bubble column paper

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Author's Accepted Manuscript

Experimental study of the bubble size dis-tribution in a pseudo-2D bubble column

Y.M. Lau, K. Thiruvalluvan Sujatha, M. Gaeini,N.G. Deen, J.A.M. Kuipers

PII: S0009-2509(13)00355-2DOI: http://dx.doi.org/10.1016/j.ces.2013.05.024

Reference: CES11068

To appear in: Chemical Engineering Science

Received date: 20 December 2012Revised date: 8 May 2013Accepted date: 14 May 2013

Cite this article as: Y.M. Lau, K. Thiruvalluvan Sujatha, M. Gaeini, N.G. Deen, J.A.M. Kuipers, Experimental study of the bubble size distribution in a pseudo-2D bubble column, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2013.05.024

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Experimental study of the bubble size distribution in a

pseudo-2D bubble column

Y.M. Lau, K. Thiruvalluvan Sujatha, M. Gaeini, N.G. Deen, J.A.M.Kuipers

Multiphase Reactors Group, Department of Chemical Engineering and Chemistry,Eindhoven University of Technology, The Netherlands

P.O.Box 513, 5600MB Eindhoven

Abstract

This work presents an experimental study of the bubble size distribution of

a bubbly flow using digital image analysis (DIA). In order to facilitate the

image measurement technique a pseudo-2D bubble column is chosen for the

experiments. To obtain well-defined inlet conditions a gas sparger, consisting

of 20 needles, is used. By employing DIA, the bubble size distribution (BSD)

has been measured for a range of superficial gas velocities. The resulting

BSDs are expressed in terms of a probability density function (PDF). For

low superficial gas velocities of 5 and 10 mm/s the PDF has a unimodal

shape, while for higher superficial gas velocities of 15 and 20 mm/s the PDF

has a bimodal shape. The effects of coalescence and break-up of bubbles

are visible by evaluating the changes of the resulting BSDs for increasing

superficial gas velocity. A comparison of gas hold-ups is made between the

calculated BSD and the liquid expansion height. This comparison shows

how well the BSD obtained with DIA describes the actual gas hold-up in the

Corresponding author: [email protected]

Preprint submitted to Chemical Engineering Science May 17, 2013


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column.

Keywords: Digital Image Analysis, Gas-liquid flow, Bubble columns,

Bubble size distribution, Gas hold-up

1. Introduction

Gas-liquid bubble column reactors are widely used in many industrial

applications, e.g. Fischer-Tropsch process for hydrocarbon synthesis, hydro-

genation of unsaturated oil, coal liquefaction, fermentation and waste water

treatment. One of the important factors in the design of mass transfer in

such reactors is the gas-liquid interfacial area, which depends on the bub-

ble size distribution (BSD). In general, the gas-liquid interfacial area is a

function of geometrical configuration, operating parameters, physical and

chemical properties of both phases. To optimize bubble column processes, it

is essential to know the BSD in the particular system at different operating

conditions. However it is very difficult to measure the BSD in an industrial

bubble column. Therefore, different types of laboratory-scale bubble columns

have been employed to study the bubble size. Broder and Sommerfeld (2007)

measured bubble sizes in a lab-scale 3D column with an average gas volume

fraction between 0.5 5.0 % and a mean bubble diameter ranging between24 mm. Mena et al. (2005) measured the bubble size distribution in a masstransfer system in a lab-scale 3D column at a low superficial gas velocity of

2.8 mm/s. Majumder et al. (2006) reported the bubble size in a modifiedbubble column reactor at superficial liquid velocities of 70.7-141.4 mm/s and

superficial gas velocities of 1.7-13.58 mm/s. Schafer et al. (2002) discussed

the influence of operating conditions and physical properties of the gas and

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liquid phases on the initial and stable bubble sizes in a bubble column reactor

operating in the homogeneous regime. Other than these mentioned studies,

there are many more (Polli et al. (2002), Mandal et al. (2005), Wongsuchoto

et al. (2003), Montante et al. (2008), Diaz et al. (2008), Bordel et al. (2006),

Lage and Esposito (1999), etc.). Most of these experimental studies on the

bubble size distribution are performed using Digital Image Analysis (DIA)

for low void fraction bubbly flow or only near-wall measurements for high

void fraction bubbly flow. DIA is a non-intrusive technique, which can mea-

sure irregular-shaped bubbles accurately with a wide range of bubble sizes

(Honkanen et al. (2005)). Non-intrusive techniques are preferred above intru-

sive ones, as these do not disturb the flow. Recognizing individual bubbles

from digital images is tedious. This is because even at low void fraction

( 1 %) a large number of bubbles is overlapping (40 %) (Lecuona et al.(2000); Rodriguez-Rodriguez et al. (2003)). The objective of this work is to

investigate the BSD in a pseudo-2D bubble column with the use of DIA. The

image analysis incorporates the watershed transformation by Meyer (1994)

to separate overlapping bubbles. Measurements are performed for bubbly

flows up to the limit where bubble detection is no longer possible due to the

high void fraction. The main subject of this work is to investigate the effect

of the superficial gas velocity and the evolution of the BSD along the height

of the column.

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2. Experimental set-up and technique

2.1. Pseudo-2D bubble column

Bubble size distributions are measured in a pseudo-2D bubble column.

Air and distilled water are used as the gas and the liquid phase respectively.

A schematic representation of the column and its measurement zones are

illustrated in Figure 1. The measurement zones are maintained for different

initial liquid heights (H0). The column is made of glass with dimensions of

0.20 0.03 1.0 m (W D H). It is equipped with a needle sparger,which is used to obtain well-defined inlet conditions at the gas distributor.

The sparger consists of a row of 20 needles and is aligned in the centre of the

bottom-plate of the column. The needles have an inner diameter of 1 mm and

an outer diameter of 1.3 mm. The needles extend 10 mm above the bottom

plate and are spaced with a centre-to-centre distance of 10 mm. The gas flow

rate is controlled with mass flow controllers. For the BSD measurements,

series of 5000 images with a frequency of 50 Hz are obtained using a high-

speed CMOS camera (Lavision, HighSpeedStar 3G). The focal length of the

lens is 50 mm. The camera is positioned at a distance of 1.50 m in front of

the pseudo-2D column and the column is illuminated from the back. The

acquired images are gray scale images with a resolution of 10241024 pixels,yielding a spatial resolution of 0.18 mm. The field of depth is 0.14 m, which

is larger than the column depth.

2.2. Digital Image Analysis

The bubble properties that can be obtained from an image are the pro-

jected area and shape. Subsequently, from these quantities the centroids and

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air

needle sparger

0.03m

0.2m

0.005m

top

needle sparger

water

0.6m

middle

bottom 0.188m

0.200m

0.383m

0.400m

0.583m

0.183mmeasurement

windows

olumn height

column width

column depth

Figure 1: Schematic overview of the pseudo-2D bubble column set-up with the measure-

ment windows (top, bottom and middle).

equivalent diameter can be calculated. To acquire these values, a number of

operations are performed upon the images (see overview in Figure 2). Start-

ing with the obtained image, the background is removed using local area

thresholding, where the image is divided in blocks, each of which is inde-

pendently thresholded by employing the Otsu (1979) filter. Subsequently, a

global threshold is applied to create a binary image, separating the bubbles

from the background. To this end, an appropriate global threshold value is

chosen from the histogram of the image gray scales. After these filters have

been applied, the detected objects are divided into solitary bubbles and over-lapping/clustering bubbles on the basis of the roundness. The roundness is

determined as:

Ro =S4A

(1)

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with S the surface perimeter and A the area. The applied criteria to dis-

tinguish isolated single bubbles is Ro < 1 1.5, which is determined bytrial and error on an initial set of images. The resulting two images are seg-

mented independently and subsequently combined to yield an overall image

with solitary and separated overlapping/clustering bubbles. The image with

the solitary bubbles is segmented by labelling the solitary areas, and the im-

age with the overlapping/clustering bubbles is segmented using a watershed

transform by Meyer (1994). Finally, the area of pixels of each bubble object

of both images is counted and converted from pixel to metric values using the

magnification of the image. From the measured area, the equivalent diameter

is calculated as follows:

de =

4A

(2)

This image measurement technique is described in detail in the paper of Lau

et al. (2013). Examples of the detected bubbles in the pseudo-2D bubble

column are shown in Figure 3. Note that the smallest bubble diameter thatcan be detected in the images is equal to 0.9 mm, which corresponds with

5 pixels. The measured BSDs are expressed in the form of a number-based

Probability Density Function (PDF).

3. Results and discussion

3.1. Visual description

Measurements are performed for different initial liquid heights (0.5, 0.6

and 0.7 m) with superficial gas velocities ranging from 5 to 30 mm/s for

an air-water system. The measurement zones (top, middle and bottom) are

shown in Figure 1. Samples of the obtained camera images with an initial

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ficial gas velocity of 10 mm/s (see Figures 4b, 4e and 4h), coalescence and

break-up of bubbles start to play a role. This results in a wider BSD than

the BSD observed with a superficial gas velocity of 5 mm/s. Occasionally,

there are some regions where the bubbles rise faster. For a superficial gas

velocity of 15 mm/s (see Figures 4c, 4f and 4i), a bubble plume becomes

more evident and bubbles rise faster in the column. A plume is a dynamic

region within the bubble column, where the bubbles rise with a higher veloc-

ity. Bubbles in this dynamic region are larger due to coalescence of bubbles.

The smaller bubbles accumulate close to the side walls and are dragged down

by the down-flow of the liquid. A wide bubble size distribution in the col-

umn is obtained and small vortical structures are formed close to the side

wall regions. At 20 mm/s (see Figures 5a, 5d and 5g), two bubble regions

(plumes) with high bubble rise velocity are observed and down-flow of smaller

bubbles at the side walls is clearly visible. Some small vortices also occur

at the region between the plumes. At even higher superficial gas velocities

of 25 mm/s (see Figures 5b, 5e and 5h) and 30 mm/s (see Figures 5c, 5f

and 5i), a large number of small bubbles is formed due to intense bubble

break-up. The bubbly flow is very chaotic, which makes visual observation

very difficult.

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(a) top, vsup = 5 mm/s (b) top, vsup = 10 mm/s (c) top, vsup = 15 mm/s

(d) middle,

vsup = 5 mm/s

(e) middle,

vsup = 10 mm/s

(f) middle, vsup =

15 mm/s

(g) bottom,

vsup = 5 mm/s

(h) bottom, vsup =

10 mm/s

(i) bottom,

vsup = 15 mm/s

Figure 4: High-speed camera images of the bubbly flow for the different measurement zones

(top, middle and bottom) in the pseudo-2D bubble column for superficial gas velocities

ranging from 5 to 15 mm/s and an initial liquid height of H0 = 0.6 m.

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(a) top, vsup = 20 mm/s (b) top, vsup = 25 mm/s (c) top, vsup = 30 mm/s

(d) middle,

vsup = 20 mm/s

(e) middle,

vsup = 25 mm/s

(f) middle, vsup =

30 mm/s

(g) bottom, vsup =

20 mm/s

(h) bottom, vsup =

25 mm/s

(i) bottom,

vsup = 30 mm/s

Figure 5: High-speed camera images of the bubbly flow for the different measurement zones

(top, middle and bottom) in the pseudo-2D bubble column for superficial gas velocities

ranging from 20 to 30 mm/s and an initial liquid height of H0 = 0.6 m.

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3.2. Bubble velocities

Bubble velocity measurements have been performed via bubble image

velocimetry (Deen (2001)) for the superficial gas velocity range from 5 to

30 mm/s with an initial liquid height H0 = 0.6 m. Series of 5000 image

pairs of the entire column with a frequency of 50 Hz are obtained for bubble

velocity calculations. The average vertical bubble velocities across the width

of the pseudo-2D bubble column at heights of 0.15, 0.30 and 0.45 m are given

in Figure 6. This figure shows for a low superficial gas velocity of 5 mm/s

an uniform up-flow of the rising bubbles. By increasing the superficial gas

velocity, bubble down-flow regions near the side walls and a bubble up-flow

region in the centre across the width of the bubble column are developed.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

x/D

bubblevelocity[m/s]

0.5 cm/s

1.0 cm/s

1.5 cm/s

2.0 cm/s

2.5 cm/s

3.0 cm/s

vsup

(a) H = 0.15 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

x/D

bubblevelocity[m/s]

0.5 cm/s

1.0 cm/s

1.5 cm/s

2.0 cm/s

2.5 cm/s

3.0 cm/s

supv

(b) H = 0.30 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

x/D

bubblevelocity[m/s]

0.5 cm/s

1.0 cm/s

1.5 cm/s

2.0 cm/s

2.5 cm/s

3.0 cm/s

vsup

(c) H = 0.45 m

Figure 6: Average vertical bubble velocities across the width of the pseudo-2D bubble

column at 0.15, 0.30 and 0.45 m column heights for an initial liquid height of H0

= 0.6 m

and different superficial gas velocities.

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3.3. Integral gas hold-up

To illustrate how well the BSD obtained with DIA describes the actual

gas hold-up in the column, the integral gas hold-up is calculated on basis

of the measured bubble sizes and is compared with the integral gas hold-up

calculated using the liquid expansion height. Using the measured bubble

sizes, the gas hold-up (BSDg ) is calculated as follows from the DIA data:

BSD

g =

N

i=1(6

d3i )

Vwindow (3)

Here, Vwindow is defined as the volume of the measurement zone minus the

border volumes, where bubbles crossing/touching the borders are not taken

into account in the detection algorithm (borderkill). With a length of the

mean bubble diameter db from each side of the height H and width W of the

measurement zone and the depth D, Vwindow (see Figure 7) is calculated as

follows:

Vwindow = (W 2db) (H 2db) D (4)

For the actual gas hold-up (Hg ) in the bubble column, the expansion of the

liquid height in the column is used:

Hg =Hf H0

Hf(5)

where Hf is the height of aerated liquid.

Figure 8 shows the comparison of the gas hold-up determined by DIA/BSD

and liquid height expansion. On increasing the superficial gas velocity, the

gas hold-up in the column increases. Increase of the initial liquid height

in the column has no significant effect on the gas hold-up. At low super-

ficial gas velocity of 5 mm/s, BSDg seems to be larger than Hg . This is

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column wall column wall

measurement window

measurement window

minus border volumes

height

w

db

db db

db

Vwindow

Figure 7: Schematic representation of Vwindow for the calculation of the gas hold-up.

because of the Vwindow for which too much border volumes are subtracted.

In comparison with higher superficial gas velocities, for 5 mm/s there are

only a small number of bubbles crossing/touching the borders. This results

in an underestimation of the actual liquid volume, which in turn results in

an overpredicted integral gas hold-up. In spite of the imaging errors (noise

and oversegmentation) introduced by the images, DIA/BSD is reasonably

accurate at lower superficial gas velocities up till 20 mm/s, but at higher

velocities the error becomes very large. At high superficial gas velocities, the

presence of undetected small bubbles as shown in Figure 5 will contribute

largely to the gas hold-up error. Therefore the BSDs obtained at superficial

gas velocities exceeding 20 mm/s are omitted in this work.

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differences can be explained by the location of the top measurement zone,

as for an initial liquid height of 0.5 m, the gas-liquid mixture only fills half

of the measurement section, causing exit effects on the PDF, while for the

other liquid heights the free surface area of the water is well above in the top

section. This deviation is observed for all measured superficial gas velocities.

Similar trends are observed for a superficial gas velocity of 10 mm/s for

all three initial liquid heights (see Figures 9d, 9e and 9f), but with a wider

bubble size distribution and a single peak at 5 mm. Coalescence and break-

up of bubbles are starting to play a role and it seems that its equilibrium is

almost reached in the bottom section, since the shape does not change much

throughout the middle and top sections. At a superficial gas velocity of

15 mm/s (see Figures 10a, 10b and 10c) a bimodal bubble size distribution

is observed with a small peak at 2.5 mm and a large peak at 5 mm. In

the bottom section, the PDF is a non-bimodal wide distribution, developing

into a bimodal distribution in the middle and top sections due to coalescence.

Increasing the superficial gas velocity to 20 mm/s leads to similar effects, but

also to more break-up (small peak at approximately 5 mm and a large peak at

2.5 mm).At 15 and 20 mm/s, the equilibrium between coalescence and break-

up is not obtained in the bottom section, but still develops throughout the

column. From these reported BSDs, it seems that the initial liquid heights

of 0.5, 0.6 and 0.7 m has almost no effect on the resulting BSDs.

The calculated number mean bubble diameter , the standard deviation and the Sauter mean diameter d32 are listed in Table 1. It shows that with

the increase of superficial gas velocity, increases up till a superficial gas

velocity of 20 mm/s, while and d32 both keep increasing.

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0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

0.35

diameter [mm]

PDF

[]

bottommiddletop

(a) H0 = 0.5 m &

vsup = 5 mm/s

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

0.35

diameter [mm]

PDF

[]

bottommiddletop

(b) H0 = 0.6 m &

vsup = 5 mm/s

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

0.35

diameter [mm]

PDF

[]

bottommiddletop

(c) H0 = 0.7 m &

vsup = 5 mm/s

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

diameter [mm]

PDF

[]

bottommiddletop

(d) H0 = 0.5 m & vsup =

10 mm/s

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

diameter [mm]

PDF

[]

bottommiddletop

(e) H0 = 0.6 m & vsup =

10 mm/s

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

diameter [mm]

PDF

[]

bottommiddletop

(f) H0 = 0.7 m & vsup =

10 mm/s

Figure 9: Bubble size distribution for the superficial gas velocities of 5 and 10 mm/s with

initial liquid heights (H0) of 0.5, 0.6 and 0.7 m.

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0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

diameter [mm]

PDF

[]

vsup = 5 mm/sv

sup= 10 mm/s

vsup

= 15 mm/s

vsup

= 20 mm/s

Figure 11: Evolution of the bubble size distribution for increasing superficial gas velocity

with an initial liquid height (H0) of 0.6 m.

4. Conclusions

In this work a novel digital image analysis (DIA) technique is used to

measure bubble size distributions (BSDs) in a pseudo-2D bubble column.

From the resulting BSDs, it can be seen that the initial bubble size distri-

bution created at the bottom of the column prevails throughout the height

of the column. It appears that quickly an equilibrium is reached between the

coalescence and break-up. The effect of break-up increases, as the superficial

gas velocity is increased. The superficial gas velocity has a major effect on

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H0 = 0.5 m H0 = 0.6 m H0 = 0.7 m

vsup d32 d32 d32

[mm/s] [mm] [mm] [mm] [mm] [mm] [mm]

5 3.88 0.79 4.22 3.88 0.80 4.23 3.90 0.80 4.25

10 4.46 1.37 5.36 4.45 1.38 5.37 4.46 1.34 5.33

15 4.57 1.99 6.50 4.55 1.97 6.46 4.56 1.94 6.41

20 4.45 2.35 7.37 4.41 2.32 7.28 4.43 2.28 7.20

Table 1: The mean, standard deviation and d32 of the detected bubbles for different initial

liquid heights and superficial gas velocities.

the hydrodynamics and henceforth on the bubble size distribution within the

bubble column. The initial liquid height in the bubble column during the ex-

periments has little influence on the bubble size distribution. Increasing the

hold-up in the column makes it difficult to determine the bubble size due to

increased bubble overlap in the images. The hold-up in the column measured

by the DIA is lower than determined by liquid expansion. This is because 2D

images are used to extract 3D bubble shape information, whereas the actual

bubble shape could be different. For velocities more than 20 mm/s, small

bubbles contribute largely to the gas hold-up, whereas the gas hold-up from

DIA is determined only using the large bubbles.

Nomenclature

A area, [m2]

g integral gas hold-up via the liquid expansion height, [-]

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BSD bubble size distribution

D depth of the column, [m]

DIA digital image analysis

d diameter, [m]

d32 Sauter mean diameter, [m]

de equivalent diameter, [m]

db mean bubble diameter, [m]

H height of the column, [m]

H0 initial liquid height, [m]

Hf final liquid height, [m]

i index

N number of bubbles, [-]

PDF probability density function

Ro roundness, [-]

S surface perimeter, [m]Vwindow volume of the measurement window, [m

3]

vsup superficial gas velocity, [m/s]

W width of the column, [m]

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Acknowledgements

This project is part of the Industrial Partnership Program Fundamentals

of Heterogeneous Bubbly Flow, which is funded by FOM, AkzoNobel, DSM,

Shell and TataSteel.

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