (hgc + hpc), the Galileo number Ga,
and the Prandtl number Pr
where cp and cg are the specific heat capacities of
particles and gas, respectively.
* To whom correspondence should be addressed: Martin
Rhodes, Department of Chemical Engineering, Monash Uni-versity,
VIC 3800, Australia. Tel.: Int ++61-3-9905-3445.
Fax: ++61-3-9905-5686. E-mail: rhodes@eng.monash.edu.au.
Numax ) 0.4Ga0.16(Fp
Fg)0.14(cp
cg)0.3
+ 0.0013Ga0.63 Pr
(1)
5562 Ind. Eng. Chem. Res. 2004, 43, 5562-5570
10.1021/ie030777b CCC: $27.50 © 2004 American Chemical Society
Published on Web 04/23/2004

2. According to Borodulya et al.,1 eq 1 is valid for
particles in the size range from 100 ím to 4 mm and
the operating pressure range from atmospheric to 10
MPa. The exponents of the Galileo number and the
density ratio in eq 1 are almost equal, and the depen-dence
of the particle convective heat-transfer coefficient
on pressure is very weak.
Because the gas convective heat-transfer coefficient
is proportional to the square root of gas density,
fluidization at elevated pressures is expected to enhance
this component. Experimental confirmation of higher
heat-transfer coefficients in pressurized fluidized beds
of coarse particles can indeed be found in the literature
(e.g., refs 7, 8, 11, and 13).
The experimental data presented by Borodulya et al.13
show that the effect of pressure increases with particle
size. A pressure increase from 1100 to 8100 kPa resulted
in a 29% increase in the maximum heat-transfer coef-ficient
for 126-ím sand particles, a 110% increase for
1.22-mm sand particles, and a 140% increase for 3.1-
mm glass ballotini.
For particles less than 500 ím, the effect of pressure
on the bed-to-surface heat transfer is considered to be
negligible.2,14 However, according to Molerus and Wirth,9
heat transfer clearly depends on pressure within the
range of particle sizes from 50 ím to 1 mm, and the
influence of particle motion on heat transfer should
manifest itself in a similar pressure dependence.
Here, we present the results of a study of the
influence of operating pressure on the motion of par-ticles
near the fluidized-bed wall surface for Geldart
group A and B particles using luminescent pigment as
bed solids in a vessel of 146-mm diameter. The results
are analyzed, and the implications for heat-transfer
modeling are considered.
2. Experimental Method
The process and instrumentation diagram of the
pressurized fluidized bed used in this study of the effects
of pressure on fluidization is given elsewhere.15 The
pressure vessel, capable of operating at pressures up
to 2600 kPa, was 2.38 m high and was equipped with
five glass observation ports. The fluidized-bed vessel
was 146 mm in diameter, had transparent walls of
Perspex, and was inserted into the pressure vessel and
positioned vertically. Fluidizing gas for the experiments
was supplied either from a building compressed air
supply or from dedicated nitrogen and compressed air
cylinders and metered by variable-area flow meters. The
variable-area flow meters had an accuracy class 1.6,
according to German Standard VDI/VDE 3513 Part 2,
and were properly compensated for differences in gas
properties at different operating pressures and temper-atures.
The operating pressure in the fluidized bed was set
with a back-pressure control valve. The experimental
facility was of an open circuit type so the same gas was
used for pressurizing the system and for fluidizing the
solids. The apparatus was pressurized to the desired
operating pressure before the fluidizing gas flow rate
was adjusted to a desired value.
With transparent side walls of the fluidized-bed
column, direct observation of the motion of particles
along the wall was possible through one of the pressure
vessel’s observation windows. Experimental observation
of the motion of particles near the wall surface was
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5563
Figure 1. Experimental setup for studying particle motion along
the wall.
based on the pulsed-light method described by Molerus
and Wirth.9
The motion of particles at the wall surface was
visualized by using particles of a luminescent pigment
as bed solids. Six kilograms of the original luminescent
pigment Lumilux (pigment A), with a Sauter mean
diameter of 62 ím, was used for charging the fluidized
bed in the series of experiments with a Geldart A
material. To study the particle motion in a bed filled
with a Geldart B material, 6 kg of the agglomerated
pigment (pigment B), with a Sauter mean diameter of
234 ím, was used.
A well-known method of measuring the dependence
of the bed pressure drop on the superficial gas velocity
was used to establish the experimental values of the
minimum fluidization velocity. For pigment A, the
minimum fluidization velocity was 0.003 m/s and inde-pendent
of pressure. For pigment B, the minimum
fluidization velocity decreased from 0.112 m/s at atmo-spheric
pressure to 0.103 m/s at 1300 kPa.
A pulse of bright light from a conventional photoflash
with an adaptor was transmitted from outside the
pressure vessel via a specially made fiber-optic light
guide. The flash illuminated a 7-mm-diameter spot of
the luminescent bed material adjacent to a transparent
fluidized-bed vessel wall inside the pressure vessel.
After illumination, the spot, consisting of a cluster of
particles, showed an afterglow for several seconds. The
fiber-optic light guide was positioned in such way that
the illuminated spot was at approximately mid-height
of the bed level and could be clearly seen through one
of the observation windows (Figure 1).
A digital video camera was mounted in front of the
window and covered with some lightproof fabric. All of
the remaining observation windows were blocked so that
it was completely dark inside and only the illuminated
spot on the black background was visible through the
camera viewfinder.
Under packed-bed conditions, the illuminated spot
was still visible after 3 min. When the bed was fluidized,
the illuminated spot shifted along the wall surface while
its shape deformed and its luminosity decreased. How-ever,
the illuminated particles stayed in close proximity
as a cluster, and the spot remained a single identifiable
object until it disappeared from the field of view. When
an image disappeared from view, it could be assumed
that, depending on the gas velocity, the image either
moved out of the camera view or its brightness dimin-ished.

3. Experiments were carried out at different gas veloci-ties
up to 15 times the minimum fluidization velocity
under various pressure conditions. The pressure range
was from atmospheric to 2100 kPa for experiments with
pigment A and up to 1600 kPa for experiments with the
agglomerated pigment B. However, because of the
relatively high material density and the gas supply
limitations, it was not possible to fluidize pigment B at
velocities well above the minimum fluidization velocity
at operating pressures higher than 800 kPa.
At the predetermined operating pressure and gas
velocity, an experiment proper consisted of illuminating
a small cluster of particles with the photoflash and
filming the spot until it disappeared. At each gas
velocity, at least 10 separate flashes were recorded, and
the fate of each illuminated spot was analyzed sepa-rately
using image analysis techniques.
3. Data Analysis
The images of the illuminated spot were captured by
a digital video camera at a rate of 25 frames per second.
Digital videos were downloaded onto a dedicated com-puter
and edited in order to extract separate frames and
organize them in stacks for each light pulse. Image
analysis was then carried out to quantify the statistics
of particle movement near the wall surface. Each pixel
of the image was characterized by its X and Y coordi-nates
and luminosity, expressed in dimensionless form
on a grayscale, where 0 is black and 255 is white. From
filming a reference ruler in daylight, it was determined
that, on the linear scale, each pixel was equal to 0.25
mm.
Under packed-bed conditions, it was observed that the
cluster of illuminated particles remained visible as an
unmoving spot decreasing in intensity with time. The
initial step in digital data analysis involved discrimina-tion
of illuminated spots from the rest of the bed
material. In general, the procedure for this image
identification involves examination of the histogram of
grayscale values for a normal image consisting of both
illuminated spot and dark background. Because the
lighting conditions were uniform and the image contrast
was quite high, accurate detection of the image bound-ary
was possible using the global thresholding method.16
As a result, it was found that applying a grayscale
threshold (Lthreshold) of 60 accurately characterized il-luminated
spots while they were visible.
On each frame, the following data for the illuminated
spot were obtained: image area; mean, maximum, and
minimum luminosity within the image threshold; and
X-Y coordinates of the center of gravity of the image.
More than 160 000 files were processed, and the results
were organized for separate light pulses at each gas
velocity. Further statistical analysis was performed
using special software, where for each gas velocity data
from 10 to 14 flashes were averaged and plotted and
nonlinear regression was applied.
Because the detection of clusters depended on their
visibility, it could be possible that the disappearance of
images resulted from loss of material luminosity with
time or possibly from the mixing of clusters. A simple
analysis showed that the light source had enough power
to sufficiently illuminate a spot and the material had
sufficient luminosity that the illuminated object could
still be observed by the end of each test.
The effect of particle motion in a fluidized bed on
cluster maximum luminosity compared to that in a
Figure 2. Decay of maximum image luminosity on a grayscale
in a packed bed of pigment A compared to fluidized bed at
atmospheric pressure (fluidization gas velocity U ) 0.012 m/s).
packed bed is illustrated in Figure 2. In both cases, the
luminosity decay was found to be exponential in time;
however, the rate of decay was much higher in the
fluidized bed. It was found that the motionless il-luminated
spot in the packed bed was clearly visible for
at least 100 s (2500 frames), and some afterglow could
be distinguished on the dark background even after
3 min.
In comparison, the experiments showed that, in a
fluidized bed, the illuminated spot always became
invisible in less than 4 s (100 frames). On the basis of
such a large difference between the natural material
luminosity decay and the luminosity loss during fluidi-zation,
it was assumed that the luminosity decay during
fluidization is caused only by the fact that the il-luminated
cluster particles move away from the wall
and are replaced by dark particles.
Although the natural material luminosity decay with
time for agglomerated pigment B was less than that for
the original pigment, it was still much greater than the
image luminosity decay during the fluidization experi-ments.
4. Particle Motion at Similar Fluidizing
Velocities
Some influence of operating pressure on pigment A
particle motion near the fluidized-bed wall can be
illustrated through the results of experiments carried
out at similar fluidization velocities at different pres-sures.
The gas fluidization velocity in the following
examples equals approximately 5 times the minimum
fluidization velocity.
As can be seen in Figures 3-7, the illuminated spot
shifts down along the wall surface while its shape
deforms and luminosity decreases.
These images (Figures 3-7) were produced by super-imposing
all of the separate frames during the image
lifetime, and they show the motions of the illuminated
clusters of particles along the wall surface. These images
are typical, and similar observations were made under
different operating conditions. Some qualitative conclu-sions
emerge from the visual analysis of these results.
For example, in these videos, the direction of motion of
the illuminated clusters of particles was observed to be
downward, as expected.
5564 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

4. As can be seen in Figure 3, at ambient conditions, the
illuminated cluster travels down along the wall and
disappears from the camera view. Its brightness de-creases
slightly, but the image is expected to be visible
at the wall for some time after it disappears below the
camera view. It seems that, under the given experimen-tal
conditions, the majority of cluster particles move
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5565
downward in close proximity to the wall and only a
small number of particles are replaced by particles
coming from within the bed.
At higher operating pressures, the motion behavior
appears to change. Although the clusters also move
downward, they do not disappear below the camera
view. The brightness of the clusters decreases much
more quickly, and it appears that the lateral mixing
becomes predominant and the illuminated particles
move inside the bed. With increasing pressure, this
behavior becomes stronger (Figures 4-7).
In an attempt to quantify these observations, the
decay of mean luminosity of the illuminated clusters at
different pressures and similar gas velocities for pig-ment
A is presented in Figure 8.
In all cases, the luminosity decay was found to be
exponential in time. A number of linear and nonlinear
regression models were tested, and it was found that
an exponential decay model17,18 predicted the experi-mental
data very well. The following equation was used
for the decay model
where the function of luminosity on a grayscale (L)
starts at an initial level of span (L0 - Lthreshold) above a
constant plateau (Lthreshold) and decays with time (t) to
the plateau (Lthreshold) at a rate constant (k). The value
of the plateau (Lthreshold) was determined by the thresh-old
applied to the images during the processing.
One of the characteristic parameters of an exponential
decay model is the half-life, which is the time it takes
for the parameter (L), or image luminosity, to drop by
one-half. In the case presented in Figure 8, the half-life
decreased from 0.62 s at atmospheric pressure to
0.11 s at 2000 kPa. For comparison, the half-life of the
natural luminosity decay of pigment A established in
the packed bed was 41.84 s.
5. Particle Motion at Similar Fluidizing
Velocities
5.1. Analysis of Experimental Data. As illustrated
above (Figure 2), the increased rate of decay in luminos-ity
in a fluidized bed, compared to that in a packed bed,
is attributed to the fact that the originally illuminated
Figure 3. Image trajectory for pigment A at atmospheric pressure
and a gas velocity of 0.012 m/s (actual size).
Figure 4. Image trajectory for pigment A at 500 kPa and a gas
velocity of 0.011 m/s (actual size).
Figure 5. Image trajectory for pigment A at 1100 kPa and a gas
velocity of 0.011 m/s (actual size).
Figure 6. Image trajectory for pigment A at 1500 kPa and a gas
velocity of 0.011 m/s (actual size).
Figure 7. Image trajectory for pigment A at 2000 kPa and a gas
velocity of 0.011 m/s (actual size).
Figure 8. Difference between mean image luminosities on a
grayscale for pigment A at different operating pressures and
similar fluidization velocities.
L - Lthreshold ) (L0 - Lthreshold) exp(-kt) (2)

5. particles move away from the wall during the fluidiza-tion
process and are replaced by particles coming from
the rest of the bed.
Using the rules for conditional probability, Molerus
and Wirth9 deduced an equation for the exchange
frequency of particles, f, perpendicular to a solid surface.
It was postulated that the probability, W(t), that a
particle in contact with the wall at time t ) 0 moves
inside the fluidized bed is proportional to the time
interval ¢t, i.e., equivalent to f¢t. Using the initial
condition when W(0) ) 1, Molerus and Wirth9 obtained
the following equation:
This equation indicates that the luminosity decay L,
related to the initial brightness L0, directly corresponds
to the constant slope of the curve and the parameter f
can be determined by plotting ln(L/L0) versus time:
Using the area of the original illuminated spot and the
particle size, the initial number of the illuminated
particles next to the bed wall, np0, can be estimated from
the following relationship
2
4
2
4
where dp is the mean particle diameter, D0 is the
diameter of the illuminated spot, and is bed voidage.
According to Molerus and Wirth,9 the illuminated spot
diameter D0 is equivalent to the fiber-optic diameter,
which is true only if the fiber optic is positioned
perpendicular to the wall surface right against it.
However, positioned in this way, the fiber optic would
completely block the original illuminated spot, so that
filming and further image analysis of the original spot
would not be possible. For clear view in this study, the
3-mm-diameter fiber optic did not touch the wall surface
and was positioned at a slight angle in such way that,
in a packed bed, the diameter of the initial illuminated
spot was 7 mm.
Using eq 5 and experimentally obtained values of the
bed voidage at the initial conditions, the original
number of illuminated particles was estimated to be
around 6375 for pigment A and around 260 for pigment
B.
Because the luminosity decay in a fluidized bed is
caused by the motion of particles, Molerus and Wirth9
estimated the number of particles in an image with
luminosity L from L/np ) L0/np0 as follows:
In this study, using the image threshold value of 60 and
eq 6, the final number of particles left at the wall can
be estimated at 21 for pigment A and just 1 for pigment
B.
Comparing eq 2 to eq 4 shows that the rate constant
k determined above corresponds to the particle exchange
frequency f defined by Molerus and Wirth.9
5.2. Mean Residence Times of Particles at the
Wall. The mean residence time of illuminated particles
near the wall was deduced by Molerus and Wirth9 as
the reciprocal of the particle exchange frequency f. The
mean residence time ô, established in this work as the
reciprocal of rate constant k, is shown in Figure 9 for
pigment A and in Figure 10 for pigment B.
For pigment A, as can be seen in Figure 9, mean
residence times measured close to the wall decrease
with increasing gas velocity in the range 3-10Umf and
become practically independent of gas velocity in vigor-ously
bubbling fluidized bed.
The values of the mean residence time settle at below
0.1 s, which means that, during the experiments, the
illuminated images disappeared within only three frames
on video and could not be measured with higher ac-curacy.
Considering the experimental error of (0.04 s,
it is not possible to establish any significant effect of
pressure on particle residence times at the wall.
As previously mentioned, the highest rates of heat
transfer between a surface and a fluidized bed are
obtained when the particle residence times at the
surface are very short. Therefore, from Figure 9, it can
be estimated that the typical mean residence times
measured close to the wall at maximum heat transfer
W(t) ) exp(-ft) (3)
ln(L
L0)) -ft (4)
np0
ðdp
) (1 - )
ðD0
(5)
np ) (1 - )(D0
dp)2(L
L0) (6)
Figure 9. Mean time between pigment A particle illumination
and departure from the wall versus gas velocity at various
operating pressures.
Figure 10. Mean time between pigment B particle illumination
and departure from the wall versus gas velocity at various
operating pressures.
5566 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

6. are practically independent of pressure and approxi-mately
equal to 0.1 s.
This result, however, does not agree well with the
experimental data presented by Molerus and Wirth,9
who observed the following mean residence times of
illuminated particles with a size of 50 ím at vertical
solid surfaces in a fluidized bed at maximum heat
transfer: 1.28 s at 100 kPa, 0.35 s at 500 kPa, 0.52 s at
1000 kPa, and 0.45 s at 2000 kPa. Contrary to their
claim that the heat transfer clearly depends on pressure
and expectations of a similar pressure dependence on
particle motion, there is no clear trend in their data,
but the magnitude is considerably higher than the
values measured in the present work.
For pigment B, the investigated range of superficial
gas velocities was much narrower and did not exceed
2Umf at atmospheric pressure. As was found with
pigment A, mean residence times measured close to the
wall for pigment B were found to decrease with increas-ing
gas velocity (Figure 10).
Again, no significant effect of pressure on the particle
residence times at the wall can be observed in the
somewhat limited range of experimental pressures and
velocities. However, absolute residence time values are
again lower than those observed by Molerus and Wirth9
for a similarly sized material.
In their work, it is not clear how the illuminated
image was distinguished from the background. If they
applied linear regression to the luminosity decay curve,
plotted in semilog coordinates for the whole image
grayscale (0-255), as opposed to the nonlinear regres-sion
for only the visible image threshold presented here,
then that could possibly produce different results.
5.3. Relating Contact Time to Heat Transfer. In
practice, it is common for fluidized beds to contain fixed
surfaces to extract heat. For fluidized-bed combustion,
the important heat-transfer surfaces are vertical and
horizontal heat-transfer tubes immersed in the bed. By
using internal cooling tubes, a large total heat-transfer
surface can be obtained. The effect of pressure on heat
transfer from the bed to the immersed horizontal tube
was investigated by Olsson and Almstedt,10 who found
a significant increase in the heat-transfer coefficient
with increasing operating pressure.
One way of evaluating the impact of the observed
mean particle residence times at the wall is to use them
in conjunction with the cluster renewal model developed
for bubbling fluidized beds by Mickley and Fairbanks.19
According to this model, it was found that, for the
particle convective heat-transfer component hpc, the
following equation holds20
where ä equals the distance between the illuminated
particles and the wall; ìg is the gas thermal conductivity
of this gap; ô is the time during which particles are
moving in contact with the wall before moving into the
bulk of the bed; and ìp, Fp, and cp are the thermal
conductivity, density, and specific heat capacity of the
particles, respectively.
The only gas-related parameter in eq 7, the gas
thermal conductivity ìg, is independent of pressure for
the ideal (perfect) gas. For real gases, however, the gas
thermal conductivity is a rather complex function of
pressure and temperature, and usually increases with
an increase in either pressure or temperature.21 Ignor-ing
the effect of the gas gap, the particle convective heat-transfer
component hpc is proportional to ô0.5.
For Geldart A solids, Figure 9 shows that, at super-ficial
gas velocities below 0.015 m/s, the mean residence
times slightly decrease with pressure, and therefore, the
particle convective heat-transfer component is expected
to increase slightly with elevated pressure. However,
with a further increase in gas velocity, the mean
residence times reach a minimum value and are not
influenced by pressure. Thus, the particle convective
heat-transfer coefficient should also reach a maximum
in a bubbling bed that must be dependent only on
particle physical properties and not on operating pres-sure
or superficial gas velocity, provided a certain gas
velocity is exceeded.
This observation of the effect of pressure is in line
with findings of other workers2,5,11,22 who did not observe
much variation in the particle convective heat transfer
for small particles at pressures above atmospheric.
According to Borodulya et al.,1 the weak dependence of
the conductive-convective heat-transfer coefficient on
pressure in fluidized beds of small (less than 1 mm)
particles is a well-known experimental fact, although
some researchers would probably disagree.9
The present work forms part of a larger program in
which the operation of a pressurized steam-fluidized-bed
dryer was studied. The program included a study
of the influence of operating pressure on fluidized-bed-wall
heat transfer. A comprehensive account of this
work can be found in Looi et al.23 Analysis of these
results24 shows that the particles on the heat-transfer
surface are at thermal equilibrium with the heat source
such that the mechanism of heat removal is left to the
wall-to-gas route. Consequently, any further increase
in the gas velocity from the incipient conditions would
raise the wall-to-bed heat-transfer coefficient. This
phenomenon remains prevalent for ratios between the
Reynolds and Archimedes numbers of Re/Ar 0.002,
at which point particle mobility from the heated wall
becomes significant. When the fluidized bed becomes
vigorously bubbling, i.e., Re/Ar 0.002, there is no
further increment in the heat-transfer coefficient for
systems with Ar 100. This observation shows that,
when the Ar value is sufficiently high, the buoyancy
effect dominates over the inertial effect. This leads to
the tendency of particles to migrate radially away from
the heat-transfer wall. These heat-transfer results are
consistent with the observations made in the study of
particle motion reported here, namely, that there is
minimal bubbling effect such that very little particle
migration occurs on the heat-transfer wall when the
superficial gas velocity is low. As the gas velocity is
increased, the particle migration from the heat-transfer
wall becomes more rapid and hence results in a greater
wall-to-bed heat-transfer rate.
6. Particle Motion Velocity
6.1. Observation of Particle Motion Parallel to
the Wall. Solids motion in bubbling fluidized beds is
driven by bubbles, which carry particles upward in their
drifts and wakes. This upward flow of solids is balanced
by a downward solids flow that occurs in regions where
there are no bubbles.
Previously presented images (Figures 3-7) represent
the summations of separate frames during the image
lifetimes and show typical trajectories of the illuminated
1
hpc
) ä
ìg
+x ðô
ìpFpcp
(7)
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5567

7. clusters of particles along the wall surface. Similar
observations were made under different operating con-ditions.
As expected, the predominant direction of
movement of the illuminated image along the wall was
downward.
On each frame, the X-Y coordinates of the center of
gravity of the illuminated image were also obtained. For
each image, the variation of the center of gravity in the
vertical and horizontal directions with time was plotted
and analyzed. Visual analysis of all plots representing
image motion in the vertical direction (downward) and
in the horizontal direction (sideways) at various operat-ing
conditions showed that the axial movement was
approximately linear.
Initial X0-Y0 coordinates correspond to the center of
gravity of the original image at the time of light impulse
t ) 0, and the final Xn-Yn coordinates describe the
center of gravity of the disappearing image at the time
equal to the mean residence time t ) ô. The distance
travelled by the image during the mean residence time
was established as (Xn - X0) in the horizontal direction
and as (Yn - Y0) in the vertical direction.
Axial particle motion velocities were obtained for each
light impulse at various operating conditions by dividing
these distances by the corresponding mean residence
time. Resulting velocities were then averaged according
to the operating conditions and plotted.
6.2. Axial Particle Motion Velocity at Elevated
Pressures. Vertical Velocity. The main direction of
the illuminated spot movement was downward, and the
vertical image velocity is plotted in Figure 11 for
pigment A and in Figure 12 for pigment B.
For pigment A, the particle migration velocities Uy
along the wall in the vertical direction were oriented
downward and reached a maximum value of about 0.08
m/s at atmospheric pressure. At operating pressures
above 500 kPa, the particle migration velocities Uy along
the wall in the vertical direction are much lower than
those obtained at ambient conditions. Some trend for
the vertical motion velocity to decrease with increasing
operating pressure can be observed in Figure 11. Similar
results can also be qualitatively estimated from the
image trajectories presented in Figures 3-7.
For pigment B, the particle motion velocities Uy along
the wall in the vertical direction were also oriented
downward and reached a maximum value of only about
0.004 m/s at atmospheric pressure. Within the studied
range, no effect of pressure on the vertical particle
motion velocity could be established (Figure 12).
Horizontal Velocity. Because the predominant move-ment
of the illuminated image was downward, the
particle motion velocity in the horizontal direction was
much smaller for pigment A (presented in Figure 13 on
the same scale as Figure 11) and practically nonexistent
for pigment B.
This observation is in line with the experimental
results of Bellgardt and Werther,25 who found at ambi-ent
conditions in a large fluidized bed that vertical solids
mixing was at least 1 order of magnitude higher than
lateral mixing.
In a bubbling fluidized bed with pigment A as the bed
material, some apparently random horizontal deviation
off the vertical axis was observed while the illuminated
image shifted downward. As shown in Figure 13, in
general, lateral particle migration velocities Ux lower
than 0.01 m/s were measured. Although small by itself,
the horizontal movement of the illuminated cluster at
operating pressures above 700 kPa was less obvious
than at ambient conditions.
Figure 11. Particle motion velocity in the vertical direction versus
superficial gas velocity at various operating pressures for pig-ment
A.
Figure 12. Particle motion velocity in the vertical direction versus
superficial gas velocity at various operating pressures for pig-ment
B.
Figure 13. Particle motion velocity in the horizontal direction
versus superficial gas velocity at various operating pressures for
pigment A.
5568 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

8. 7. Conclusions
Major factors in the heat transfer between a wall and
a fluidized bed are the movement of particles close to
the wall and their residence time at the wall. Experi-mental
measurement of particle motion in a bubbling
fluidized bed can provide a better understanding of wall-to-
bed heat transfer.
The influence of operating pressure, up to 2100 kPa,
on the motion of Geldart A and B particles near the
fluidized-bed-wall surface was studied using lumines-cent
pigment as bed solids. Digital image analysis was
applied to the experimental data with the aim of
quantifying the statistics of particle motion near the
wall. Image analysis of the movement of the illuminated
cluster of particles gave its statistically determined axial
velocities along the surface, and the decay in luminosity
defined the particle exchange frequency in the direction
perpendicular to the wall surface.
For both Geldart A and B solids, no significant effect
of pressure on particle residence times at the wall within
the vigorously bubbling fluidized bed was established.
This observation is in line with findings of other
researchers who observed minimal variation in the
particle convective heat transfer for small particles at
pressures above atmospheric.
Solids motion in bubbling fluidized beds is driven by
bubbles, which carry particles upward in their drifts and
wakes. This upward flow of solids is balanced by a
downward solids flow that occurs in regions where there
are no bubbles. As expected, the predominant direction
of movement of the illuminated image along the wall
was downward. For Geldart A solids, the particle
migration velocities along the wall in the vertical
direction were much lower at operating pressures above
500 kPa than at ambient conditions. For Geldart B
solids, within the pressure range and narrow range of
gas velocities studied, no pressure effect on the vertical
particle motion velocity was established.
Acknowledgment
We gratefully acknowledge the financial support
received for this research from the CRC for Clean Power
from Lignite, which is established under the Australian
Government’s Cooperative Research Centres Scheme.
Nomenclature
Ar ) Archimedes number
cg ) specific heat capacity of the gas
cp ) particle specific heat capacity
dp ) mean particle diameter
D0 ) diameter of the illuminated spot
f ) particle exchange frequency (eq 3)
Ga ) Galileo number
hgc ) particle conductive heat-transfer coefficient
hpc ) particle convective heat-transfer coefficient
k ) rate constant (eq 2)
L ) luminosity on a grayscale
Lthreshold ) threshold level of luminosity on a grayscale
L0 ) initial level of luminosity on a grayscale
np ) number of the illuminated particles
np0 ) initial number of illuminated particles (eq 5)
Nu ) Nusselt number
Pr ) Prandtl number
Re ) Reynolds number
t ) time
Umf ) superficial gas velocity at incipient fluidization
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5569
Uv ) particle motion velocity along the wall in the vertical
direction
W(t) ) probability that a particle is in contact with the wall
at time t (eq 3)
W(0) ) probability that a particle is in contact with the
wall at time t ) 0 (eq 3)
X ) x coordinate of the center of gravity of the illuminated
image (section 6.1)
Y ) y coordinate of the center of gravity of the illuminated
image (section 6.1)
) bed voidage
ä ) distance between illuminated particles and the wall
ìg ) gas thermal conductivity of the gap ä
ô ) time during which particles are moving in contact with
the wall
ìp ) thermal conductivity of the particles
Fp ) particle density
ìg ) gas thermal conductivity
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Received for review October 16, 2003
Revised manuscript received February 18, 2004
Accepted February 26, 2004
IE030777B
5570 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004