Effects of column diameter and liquid height on gas holdup in air-water bubble columns

Experimental Thermal and Fluid Science 82 (2017) 359–366

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Effects of column diameter and liquid height on gas holdup in air-water bubble columns Shohei Sasaki, Kengo Uchida, Kosuke Hayashi, Akio Tomiyama ⇑ Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe, Japan

a r t i c l e

i n f o

Article history: Received 29 June 2016 Received in revised form 28 September 2016 Accepted 27 November 2016 Available online 29 November 2016 Keywords: Bubble column Gas holdup Column diameter Initial liquid height Froude number

a b s t r a c t Experiments on the total gas holdup, aG, in air–water cylindrical bubble columns were carried out to investigate effects of the column diameter, DH, and the initial liquid height, H0, on aG. Ranges of DH and H0 were 160 6 DH 6 2000 mm and 400 6 H0 6 4000 mm, respectively. The superficial gas velocity, JG, was varied from 0.025 to 0.35 m/s. The characteristics of gas holdup showed that all the flows in the present experiments were pure heterogeneous. The following conclusions were obtained for aG in air–water bubble columns: (1) the effects of DH and H0 on aG are negligible when scaling up from small to large bubble columns, provided that aG in the small columns are obtained for DH P 200 mm and H0 J 2200 mm. The height-to-diameter ratio is useless in evaluation of the critical height, above which aG does not depend on H0, (2) for the above ranges of DH and H0, Akita-Yoshida’s and Koide’s correlations can give good evaluations of aG for a wide range of JG by tuning the model constants, (3) for DH < 200 mm, the decrease in DH increases the population of large bubbles, which results in the decrease in aG, and (4) for H0 [ 2200 mm and DH P 200 mm, aG at a constant JG decreases with increasing H0 and approaches an asymptotic value, and the Froude number using JG and H0 as the characteristic scales well correlates aG in this regime. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction Bubble column reactors have been widely used in chemical, biochemical and metallurgical industries and so on [1,2]. The total gas holdup, aG, of a bubble column is basic information required in column design, scale-up and the optimization of operating conditions. There are various parameters affecting aG such as the superficial gas velocity JG, column geometries, fluid properties, the types of gas spargers and so on. Many studies on the effects of these parameters have therefore been carried out [3–15]. Among the geometric parameters, the column diameter, DH, and the liquid height in a column are of great importance in scale-up [7]. When dealing with the effects of the liquid height on aG, the liquid height, HC, in operation (aeration height) or the initial liquid height, H0, before starting aeration has often been used. It is known that DH and H0 affect aG when they are less than certain critical values, whereas aG is independent of DH and H0 at larger values [3–7,11]. Hence the knowledge on aG in lab-scale bubble columns obtained for DH and H0 larger than the critical values would be useful in designing pilot- and industrial-scale columns [7].

⇑ Corresponding author. E-mail address: [email protected] (A. Tomiyama). http://dx.doi.org/10.1016/j.expthermflusci.2016.11.032 0894-1777/Ó 2016 Elsevier Inc. All rights reserved.

Wilkinson et al. [7] investigated the effects of DH on aG at several DH and system pressures. Comparisons between aG at DH = 150 and 230 mm showed that DH has little influence on aG for the pressure ranging from 0.1 to 0.62 MPa. They also compared their data at DH = 150 mm with those at DH = 50 mm [16] and pointed out that the latter are much larger than the former due to the presence of wall affecting the flow structure. Many studies after Wilkinson et al. [7] assumed that aG is independent of DH, provided that DH P 150 mm. However, in these comparisons between aG at different DH, H0 were not the same. Lemoine et al. [11] investigated effects of DH on aG in alumina–loaded slurry bubble columns by using a neural-network-based aG correlation developed by Behkish et al. [17,18]. The correlation indicated that DH affects aG even for DH > 150 mm and DH is required to be >700 mm to make aG independent of DH. Leonard et al. [2] supported this criterion in their recent review paper for bubble column reactor technology. The effects of H0 were however not accounted for in the neural-network-based correlation as a parameter in the input layer of the neural network. The uncertainty in the predicted aG due to the neglect of the H0 effect is therefore not clear. Although Lemoine et al. [11] pointed out that the aG data obtained by Vandu and Krishna [19] showed that aG decreased with increasing DH up to DH = 630 mm, H0 also increased with increasing DH in their experimental condition.

S. Sasaki et al. / Experimental Thermal and Fluid Science 82 (2017) 359–366

2. Experimental 2.1. Experimental setup Fig. 1 shows the experimental setup. The cylindrical bubble columns of DH = 160, 200 and 300 mm were used. They were made of transparent acrylic resin for visualization. The stainless steel diffuser plate of 5 mm thickness was placed at the bottom of the columns. Bubbly flows in bubble columns are often classified into either homogeneous or heterogeneous flow regimes. The former tends to be formed at low JG, and the increase in JG makes flows heterogeneous. Flows in bubble columns having diffuser plates with gas inlet holes of large diameters, dh, can however be heterogeneous even at low JG as reported in literature, e.g. Wilkinson et al. [7], Zahradník et al. [9] and Ojima et al. [22]. The bubbly flow is referred to as the pure-heterogeneous flow when the homogeneous regime does not appear, and the pure-heterogeneous regime is realized for dh > 1 mm [9]. The present study focused only on aG in the pure-heterogeneous regime. Therefore dh = 1.4 mm in the present experiments. The ratio, rh, of the total hole area to the cross-sectional area of the column was set at 0.18%. Consequently the numbers, Nh, of holes were 23, 37 and 83 for DH = 160, 200 and 300 mm, respectively. The holes were located so as to be equidistant from each other as shown in Fig. 2, where the hole pitch, ph, was 25 mm.

Column diameter DH Cylindrical bubble column

C

Air compressor

D

Air dryer

R

Regulator

Control valve

T

Initial liquid height H0

Thus the DH effect on aG must be investigated while keeping H0 constant. Koide et al. [20] measured aG in a large-scale air–water bubble column of DH = 5500 mm and compared aG with those in columns of DH from 100 to 600 mm. In spite of some scatter in the aG data, aG in the large DH column were similar to those in the smaller columns. Koide et al. [5] also investigated the effects of DH on aG in air–water bubble columns for 100 mm 6 DH 6 300 mm and at H0 = 1500 mm. They concluded that aG in the air–water heterogeneous bubbly flows is independent of DH. The data however clearly show some DH effect for DH less than 218 mm. In contrast to the studies on DH, there are only a few studies on the H0 effect on aG [7,10,12,14,15]. As is well known, the increase in H0 decreases aG at H0 smaller than a certain critical value. Several criteria for the critical H0 have been proposed in the dimensionless form as H0/DH, e.g. H0/DH = 4 [21], 5 [7] and 7 [5]. Most of studies on bubble columns therefore carried out experiments for DH > 150 mm and H0/DH > 5. The critical H0 is 10,000 mm for the Wilkinson criterion when DH = 2000 mm. It has not been investigated using large bubble columns whether or not H0 affects aG up to that large value of H0. The H0/DH might be an inappropriate indicator for representing the effects of H0 at least for DH P 150 mm since DH should be excluded in consideration of the dynamic similarity if DH plays no role in aG. Experiments on aG of air–water heterogeneous bubbly flows in a column of DH = 200 mm at various H0 up to 1000 mm were carried out in our previous study [14]. The parameters in the experiments were JG and H0 only, and the aG data were well correlated in terms of the Froude number defined by using JG and H0 as the characteristic scales and an aG correlation in terms of the Froude number was proposed. However the applicability of the Froude number in correlating aG in columns of different sizes has not been examined. Total gas holdups in air–water bubble columns were measured in this study to obtain systematic databases of aG at various H0 and DH, which allowed us to investigate the DH and H0 effects independently. The ranges of DH, H0 and JG were 160 6 DH 6 2000 mm, 400 6 H0 6 4000 mm and 0.025 6 JG 6 0.35 m/s, respectively.

Column height

360

Diffuser plate z

Thermometer Flow meter

Pressure gauge

F

P

x Air Chamber

Fig. 1. Experimental setup.

Circular hole dh = 1.4 mm

ph = 25mm ph ph

Plate thickness: 5.0 mm Fig. 2. Diffuser plate (Nh = 37).

The bubble column was initially filled with tap water at room temperature (19 ± 1 °C) and atmospheric pressure. The H0 was varied from 400 to 1800 mm. Air supplied from the compressor (Iwata, RDG-150C) flowed into the column through the air dryer (Iwata, SLP-1501 EB), the air chamber and the diffuser plate. The gas volume flow rate was measured using the flowmeters (Nippon flow cell, NVP-I, FLT-H; Tokyo Keiso, AM-1000, full-scale accuracy ±1.5%). The measured flow rate was converted into the volume flow rate at the middle height of the liquid level by taking into account gas expansion due to the decrease in static pressure. The range of JG was from 0.025 ± 0.001 to 0.35 ± 0.01 m/s, where the uncertainties were evaluated at 95% confidence. The physical properties of the gas and liquid phases are as follows: the liquid density qL = 998 kg/m3, the gas density qG = 1.2 kg/m3, the liquid viscosity lL = 1.0
103 Pas, the gas viscosity lG = 1.8
105 Pas, and the surface tension r = 0.072 N/m. Two larger bubble columns of 7000 mm high were also used to measure aG for larger H0, i.e. up to H0 = 4000 mm. Their DH were 450 and 2000 mm. The spargers for the former and latter were a plate-type and an arm-type sparger, and (dh, Nh, rh, ph) = (5.0 mm, 152, 1.88%, 22 mm) and (5.0 mm, 372, 0.23%, 10 mm) respectively. The JG was ranged from 0.057 ± 0.002 to 0.28 ± 0.01 m/s. The water

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temperature was 16 ± 1 °C, and lL = 1.1
103 Pas, r = 0.073 N/m.

therefore,

qL = 999 kg/m3,

900

800

H(t) [mm]

2.2. Total gas holdup measurement The total gas holdup in the bubble column was measured by using the image processing method [14] as shown in Fig. 3. Images of the free surface (Fig. 3(a)) were taken using a high-speed video camera (IDT, Motion Pro X-3) with the spatial and temporal resolutions of 0.36 mm/pixel and 1/100 s, respectively. They were transformed into binary images (Fig. 3(b)). After noise reduction (Fig. 3(c)), the instantaneous liquid height, H(x, t), at the horizontal position x and the time t was detected using a region growing method [23] (Fig. 3(d)). The line-averaged liquid height at t was calculated as

HðtÞ ¼

1 DH

Z

DH =2

ð1Þ

Hðx; tÞdx DH =2

The total gas holdup was then calculated as

1 aG ¼ T

Z

t 1 þT

t1

HðtÞ  H0 HðtÞ

ð2Þ

dt

where t1 is the time, at which the recording was started, and T the sampling time. Instantaneous and time-averaged HðtÞ at JG = 0.35 m/s are shown in Fig. 4, in which T is varied from 0 to 30 s to examine the convergence of the averaged HðtÞ. The instantaneous HðtÞ fluctuates largely, whose standard deviation is 32 mm, whereas the time-averaged HðtÞ at T = 30 s converges to within ±0.5% deviations. Therefore T was set at 30 s in all the measurements to assure the accuracy of mean values. The relative standard errors in aG were within ±2% at DH = 160, 200 and 300 mm. In the

(a)

700

H(t)

600

500

Time-averaged H(t)

0

10

20

Fig. 4. Instantaneous and time-averaged HðtÞ (JG = 0.35 m/s, H0 = 400 mm and DH = 300 mm).

following, several data of aG at DH = 200 mm were quoted from Sasaki et al. [14].

3. Results and discussion 3.1. Effects of column diameter on gas holdup Fig. 5 shows typical flows in the bubble columns. The bubbly flows under the present experimental conditions were heterogeneous, i.e. the flows were largely fluctuated, bubbles much larger than those at the gas inlet were formed due to bubble coalescence and disturbed the flows, and strong recirculation of the liquid flow was formed, which was clearly observed through remarkable retar-

(b) Binary image

Free surface

DH x

(c)

30

t – t1(= T) [s]

(d) H(x, t)

Noise reduction

H(t)

Fig. 3. Image processing for aG measurement (JG = 0.35 m/s, H0 = 400 mm and DH = 300 mm).

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z[mm] DH 1400

1200

1000 (= H0)

800

600

400

200

Taylor instability. The bubble frequency, fB, of large bubbles, whose widths were >100 mm (Fig. 7), were evaluated from front images for 900 6 z 6 1200 mm by using a high-speed video camera (Fastcam SA-X2, Photron Ltd.). The time-averaged fB measured using front images and that using side images were confirmed to be the same, provided that the sampling time was sufficiently long. In the present measurements, the sampling time of 60 s gave the correct time-averaged values. Fig. 8 shows fB at DH = 160, 200 and 300 mm. The trends of fB are the same, i.e. fB increases with increasing JG. The fB at DH = 200 and 300 mm are almost the same whereas fB at DH = 160 mm is larger than those at DH = 200 and 300 mm except at JG = 0.025 m/s, at which all fB are close to zero. Hence the increase in DH mitigates the formation of the large bubbles for DH < 200 mm, whereas further increase in DH does not affect fB at least for DH P 200 mm. Total gas holdups at H0 = 400 and 1000 mm are shown in Figs. 9 and 10, respectively. The relation between aG and JG is the same as that in the so-called pure heterogeneous regime, i.e. aG monotonously increases with increasing JG and the increase rate gradually decreases [12,25]. The comparisons between aG at the three DH show that aG depends on DH up to a certain DH between 160 and 200 mm, whereas it is independent of DH at least for DH P 200 mm. The cause of this trend of aG can be understood as follows. Increasing DH from 160 to 200 mm increases fB. The increase in the population of the fast large bubbles decreases aG. On the other hand, the population of the large bubbles does not change even with increase in DH for DH P 200 mm, and therefore, similar flow structures having the same aG are formed at DH = 200 and 300 mm. The agreement of aG of different DH at JG = 0.025 m/s can also be attributed to the same fB. Even though various values were proposed for the critical column diameter, e.g. DH = 150 mm [7] and 700 mm [2,11], aG of heterogeneous flows in air–water bubble columns do not depend on DH at least for DH P 200 mm at H0 = 400 and 1000 mm.

3.2. Effects of initial liquid height on gas holdup

(a) DH =160 mm (b) 200 mm

0

(c) 300 mm

Fig. 5. Bubbly flows at H0 = 1000 mm and JG = 0.30 m/s.

dation of rising velocities of small bubbles close to the side walls [1,14]. The maximum size of observable bubbles increased with increasing JG. At DH = 160 mm, bubbles of widths, wB, comparable to DH were observed. Synchronized-recording images taken from the front and side of the column showed that such bubbles occupied most of the column cross section as shown in Fig. 6. Bubbles of wB >0.8DH (= 160 mm) were also observed at DH = 200 mm. The widths of the largest bubbles in the column of DH = 300 mm were not >0.8DH (= 240 mm), but were as large as those in the column of DH = 200 mm. Bubbles of such sizes were referred to as the EL (extremely large) bubbles in the following. The EL bubbles were formed at z  400 mm, where z is the elevation from the bottom of the column. Even though the maximum stable diameter of a bubble in stagnant water is about 5 cm [24], the EL bubbles were much larger than this size and they kept their sizes until they reached the free surface. The side wall may play a role in the formation of large bubbles [1], i.e. bubbles tend to accumulate in the upward-liquid flow region (center region) due to the presence of side wall and frequent bubble coalescence in that region maintains the bubble size against bubble breakup due to Rayleigh-

Fig. 11 shows aG at various H0, where aG in air–water bubble columns only for DH P 200 mm are plotted to exclude the DH effect. The data show that all the flows are classified into pure heterogeneous flow. The increase in H0 decreases aG at small H0, whereas aG at large H0 are independent of H0. As mentioned above, EL bubbles were formed at z  400 mm. The region of z [ 400 mm was therefore under flow development and bubble coalescence was dominant. The gas holdup in this region might be larger than that for z J 400 mm due to relatively smaller bubble sizes. The ratio of the length of the latter developed region to that of the former developing region increased with increasing H0 since the length of the former would not depend on H0. Thus the total gas holdup approaches the gas holdup in the latter region as H0 increases. The aG are re-plotted against H0 in Fig. 12, in which several aG for DH > 200 mm (Table 1) are quoted from Refs. [19,26–28], to make the H0 effect on aG clearer. The data of aG at H0 larger than about 2200 mm are independent of H0. The aG at smaller H0 decrease with increasing H0 and approach constant values. The comparisons of the aG data also reconfirm that the increase in DH does not affect aG for DH P 200 mm. The present condition of H0 = 4000 mm and DH = 2000 mm corresponds to H0/DH = 2, which is much smaller than the critical H0/DH proposed in the literature, i.e. H0/DH = 4–7. This result makes it clear that H0/DH is inappropriate as an indicator for the critical liquid height. It should also be noted that geometrical configuration of spargers has no influence on aG within the range of the data collected.

S. Sasaki et al. / Experimental Thermal and Fluid Science 82 (2017) 359–366

1200

363

DH = 160 mm

145 mm

z [mm]

150 mm

900

(a) front view

(b) side view

Fig. 6. Extremely large bubble at JG = 0.35 m/s and H0 = 1000 mm (z is the vertical distance from the column bottom).

1200

z [mm]

DH = 160 mm

900

(a) 0.10m/s

(b) 0.35 m/s

(c) 0.35m/s

Fig. 7. Bubbles much larger than those at inlet (H0 = 1000 mm).

3.3. Applicability of available aG correlations The dependencies of aG of the air–water heterogeneous bubbly flows on the relevant parameters discussed above are summarized as

8 > < f D ðDH ; H0 ; J G Þ for DH < 200 mm and H0 K 2200 mm aG ¼ f H ðH0 ; JG Þ for DH  200 mm and H0 K 2200 mm > : f J ðJ G Þ for DH  200 mm and H0 J 2200 mm

ð3Þ

Let us first discuss an expression of fH for DH P 200 mm and H0 [ 2200 mm. Most of the studies on the height effect focused on the critical dimensionless liquid height, H0/DH, and available aG correlations were developed without accounting for the H0 effect. We therefore investigated the H0 effect on aG in an air–water and an air–slurry bubble columns of DH = 200 mm in our previous studies [14,15] and pointed out that aG in these systems can be correlated in terms of the Froude number defined by

JG ffi FrH ¼ pffiffiffiffiffiffiffiffi gH0

ð4Þ

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S. Sasaki et al. / Experimental Thermal and Fluid Science 82 (2017) 359–366

5.0

0.50 DH [mm] 160 200 300

4.0

0.40

0.30

G

fB [Hz]

3.0

2.0

0.20

1.0

0.10

0.0

0

0.1

0.2

0.3

H0 [m] DH [mm] Present 400 200 Present 600 300 Present 1000 300 Besagni & Inzoil [26] 3000 240 Present 3000 2000 Present 3500 2000 Present 4000 2000

0.00 0.0

0.4

0.1

0.2

JG [m/s]

0.3

0.4

JG [m/s] Fig. 11. aG plotted against JG for DH P 200 mm at various H0.

Fig. 8. Frequency fB of large bubbles for z = 900–1200 mm (H0 = 1000 mm).

0.45

0.50 Present Ref.[26] [27] [19] [28] (240) (305)(630)(800) JG [m/s] (200)(300)(450)(2000) 0.05 0.10 0.15 0.20

0.40

G

0.30

0.30

0.15

JG [m/s] 0.20

G

DH [mm] 160 200 300

0.15

0.20

0.10 0.05

0.00 0.0

0.1

0.2

0.3

0.4

0.10

JG [m/s] Fig. 9. Total gas holdup aG at H0 = 400 mm.

0.00

0

1000

2000

0.40

3000

4000

5000

H0 [mm]

G

Fig. 12. Effects of H0 on aG at various DH (=200–2000 mm) and JG (Values in the parentheses denote DH [mm]).

DH = 300 mm are well correlated in terms of FrH. The following empirical correlation was also proposed in our previous study [14]: 0.20

" DH [mm] 160 200 300

0.00 0.0

0.1

0.2

0.3

aG ¼ max

0.4

JG [m/s] Fig. 10. aG at H0 = 1000 mm.

where g is the acceleration of gravity. The aG data for H0 [ 2200 mm and at DH = 200 and 300 mm are plotted against FrH in Fig. 13. Not only aG at DH = 200 mm but also those at

C R1 1 Fr H

C R2 1 Fr H

; R2 1 þ C R1 2 Fr H 1 þ C 2 Fr H

# ð5Þ

where C1 and C2 are coefficients. Since the increasing rate of aG with respect to JG largely changed at JG  0.2 m/s, the use of single values for C1 and C2 was not appropriate to obtain accurate evaluations. Therefore (C1R1, C2R1) = (10.6, 19.9) and (C1R2, C2R2) = (7.7, 11.4) were used for aG at small FrH (Regime 1) and for aG at large FrH (Regime 2), respectively. This equation agrees well with the data as shown in the figure. Fig. 14 shows aG in air–water bubble columns for DH 6 200 mm. Here the data at DH = 100 and 150 mm were quoted from Hikita et al. [30] and Jhawar and Prakash [29], respectively. The H0 for DH = 100 and 150 mm are 650 and 1450 mm, respectively. The effects of H0 and JG at each DH are well correlated in terms of FrH.

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S. Sasaki et al. / Experimental Thermal and Fluid Science 82 (2017) 359–366 Table 1 Column diameters and gas diffusers in Refs. [19,26–28]. Reference

DH [mm]

Type of diffuser

dh [mm]

Nh

rh [%]

Vandu and Krishna [19] Besagni and Inzoil [26] Godbole et al. [27] Guan et al. [28]

630 240 305 800

Spider sparger Spider sparger Diffuser plate Diffuser plate

2.5 2–4 1.7 2.5

64 – 749 492

0.10 – 2.33 0.48

where CA = 0.20. Note that DH in the R.H.S vanishes though it is kept in the three factors to make clear relevant dimensionless groups, i.e. qLgDH2/r is the Bond number, qL2gDH3/lL2 the inverse pffiffiffiffiffiffiffiffiffi viscosity number and JG = gDH the Froude number. Experimental data used in developing Eq. (6) were for 150 6 DH 6 600 mm, 2000 6 HC 6 3000 mm and 0.003 6 JG 6 0.40 m/s, where HC is the aeration liquid height. Koide et al. [5] proposed the following aG correlation for the range of 140 6 DH 6 300 mm, H0 P 1000 mm, 1.64
104 6 JGlL/r 6 2.92
102 and 1.69
1011 6 glL4/qLr3 6 2.84
106:

0.50

0.40

DH [mm]

0.30

H0 [mm] 400 600 1000

G

200 300

0.20 Eq. (5)

(C1, C 2) (10.6, 19.9)



aG J l ¼ CK G L r ð1  aG Þ4

(7.7,11.4)

0.10

0.00 0.00

0.05

0.10

0.15

0.20

0.25

Fig. 13. aG correlated in terms of FrH (0.025 6 JG 6 0.35 m/s).

ð7Þ

qL r3

Decreasing DH

G

0.30

0.20 DH [mm] H0 [mm] 200 400-1000 Present 160 400-1000 Present Jhawar & Prakash [29]150 1450 100 650 Hikita et al. [30]

0.10

0.00 0.00

0.05

0.10

0.15

0.20

FrH

q

2 L gDH

r

q

3 2 L gDH 2 L

l

JG pffiffiffiffiffiffiffiffi ffi gDH

ð6Þ

0.40

0:096M0:011 ð8Þ

H0 [mm] DH [mm] 3000 2000 Present 3500 2000 Present 4000 2000 Present 2600 305 Godbole et al. [27] 240 Besagni & Inzoil [26] 3000 [28] 4100(= H) 800 Guan et al.

Eq. (8)

0.30 G

However the DH effect should be taken into account to correlate all the data. Multiplying the factor, / = min[2.61–1.11/(0.6 + 7
106  e11:4DH ), 1] to Eq. (5), where DH⁄ is the ratio of DH to 200 mm, yields a tentative expression for fD(DH, JG, H0) which gives reasonable evaluations of aG as shown in the figure. Although the expression of the DH effect multiplier can be improved by obtaining aG data at various DH for DH 6 200 mm, the improvement for small DH columns, from the practical point of view, would be less important compared with the importance of taking into account another relevant parameters such as fluid properties. Various empirical correlations for aG independent of DH and H0 have been proposed so far. The following equation is the well known correlation proposed by Akita & Yoshida [4]:

!1=12

qG qL

0.50

Fig. 14. aG vs. FrH for DH 6 200 mm.

!1=8

!0:21M0:0079 

where M is the Morton number defined by M = lL4(qL  qG)g/qL2r3. The aG data cover the ranges of 100 6 DH 6 610 mm, HC/DH > 5, 0.05 6 JG 6 0.69 m/s, 668 6 qL 6 2965 kg/m3, 0.29 6 lL 6 30 mPas, 0.019 6 r 6 0.073 N/m and 0.2 6 qG 6 90 kg/m3. These correlations are compared with the experimental data for DH P 200 mm and H0 J 2200 mm in Fig. 15. Though the applicable range of Fan’s correlation covers JG up to 0.69 m/s, agreement for JG > 0.1 m/s is poor. The Akita-Yoshida and Koide correlations qualitatively agree with the data, whereas aG are underestimated. The underestimation might be because the aG data used in developing their correlations include aG for DH < 200 mm, under which aG decreases with decreasing DH. The correlations can however be well fitted to the data by tuning CA and CK as shown in the figure. Most of the data are to within ±10% errors.

Eq. (5) with

0.40

¼ CA

0:252

4 4:1 J G qG aG ¼ 2:9½coshðM 0:054 Þ 1  aG rg

0.50

aG

g l4L

where CK = 0.277. It should be noted that these correlations are based on data including aG for DH < 200 mm. Fan et al. [31] collected a large number of aG data not only of gas-liquid two-phase bubble columns but also of gas–slurry bubble columns and proposed the following aG correlation:

FrH

ð1  aG Þ4

0:918 

Eq. (7) (C K = 0.391)

0.20

Eq. (6) (C A = 0.20) Eq. (7) (C K = 0.277)

0.10 Eq. (6) (C A = 0.24)

0.00 0.0

0.1

0.2

0.3

JG [m/s] Fig. 15. Comparison between measured and predicted aG.

0.4

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4. Conclusion Experiments on the total gas holdup, aG, in air–water cylindrical bubble columns were carried out to investigate effects of the column diameter, DH, and the initial liquid height, H0, on aG. The DH, H0 and JG ranged from 160 to 2000 mm, from 400 to 4000 mm and from 0.025 to 0.35 m/s, respectively. The characteristics of gas holdup showed that all the flows in the present experiments were pure heterogeneous. The following conclusions were obtained for aG in air–water bubble columns: (1) The effects of DH and H0 on aG are negligible when scaling up from small to large bubble columns, provided that aG in the small columns are obtained for DH P 200 mm and H0 J 2200 mm. The height-to-diameter ratio is useless in evaluation of the critical height, above which aG does not depend on H0. (2) For the above ranges of DH and H0, the Akita-Yoshida and the Koide correlations can give good evaluations of aG for the wide range of JG by tuning the model constants. (3) For DH < 200 mm, the decrease in DH increases the population of large bubbles, which results in the decrease in aG. (4) For H0 [ 2200 mm and DH P 200 mm, aG at a constant JG decreases with increasing H0 and approaches an asymptotic value. The Froude number using JG and H0 as the characteristic scales well correlates aG in this regime. Acknowledgement The authors would like to express their thanks to NIPPON STEEL & SUMIKIN ENGINEERING CO., LTD. for permitting us the use of the large columns. This work has been supported by the Japan Society for the promotion of Science (JSPS) (Grants-in-Aid for Scientific Research (B), No. 15H03920). References [1] N. Kantarci, F. Borak, K.O. Ulgen, Bubble column reactors, Process Biochem. 40 (2005) 2263–2283. [2] C. Leonard, J.H. Ferrasse, O. Boutin, S. Lefevre, A. Viand, Bubble column reactors for high pressures and high temperatures operation, Chem. Eng. Res. Design 100 (2015) 391–421. [3] F. Yoshida, K. Akita, Performance of gas bubble columns: volumetric liquid– phase mass transfer coefficient and gas holdup, AIChE J. 11 (1965) 9–13. [4] K. Akita, F. Yoshida, Gas holdup and volumetric mass transfer coefficient in bubble columns, Ind. Eng. Chem. Process Des. Dev. 12 (1973) 76–80. [5] K. Koide, A. Takazawa, M. Komura, H. Matsunaga, Gas holdup and volumetric liquid–phase mass transfer coefficient in solid–suspended bubble columns, J. Chem. Eng. Jpn. 17 (1984) 459–466. [6] F. Yamashita, Effect of liquid depth, column inclination and baffle plates on gas holdup in bubble columns, J. Chem. Eng. Jpn 18 (1985) 349–353. [7] P.M. Wilkinson, A.P. Spek, L.L. van Dierendonck, Design parameters estimation for scale-up of high-pressure bubble columns, AIChE. J. 38 (1992) 544–554. [8] R. Krishna, J. Ellenberger, Gas holdup in bubble column reactors operating in the churn–turbulent flow regime, AIChE J. 42 (1996) 2627–2634.

[9] J. Zahradník, M. Fialová, M. Ru˚zˇicˇka, J. Drahoš, F. Kaštánek, N.H. Thomas, Duality of the gas–liquid flow regimes in bubble column reactors, Chem. Eng. Sci. 52 (1997) 3811–3826. [10] B.N. Thorat, A.V. Shevade, K.N. Bhilegaonkar, R.H. Aglawe, U. Parasu Veera, S.S. Thakre, A.B. Pandit, S.B. Swant, J.B. Joshi, Effect of sparger design and height to diameter ratio on fractional gas hold–up in bubble columns, Trans. Inst. Chem. Engrs. 76 (1998) 823–834. [11] R. Lemoine, A. Behkish, L. Sehabiague, Y.J. Heintz, R. Oukaci, B.I. Morsi, An algorithm for predicting the hydrodynamic and mass transfer parameters in bubble column and slurry bubble column reactors, Fuel Process. Technol. 89 (2008) 322–343. [12] M.C. Ruzicka, J. Drahoš, M. Fialová, N.H. Thomas, Effect of bubble column dimensions on flow regime transition, Chem. Eng. Sci. 56 (2001) 6117–6124. [13] R. Lau, P.H.V. Lee, T. Chen, Mass transfer studies in shallow bubble column reactors, Chem. Eng. Process. 62 (2012) 18–25. [14] S. Sasaki, K. Hayashi, A. Tomiyama, Effects of liquid height on gas holdup in air–water bubble column, Exp. Therm. Fluid Sci. 72 (2016) 67–74. [15] S. Sasaki, K. Uchida, K. Hayashi, A. Tomiyama, Effects of particle concentration and slurry height on gas holdup in a slurry bubble column, J. Chem. Eng. Jpn. 49 (2016) 824–830. [16] K. Idogawa, K. Ikeda, T. Fukuda, S. Morooka, Effects of gas and liquid properties on the behavior of bubbles in a column under high pressure, Int. Chem. Eng. 27 (1987) 93–99. [17] A. Behkish, Hydrodynamic and mass transfer parameters in large-scale slurry bubble column reactors, PhD Thesis, University of Pittsburgh, 2004. [18] A. Behkish, R. Lemoine, L. Sehabiague, R. Oukaci, B.I. Morsi, Prediction of the gas holdup in industrial–scale bubble columns and slurry bubble column reactors using back–propagation neural networks, Int. J. Chem. Reactor Eng. 3 (2005) 1–37. [19] C.O. Vandu, R. Krishna, Volumetric mass transfer coefficients in slurry bubble columns operating in the churn–turbulent flow regime, Chem. Eng. Sci. 59 (2004) 5417–5423. [20] K. Koide, S. Morooka, K. Ueyama, A. Matsuura, F. Yamashita, S. Iwamoto, Y. Kato, H. Inoue, M. Shigeta, S. Suzuki, T. Akehata, Behavior of bubbles in large scale bubble column, J. Chem. Eng. Jpn. 12 (1979) 98–104. ˇ ermák, Modeling of large–scale [21] F. Kaštánek, J. Zahradník, J. Kratochvíl, J. C bubble column reacters for non–ideal gas liquid systems, Front. Chem. React. Eng. 1 (1984) 330–344. [22] S. Ojima, K. Hayashi, S. Hosokawa, A. Tomiyama, Distributions of void fraction and liquid velocity in air–water bubble column, Int. J. Multiphase Flow 67 (2014) 111–121. [23] S.A. Hojjatoleslami, J. Kittler, Region growing: a new approach, IEEE Trans. Image Process. 7 (1998) 1079–1084. [24] R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops, and Particles, Academic Press, 1978. [25] S. Sharaf, M. Zednikova, M.C. Ruzicka, B.J. Azzopardi, Global and local hydrodynamics of bubble columns–effect of gas distributor, Chem. Eng. J. 288 (2016) 489–504. [26] G. Besagni, F. Inzoli, Comprehensive experimental investigation of counter– current bubble column hydrodynamics: holdup, flow regime transition, bubble size distributions and local flow properties, Chem. Eng. Sci. 146 (2016) 259–290. [27] S.P. Godbole, S. Joseph, Y.T. Shah, Hydrodynamics and mass transfer in a bubble column with an organic liquid, Can. J. Chem. Eng. 62 (1984) 440–445. [28] X. Guan, Y. Gao, Z. Tian, L. Wang, Y. Cheng, X. Li, Hydrodynamics in bubble columns with pin–fin tube internals, Chem. Eng. Res. Design 102 (2015) 196– 206. [29] A.K. Jhawar, A. Prakash, Influence of bubble column diameter on local heat transfer and related hydrodynamics, Chem. Eng. Res. Design 89 (2011) 1996– 2002. [30] H. Hikita, S. Asai, K. Tanigawa, K. Segawa, M. Kitao, Gas hold-up in bubble columns, Chem. Eng. J. 20 (1980) 59–67. [31] L.-S. Fan, G.Q. Yang, D.J. Lee, K. Tsuchiya, X. Luo, Some aspects of high–pressure phenomena of bubbles in liquids and liquid–solid suspensions, Chem. Eng. Sci. 54 (1999) 4681–4709.