determination of bubble diameter and axial velocity for a polyethylene fluidized bed using x-ray...

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Powder Technology 1

Determination of bubble diameter and axial velocity for a polyethylene

fluidized bed using X-ray fluoroscopy

Ian Hulmea, Apostolos Kantzasa,b,*

aDepartment of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive, Calgary, Alberta, Canada T2N 1N4bTomographic Imaging and Porous Media Laboratory, Calgary, Alberta, Canada T2N 1N4

Received 10 July 2003; received in revised form 15 July 2004; accepted 10 August 2004

Available online 2 November 2004

Abstract

Gas–solid fluidized bed reactors have many industrial applications and have been studied extensively. Yet despite the amount of research

on the subject there is considerable disagreement to their behaviour. Part of the disagreement is due to the varied techniques used to examine

them. In this study we are examining, using non-intrusive techniques, the hydrodynamics of a partially scaled down reactor used in the

production of polyethylene. In particular, we are using digital fluoroscopy to determine the properties of bubbles that form in the reactor. The

goal of the research is to develop a tool that can be used to validate CFD models. The first part of the paper examines the tools used and

software developed to study the properties of the bubbles. The second part of the paper discusses results from experiments conducted using

glass beads (150 to 250 Am) and polyethylene particles (mean diameter of 850 Am and density of 650 kg/m3 with a wide particle size

distribution), which were used to validate the developed experimental technique and software using correlations in literature.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Gas–solid; Fluidized bed; X-rays; Bubble diameter; Bubble axial velocity

1. Introduction

Due to the contact between the solid and gas, gas–

solid fluidized bed reactors are ideal for processes that

require inter-phase contact. These reactors find many

applications for coating, drying, adsorption, and catalytic

reactions, to mention a few. Despite their widespread use,

and the large amount of literature dealing with these

reactors, they are not fully understood. As a result, many

of the design criteria used for these reactors are empirical.

Also, there are problems when scaling these reactors.

Because most of the research is conducted on laboratory

scale reactors, some people question the usefulness of

these results for industrial reactors. Yet, despite the

criticism of laboratory scale data, this data remains one

of the only means for validating computational fluid

0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2004.08.008

* Corresponding author. Tel.: +1 403 2205752; fax: +1 403 2825060.

E-mail address: [email protected] (A. Kantzas).

dynamic models, which is considered by many to be the

next design tool.

There are many interesting properties that can be

measured in these reactors. However, the flow of gas,

whether in the form of bubbles or emulsion, is one of the

most important factors determining the behaviour of a

fluidized bed [1]. Many design parameters, in gas–solid

fluidized bed reactors, require knowledge of the bubble

diameter. The mass and heat transfer coefficient of Davidson

and Harrison [2], Kunii and Levenspiel (1969), Sit and

Grace (1981), and Peters et al. (1982) cited in Hatzantonis et

al. [3] all require the bubble diameter and are important

design equations. As a result, many attempts have been

made to understand the behaviour of the gas phase, and in

pa rticular the bubbles, starting from the btwo-phaseQ theoryof Toomey and Johnstone [4], the Davidson theory for

bubble movement (1961), and the Geldart classification of

fluidized particles [5].

Early work on visualizing bubbles centred on two-

dimensional columns. However, due to the narrow width,

47 (2004) 20–33

Fig. 1. Picture of the experimental setup.

I. Hulme, A. Kantzas / Powder Technology 147 (2004) 20–33 21

wall effects are considerable and the applicability of the

results to a three-dimensional column is questionable. While

the emphasis shifted to developing experimental techniques

to determine the properties of bubbles in cylindrical

columns, most of the data available in open literature is a

result of studying a limited number of bubbles. Often

studies are conducted using probes inserted into the column,

which disturbs the shape of the bubbles. While non-

intrusive techniques have been developed to study the

behaviour of the gas phase, they have not been applied to

study the behaviour of a large number of bubbles in a

bubbling bed.

Due to the limited amount of information in literature

dealing with the measurement of bubble properties, and the

smaller amount of information on bubble properties for low

density particles, laboratory measurements were needed.

Not only were new measurements needed, but a new

technique needed to be developed that could capture and

analyze a statistically relevant number of bubbles. The result

was an experimental system, X-ray fluoroscopy, that can

capture real time footage of bubble movement, and software

that can analyse this data. The number of bubbles studied is

approximately 10,000 for each run. These experimental

results can be used as a tool to compare with the results

obtained from computational fluid dynamics. While other

parameters can be used, bubble size and velocity provide a

good basis for comparison of process conditions and model

parameters.

2. Experimental setup

2.1. General configuration

The experiments were conducted on a scaled down gas–

solid fluidized bed reactor used for the production of

polyethylene. The reactor is 0.1 m in diameter and 1.0 m in

height with a disengagement zone. Fig. 1 shows the

experimental setup with the column outlined.

The column is made of Plexiglas which allows for

visual confirmation of what is observed used X-ray

fluoroscopy. The vessel was fitted with a porous plate

distributor through which air, at ambient conditions, was

passed at varying superficial gas velocities. Gas ve-

locities ranged from 2.5 to 3.5 times minimum fluidiza-

tion for the polyethylene solid bed (minimum fluidization

velocity is 7.7 cm/s). The lower value of 2.5 times

minimum fluidization was chosen since bubbling

was not observed below this velocity and above 3.5

times minimum fluidization the bed was predominantly

slugging.

2.2. X-ray analysis

Images of bubble movement were obtained using X-ray

fluoroscopy. The generator was an MPX 100 with the

bucky (X-ray tube, table and intensifier) being a GE

RFXII. The tube operates from 60 to 120 kVp and an

image intensifier transforms the X-rays into visible light

for display. The field of view of the image intensifier is a

circle of diameter 0.135 m. As a result of the image size,

three different camera heights were required to capture the

movement of bubbles throughout the solids bed of

approximately 0.4 m in height. The images were captured

at a rate of 30 frames/s using a Matrox Meteor II frame

grabber for 2 min, and a high speed hard drive was used in

order to store the large amount of data resulting from the

images. Fig. 2 is a sample image obtained using X-ray

fluoroscopy.

Once the images were acquired they were processed off

line using software developed in house.

2.3. Bed material

The solid phase used in these experiments was a linear

low-density polyethylene (LLDPE), which has the same

appearance as laundry detergent. The sample used has a

wide particle size distribution ranging from particles less

that 100 Am, to particles larger than 1500 Am with a volume

mean diameter of 850 Am. The bulk density of the

polyethylene particles, measured in the laboratory, was

approximately 650 kg/m3 (Wright, 1999). The polyethylene

particles are porous and irregular in shape, as shown in

Fig. 3.

In addition to the LLDPE, experiments were also

conducted using glass beads to validate the software

Fig. 2. A sample image from X-ray fluoroscopy.

I. Hulme, A. Kantzas / Powder Technology 147 (2004) 20–3322

developed for this work. The glass beads had a size

distribution ranging from 150 to 250 Am.

3. Software to analyze experimental results

In order to retrieve information from the images obtained

using fluoroscopy, software had to be developed. Two

different programs were written; one identifying the bubbles

and the other tracked the bubbles from frame to frame.

Identifying bubbles automatically required the use of image

processing tools, while tracking the bubbles required certain

brulesQ be developed to account for bubble actions.

3.1. Image processing goal

For this research, the objective is to develop an

algorithm, using image processing tools, to automate the

detection of bubble boundaries. Previous work to determine

bubble boundaries was based on visual inspection [6],

calibration wedge [1,7] and minimum entropy [8]. The

criterion for detecting bubble boundaries, in this study, is

based on visual inspection. Many different algorithms were

Fig. 3. Micro CT picture of a 650 Am polyethylene particle showing the

non-spherical shape and porous nature.

attempted to determine the most accurate and repeatable

method for bubble identification. Pictorially, the imaging

objective is shown in Fig. 4 where the original image with

poor contrast and noise is processed to produce the final

binarized image from which data can be extracted.

Through a series of imaging operations the bubble

boundaries are identified. While a reduction of the random

noise can be done with smoothing and opening and closing

operations [9] to remove constant noise in the system a

background subtraction was required. Noise, perhaps is not

the best description for the constant noise in the system

because it is due to several factors such as object geometry,

X-ray beam geometry and heeling effect.

3.2. Background subtraction

The object geometry can affect the path length of the X-

ray. Since the object is circular, the beams traveling through

the edge of the column will go through less material than the

centre. As a result, the beam will attenuate less according to

the Beer–Lambert relationship and there will be a gradient

from dark in the middle to bright on the side.

I ¼ I0exp � lqlð Þ ð1Þ

A conical X-ray beam increases this gradient. The last

effect is called the heeling effect [10]. Due to the X-ray

anode angle, there is a brighter spot on the right hand side of

the image, which is present in our system. As are result of

these phenomena, a correction must be made to ensure

uniform intensity across the image. To accomplish this, a

background subtraction was performed.

While background subtraction initially seems simple,

there are some complications. The first obvious complica-

tion is creating a background image. The background image

in this work was constructed by averaging a series of images

from the run. The theory is that, if the bubbles are randomly

occurring, the brightness created by them in each frame

should average out when a sequence of frames is averaged.

Previous attempts were made to use images from a non-

Fig. 4. The image on the left is the original cropped image obtained from

the fluoroscopy unit and the image on the right is the final image with the

bubbles identified after image processing.


fluidized column. However, this was not useful for the

algorithm used in this study to determine the bubbles. The

algorithm used in this study revolves around subtracting the

background from an image and being left with only bright

regions, or bubbles. Since a packed bed has a higher bulk

density than a fluidized bed, because of decreased voidage,

the images are darker. Since a dark image has lower pixel

intensity values, upon subtraction additional pixels remain.

Therefore further modifications are necessary. Operating the

bed at minimum fluidization and to obtain a background

image resulted in similar problems. The background image

was an average of 200 frames chosen mid way through the

experimental run. This minimized any potential intensity

variations caused by the X-ray source or image intensifier.

3.3. Segmentation

Typically, when images are segmented, to separate an

object from the background, a global threshold is used. This

means that the user specifies a greyscale value so that every

value either above or below (or sometimes in between two

values) is the region of interest and is therefore separated

from the image. The reason that global thresholding does

not work in this study is due to the wake of the bubbles.

Since a wake is present on all bubbles, care has to taken

when distinguishing between small bubble and the wake

around large bubbles. It should be noted that the wake of the

small bubbles is proportionally less than large bubbles [11].

If global thresholding is used, it tends to either over-predict

Fig. 5. The steps for determining the bubble b

the size of the large bubbles and identify the smaller

bubbles, or under-predict the size of large bubbles and not

identify small bubbles. Since the amount a beam is

attenuated is due in part to the amount of material along

the length of the X-ray beam, it can shown that the amount

of mass along a beam that passes through the wake of a

large bubble can be greater than or equal to the amount of

mass along a beam that passes through a small bubble.

Local thresholding uses successive erosion and logic to

determine the number of bubbles in an image. Fig. 5 shows

the steps involved when separating the bubbles.

The image chosen for this example is one that after

examining the images before and after five separate bubbles

were identified. The present algorithm works by taking the

original image and eroding the boundaries until the bubbles

are separated. Stepping through the images in Fig. 5, Fig. 5a

is the original image. This image is binarized and the result

is stored in a separate image buffer, Fig. 5f. The original

image is then eroded by one intensity value as shown in Fig.

5b. This image is binarized and also stored in a separate

buffer as shown in Fig. 5g. This image is then compared to

the previous binarized image to see if any new bubbles have

appeared. If any new bubbles are found, they are stored in

the binarized buffer as only the bubble that is separated is

changed while the other bubbles maintain their maximum

size. This continues for five iterations until the final image

has separated the bubbles as seen in Fig. 5j. Five iterations

were chosen after examining many frames and determining

when bubble separation had occurred and when bbubblesQ

oundaries based on local thresholding.

Fig. 7. Picture showing the difference between the real bubble’s centre of

gravity and the calculated centre of gravity based on the image frame.


were being artificially created by intensity variations in the

real bbubblesQ.The last step in determining bubble boundaries is to

superimpose the final binarized image as onto the back-

ground subtracted image and to threshold the image at

30% of the maximum intensity of each individual bubble.

A sensitivity test was done on this and was found to be the

best value based on visual inspection and matching

correlation.

3.4. Tracking bubbles from frame to frame

The output file from the bubble identification program

is a text file that contains the frame number and individual

bubble properties for all the captured frames. Additionally,

each bubble is given a label, one to the number of bubbles

in the frame. The bubbles are labeled sequentially as they

are met, scanning left to right and top to bottom. Problems

arise if bubbles coalesce, break-up, go out of the frame,

come into the frame, appear or disappear. This is because

these actions change the relative labeling in successive

frames. A simple example shows the difficulties with

tracking bubbles. If there are four bubbles in one frame,

with bubble one and two joining, and three bubbles in the

next frame (Fig. 6), without any logic statements, which

account for joining bubbles, the program (details are

available in Hulme, [12]) would think the bubble labels

match (i.e. 1 with 1 and 2 with 2 and so forth). However,

since two bubbles have joined, bubble 1 in the next frame

is actually two bubbles (1 and 2) in the previous frame. It

can similarly be shown that other actions cause problems

with matching bubbles, which are resolved within the

program so that bubbles are match correctly giving them

the proper velocities.

To match the bubbles, a series of logic is used. More

detail is available in Hulme [12].

There is also one additional problem that arises because

of the size of the images. Since the diameter of the image

Fig. 6. Image showing the problem with matching bubbles when bubbles

join.

frame is only 13.5 cm, various camera heights have to be

used in order to obtain a complete picture of the bubble

properties for the entire height of the reactor. Because of the

image edges (both top and bottom), sometimes only part of

a bubble is visible in the frame. As a result, when the centre

of geometry is calculated, it is, in actual fact, not of the

brealQ bubble but only a portion, as shown in Fig. 7.

Therefore, bubble velocities will be incorrectly calculated.

Outgoing bubbles are accounted for by checking the

frame after the current frame being processed. If there is a

bubble that has a minimum point of 0 in the y direction (top

of the frame) then it is in the process of going out of the

frame. If this is the case, then the properties of the bubble on

the current frame are passed to the next frame. While the

area of the bubble remains the same, the centre of gravity is

now shifted by the amount the bottom of the bubble moves.

This is continues until the bubble completely disappears

from the frame.

Bubbles entering the frame also require modification.

When the data is read into the program, seven frames ahead

of the one being processed are also read. If a bubble has

bappearedQ in the frame from the bottom, then a bubble that

matches the space it occupies is found in subsequent frames.

This is done by looking at the following frame and

determining if the current partial bubble is within the

bounds of a bubble in the next frame. This logic continues

until a bubble is found in a subsequent frame that is

completely within the image frame.

4. Experimental results

To validate the software developed for this work, data

sets were created to simulate bubble movement. Bubbles

were drawn on graph paper, representing the resolution of

the image. The bubbles were then bmovedQ to simulate the

actions of real bubbles in the experiments. Once it was

determined that the program could pick up these actions,

the program was tested on a trial set of data using a

narrow particle size distribution of glass beads (150 to 250

Am). Several parameters had to be adjusted through trial

and error in order for the program to track the bubbles

Fig. 8. Graph showing the average bubble diameters as a function of bed height for glass beads.


correctly and predict values similar to those found by other

researchers.

4.1. Glass beads

The average bubble diameter is comparable with a

correlation by Werther et al. [13] and the correlation by

Mori and Wen [14]. However, it appears to taper off at

higher bed heights, as seen in Fig. 8, which could be due to

the scale of the reactor.

The average axial velocity, as seen in Fig. 9, also follows

trends found in literature.

Fig. 9. Figure showing the average axial velocity as a function of bed height fo

correlation by Kunii and Levenspiel [15] based on data by Werther et al. [13] using

single bubble velocity proposed by Davidson and Harrison [2].

While the absolute value for the bubble velocity is

different in Fig. 9, the shape of the curve is comparable to

the correlation of Kunii and Levenspiel [15] using the single

bubble velocity of Wallis (1969), cited in Kunii and

Levenspiel [15] which accounts for wall effects.

4.2. Polyethylene using a settled bed of 0.4 m

The system of interest for our research is a polyethylene

air system. To compare with literature a settled particle bed

height of 0.4 m was used. The raw data will be presented

using a superficial gas velocity of three times minimum

r glass beads. The difference in the correlations is that KL Wallis uses a

the velocity of a single bubble by Wallis (1969) [18]. KL Davidson uses the

Fig. 10. The frequency distribution of bubbles (for polyethylene beads) throughout the column, showing that the number of bubbles become less farther away

from the distributor.


velocity to demonstrate the distribution of the data and then

averaged to determine trends.

Before analyzing the diameters and velocities of the

bubbles, the gross distribution of bubbles in the bed was

examined. According to literature, the number of bubbles

should decrease with increased height above the distributor,

as shown in Fig. 10.

Fig. 10 represents the total number of bubbles at each

respective binned height divided by the total number of

bubble throughout the column for the duration of the

experiment. Fig. 10 agrees with what is observed visually,

Fig. 11. The raw data of the effective bubble diameters showin

in that there is a larger number of bubbles near the

distributor with fewer at higher bed heights, due to bubbles

coalescing.

The first property examined was the bubble diameter,

which can be difficult to define due to the irregular shape

of the bubbles in a bubbling bed. While the program

created can determine the feret diameter of the bubbles,

authors in literature use an effective bubble diameter. The

effective diameter is calculated assuming that the bubbles

are spheres. As such, since the present images are two-

dimensional, the diameter of the bubbles is calculated

g the wide distribution of sizes for polyethylene beads.

Fig. 12. The frequency of bubbles at certain diameters for polyethylene beads.


assuming the area of the bubble, calculated by the

program, as that of a circle. Therefore the diameter of

the bubble can be calculates as:

Db ¼�4� Total area of bubble

p

�0:5

ð2Þ

The feret diameter, calculated in the program, is a more

accurate measurement of the bubble diameter since it does

not assume the bubble is a circle. Instead, it calculates the

Fig. 13. 3D graph showing the frequency distribution of the bubbles diameters (fo

heights small bubbles are present.

length of a chord that joins two points on the surface of the

bubble. Determining this length at eight different angles, the

program then outputs the minimum, maximum, and mean

feret diameter. These values give a better idea of the shape

and size of the bubbles. However, a considerable portion of

the work is a comparison with literature and, as a result, the

effective diameter is used as a basis for comparison.

The effective bubble diameters can be plotted and

compared to the bed height as seen in Fig. 11, to get a

feel for the size and distribution of the bubbles in the reactor.

r polyethylene beads) at different binned heights. This shows that at all bed

Fig. 14. Average bubble diameter as a function of bed height for polyethylene beads. This graph also shows the difference between the average ferret diameter

and the effective diameter.


Fig. 11 demonstrates that, at every bed height, there are

small bubbles, which is confirmed by visual observation.

The scatter in the data also agrees with observations by

other researchers [16–19].

The bubble diameter distribution was also examined,

seen in Fig. 12.

As expected, Fig. 12 shows what is visually observed,

that there are a large number of small bubbles and fewer

large bubbles.

The distribution of bubble diameters at binned bed

heights further elucidates the distribution of bubble diam-

eters. The best way to visualize the distribution is on a three-

dimensional graph seen in Fig. 13, where the z-axis is the

Fig. 15. Ratio of the maximum feret diameter to the minimum feret diameter (for p

for a circular bubble would be 1.0.

binned bed heights. The bubble properties are binned in 4

cm intervals to produce the graph.

It is interesting to note that, at higher bed heights, the

fraction of small bubbles present is significant. This is

confirmed by examining the images. In many instances,

small bubbles appear and disappear brandomlyQ at all bedheights. Sometimes these small bubbles do not coalesce but

travel axially without interaction. It should also be noted

that the distribution of bubble diameters is not uni-modal.

The next step was to average the bubble diameters over

the binned bed heights. While statistically taking the mean

of a sample that is not uni-modal (see Fig. 13) is incorrect, it

does provide a means of comparison with other correlations

olyethylene beads) showing that the bubbles are nor circular, since the ratio

Fig. 16. Axial bubble velocity as a function of bed height for polyethylene beads.


and gives a feel for the predominant bubble size. The

averaged results can be seen in Fig. 14.

Fig. 14 shows a comparison of the effective and feret

diameter with correlations by Werther et al. [13] and Mori

and Wen [14]. It should be noted that there is a difference

between the feret diameter and the effective diameter.

Clearly the shape of the bubble are not circular in these

images and examining the ratio of the maximum to

minimum feret diameter, Fig. 15, the ratio deviates from

one significantly.

The bubble axial velocities were calculated based on the

movement, from frame to frame, of the geometric centre of

Fig. 17. The frequency distribution of bubb

the bubbles. Fig. 16 shows the bubble axial velocities

plotted as a function of the bed height.

Similar to the plot for bubble diameters, seen in Fig. 11,

there is considerable scatter in the velocities, which is

consistent with literature.

As with the bubble diameters, the distribution of bubble

velocities were examined to ensure a proper distribution and

to ensure there was not a large number of negative bubble

velocities, since bubbles were not observed traveling down

the column (although it has been reported by Clift and Grace

[20] that such velocities may well occur). Negative bubble

velocities were attributed to bubbles being matched incor-

le velocities for polyethylene beads.

Fig. 18. 3D graph showing the distribution of the bubbles velocities at different binned heights for polyethylene beads.


rectly and discarded in the averaging process. The frequency

distribution, seen in Fig. 17, shows that the distribution is,

as expected, Gaussian, with a few bubbles traveling quickly

(as they coalesce).

The distribution of the bubble velocities follows an

almost uni-modal distribution, as shown in Fig. 18, a three-

dimensional graph. This is similar to the graph presented for

Fig. 19. Average axial velocities obtained experimentally with correlation by K

experiment for polyethylene beads.

the bubble diameters (where the bubble properties are

binned in 4 cm intervals to produce the graph).

Due to the near Gaussian distribution of the axial bubble

velocities, averaging the bubble velocities is statistically

valid (as opposed to averaging the bubble diameters). By

averaging the bubble velocities in the same manner as the

bubble diameters, Fig. 19 is obtained.

unii and Levenspiel [15] using diameters from Mori and Wen [14] and

Fig. 20. The average axial bubble velocity for binned diameters compared with a correlation by Kunii and Levenspiel [15] for polyethylene beads.


Fig. 19 shows a strong agreement between the correlation

of Kunii and Levenspiel [15] while taking into account wall

effects (Wallis cited in [15]), and the experimental results.

Binning the experimental bubble diameters, in 1 cm

increments, the axial velocities of the bubbles can be

calculated and compared with the correlation by Kunii and

Levenspiel [15] as shown in Fig. 20.

Once again the axial velocities for the respective bubble

diameters adequately match the correlation by Kunii and

Levenspiel [15], with the maximum relative difference

being 10%.

Fig. 21. The effect on bubble diameter at different superficial gas velocities for po

[13].

4.3. The effect of superficial gas velocity on bubble

properties

The last result studied was the effect of superficial gas

velocity on the properties of the bubbles. The average

bubble diameters, at 4 cm binned bubble heights, for the

different gas velocities were calculated and plotted to

determine trends shown in Fig. 21.

Fig. 21 shows that, as the superficial gas velocity

increases, the average bubble diameter increases. This

agrees with two-phase theory, which states that any air in

lyethylene beads. The bubble diameter correleation is that of Werther et al.

Fig. 22. Bubble velocities at different superficial gas velocities for polyethylene beads.


excess of that required for minimum fluidization will form

bubbles. This also agrees with the correlations in literature

[11,13,14,21–23], where every correlation predicts there

will be larger bubbles at higher superficial gas velocities.

This being said, the correlation of Werther et al. [13] does

not predict as great an increase as the experimental values.

The next property examined was the effect of superficial

gas velocity on the axial velocity of the bubbles shown in

Fig. 22.

Fig. 22 does not show a definite trend, although there

does appear to be a slight increase in the bubble velocity as

the superficial gas velocity is increased. By binning the

bubble diameters, in 1 cm increments, and averaging the

velocities, the effect of different process conditions on

similar size bubbles can be determined as shown in Fig. 23.

Fig. 23. Graph showing that the fluidization velocity, for polyethy

Fig. 23 shows that bubble velocities do not appear to

significantly change with a change in superficial gas

velocity. The velocity correlation by Kunii and Levenspiel

[15] suggests an effect of the gas velocity on the bubble

velocities. However, for the present system, the correlation

by Kunii and Levenspiel [15] does not predict a noticeable

increase in the bubble velocities.

5. Conclusion and recommendations

X-ray fluoroscopy proved to be a powerful tool at

visualizing the movement and determining the properties of

bubbles in a laboratory scale gas–solid fluidized bed reactor.

Using this technique and software developed in house for

lene beads, does not significantly affect the bubble velocity.


analyzing the data, the properties of bubbles using glass

beads and a LLDPE for the solid phase, match the bubble

diameter and axial velocity correlations by Werther et al.

[13] and Kunii and Levenspiel [15], respectively. Experi-

ments were also conducted to determine the effect of

superficial gas velocity on the properties of the bubbles. As

expected, an increase in the superficial gas velocity caused

an increase in the bubble sizes.

While the experimental technique does provide good

resolution (0.1�0.1 mm), the contrast of the images needs

to be improved. In addition to further validation of the

experimental technique and software, the next focus will be

on calibrating the X-ray unit. Specifically, using the

intensity values to determine the mass or number of particles

along the length of the X-ray beam. Using this information,

the three-dimensional structure of the bubbles might be

obtainable. Many more experiments are to be conducted to

determine if the behaviour of polyethylene fluidized bed

behaves much differently than accounted for by correlations

presently in literature.

Nomenclature

Db effective diameter of the bubble

Acknowledgements

The authors wish to acknowledge financial assistance

from NOVA Chemicals and the Natural Sciences and

Engineering Research Council of Canada. The contribution

of Sandra Heiber in acquiring the micro CT image of the

polyethylene pellet is appreciated.

References

[1] J.G. Yates, D.J. Cheesman, Voidage variations in the regions

surrounding a rising bubble in a fluidized bed, AIChE Symp. Ser.

88 (1992) 34–39.

[2] J.F. Davidson, D. Harrison, Fluidized Particles, Cambridge University

Press, New York, 1963.

[3] H. Hatzantonis, H. Yiannoulakis, A. Yiagopoulos, C. Kiparissides,

Recent developments in modeling gas-phase catalyzed olefin poly-

merization fluidized-bed reactors: the effect of bubble size variation

on the reactor’s performance, Chem. Eng. Sci. 55 (2000) 3237–3259.

[4] R.D. Toomey, H.F. Johnstone, Gaseous fluidization of solid particles,

Chem. Eng. Prog. 48 (1952) 220–236.

[5] D. Geldart, Types of gas fluidization, Powder Technol. 7 (1973)

285–292.

[6] D.L. Pyle, D. Harrison, The rising velocity of bubbles in two

dimensional fluidized beds, Chem. Eng. Sci. 22 (1967) 531–535.

[7] J.B. Romero, D.W. Smith, Flash X-ray analysis of fluidized beds,

AIChE J. 11 (1965) 595–600.

[8] R.F. Mudde, H.B.M. Schulte, H.E.A. van den Akker, Analysis of a

bubbling 2-D gas-fluidzed bed using image processing, Powder

Technol. 81 (1994) 149–159.

[9] J.C. Russ, The Image Processing Handbook, 3rd edition, CRC Press,

USA, 1999.

[10] T.S. Curry, J.E. Dowdey, R.C. Murray Jr., Christensen’s Physics of

Diagnostic Radiology, Williams & Wilkins, Baltimore, 1990.

[11] P.N. Rowe, C. Yocono, The bubbling behaviors of fine powders when

fluidized, Chem. Eng. Sci. 31 (1976) 1179–1192.

[12] I. Hulme, Verification of the Hydrodynamics of a polyethylene

Fluidized Bed Reactor using CFD and Imaging Experiments, MSc.

Thesis, University of Calgary, 2003.

[13] J. Werther, J.F. Davidson, D.L. Keairns, Influence of the distributor

design on bubble characteristics in large diameter gas fluidized beds,

Fluidization, Cambridge University Press, London, 1978, pp. 7–12.

[14] S. Mori, C.Y. Wen, Estimation of bubble diameter in gaseous fluidized

beds, AIChE J. 21 (1975) 109–115.

[15] D. Kunii, O. Levenspiel, Fluidization Engineering, 2nd edition,

Butterworth-Heinemann, Boston, 1991.

[16] K. Goddard, J.F. Richardson, Bubble velocities and bed expansion in

freely bubbling fluidised beds, Chem. Eng. Sci. 24 (1969) 663–670.

[17] Miwa, K.S. Mori, T. Kato, I. Muchi, Behavior of bubbles in a gaseous

fludized bed, Int. Chem. Eng. 12 (1) (1972) 187–194.

[18] J. Werther, O. Molerus, The local structure of gas fluidized beds: 1. A

statistically based measuring system, Int. J. Multiph. Flow 1 (1973a)

103–122.

[19] J. Werther, O. Molerus, The local structure of gas fluidized beds: 2.

The spatial distribution of bubbles, Int. J. Multiph. Flow 1 (1973b)

123–138.

[20] R. Clift, J.R. Grace, Coalescence of bubbles in fluidized beds, AIChE

Symp. Ser. 67 (23) (1971) 23–33.

[21] R.C. Darton, R.D. La Naueza, J.F. Davidson, D. Harrison, Bubble

growth due to coalescence in fluidized beds, Trans. Inst. Chem. Eng.

55 (1977) 274–280.

[22] M. Horio, A. Nonaka, A generalized bubble diameter correlation for

gas–solid fluidized beds, AIChE J. 33 (1987) 1865–1872.

[23] J.H. Choi, J.E. Son, S.D. Kim, Generalized model for bubble size and

frequency in gas fluidized beds, Ind. Eng. Chem. Res. 37 (1998)

2559–2564.

determination of bubble diameter and axial velocity for a polyethylene fluidized bed using x-ray...

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