### 1. Introduction

_{2}, and odor abatement [1]. Gas-liquid mass transfer is one of the key factor governing the reactor performance, which relates to hydrodynamics and physical properties.

_{L}a), which is the product of the liquid-film mass transfer coefficient (k

_{L}) and the interfacial area (a), is generally used for analyzing the global mass transfer mechanism and comparing different operating conditions in a bubble column. However, this k

_{L}a coefficient is global and insufficient to describe mass transfer mechanisms relating with effects of gas diffusers and liquid phase contamination [5, 6]. It is therefore necessary to separate the parameters, the k

_{L}coefficient and the interfacial area, in order to provide a better understanding on gas-liquid mass transfer mechanism in bubble column.

_{L}) and the interfacial area (a) was used for enhance the absorption efficiency in a bubble column.

### 2. Materials and Methods

### 2.1. Experimental Setup

_{2}SO

_{3}) was used for decreasing amount of dissolved oxygen in water before k

_{L}a coefficient was analyzed.

### 2.2. Gas Diffusers Used in This Study

### 2.3. Determination of Bubble Hydrodynamic Parameters

_{B}) in this study was deduced from the measurement of 150–200 bubbles. The average bubble formation frequency, fB, (i.e., the number of bubbles formed at the membrane orifice per unit time) was determined as in Eq. (1) [4].

### 2.4. Determination of Mass Transfer Coefficients

_{L}a). Due to the absorption of oxygen in water, the gas-liquid mass transfer mechanism is governed by the liquid phase. The volumetric mass transfer coefficient (k

_{L}a) then can be determined from Eq. (4).

_{L}is the dissolved oxygen concentration, and

*C*

_{L}*is the saturation oxygen concentration in liquid phase. The coefficient k*

^{S}_{L}a is the product of the liquid-side mass transfer coefficient (k

_{L}) and the interfacial area (a). Therefore, k

_{L}coefficient can be simply determined by:

### 3. Results and Discussion

### 3.1. Volumetric Mass Transfer Coefficient (k_{L}a)

_{L}a values with the superficial gas velocity (V

_{g}) for different gas diffusers (rigid and flexible) and bubble columns types. Fig. 4(a)–(c) respectively present the k

_{L}a coefficients from the small, medium, and large column (i.e., column diameters of 5, 10, and 150 cm) with a summary in Fig. 4(d).

_{L}a coefficients were obviously affected by the V

_{g}. The increase of bubble number in the column can enhance the total surface of bubble for gas-liquid mass transfer. The k

_{L}a values of 0.001 – 0.05 sec

^{−1}were obtained for the V

_{g}of 0.000425 – 0.0283 m/sec in all experiments. The coefficients obtained from larger column were higher than those of the smaller one. Influences of V

_{g}and Q

_{G}should be applied for describing the results.

_{L}a coefficients was more pronounced in the larger column as shown in Fig. 4(d). The diffusers with single orifice (R1, F1 and Fo1) provided similar k

_{L}a coefficients from small column. However, the k

_{L}a obtained in the medium column with rigid orifice with multi-orifice (R2) were higher than those of flexible one (F2). The same tendency can also be observed in large column as k

_{L}a (R2) > k

_{L}a (F3) > k

_{L}a (F4). These results presented the advantage of using rigid orifice in bubble column, especially for large diameter. Moreover, the experimental results in this work can be validated by using the same rigid diffuser (R2) in medium and large column. The k

_{L}a coefficients were increased continuously with the superficial gas velocity. Therefore, the simple prediction model can be proposed as expressed in Eq. (6).

_{L}a values calculated by Eq. (6) are compared with the experimental results in Fig. 5 for different gas diffusers (rigid and flexible) and bubble columns types (small, medium and large). The discrepancy range of 35% can be noticed. The differences of bubble column configurations and operating conditions should be responsible for these results. In addition, the k

_{L}a coefficients are generally too global and difficultly evaluated in practical application. Therefore, local measurement of bubble diameter and the interfacial area (a) was performed and presented in next section to provide a better understanding on effects of gas diffusers and the gas–liquid mass transfer mechanisms.

### 3.2. Bubble Diameter (D_{B})

_{B}) with the superficial gas velocity (V

_{g}) in the small column are depicted in Fig. 6(a). Rigid diffusers with single orifice (R1) tended to produce constant bubble sizes (> 4.5 mm) as the orifice was unchanged with increased gas flow rate (d

_{OR}= 0.5 mm). On the contrary, bubble sizes from the flexible diffuser with single orifice (F1 and Fo1) were increased with the gas flow rate as the orifice sizes of the diffusers were enlarged at larger gas flow rate.

_{g}. It was worth noting that the bubble diameter was about 10 times of the orifice size. These results conformed to the data from flexible diffusers with small orifice size of 0.12–0.19 mm (Fo1) as well as the data from single orifice diffuser [4, 11]. The importance of orifice size and its characteristic can be concluded, especially for diffuser with single orifice. It should be noted that the flexible diffuser (Fo1) cannot be operated at higher V

_{g}due to its manual fabrication and physical properties. The results therefore cannot be used for comparing with other diffusers (F1 and R1) regarding effects of superficial gas velocity.

_{B}was more pronounced at low superficial gas velocities (V

_{g}< 7.5×10

^{−4}m/sec). At low V

_{g}, the difference in bubble diameter directly linked to the surface tension. The balance between the surface tension and the buoyancy force during the bubble growth and detachment was consequently different for dissimilar orifice diameter. However, a bubble diameter was no longer controlled by the force balance at higher V

_{g}, but instead governed by the power dissipated in a liquid phase. This can cause the break-up of and coalescence of bubbles [12, 13].

_{g}> 7.5× 10

^{−4}m/sec). Furthermore, the same ranges of bubble size (1.75–2.3 mm) were found from the rigid diffuser (R2) in the medium and the large column, but smaller than bubbles generated from the R1 diffuser. The orifice size should be responsible for these results since the orifice diameter of R2 (0.25 mm) was smaller than that of R1 (0.5 mm).

_{g}that D

_{B}from the F3 and F4 diffusers were obviously greater than that of R2 since the orifice sizes were enlarged with the gas velocity. According to the physical properties of diffusers in Table 1, the smallest bubbles were found from the F2 diffuser, which was the thinnest one (1.65 mm). Therefore, it can be stated that the physical property can affect the orifice size due to the elasticity or deflection at the centerline. The thin flexible diffuser provided small orifice size and smaller bubble size as a result.

_{g}have to be controlled for maintaining the generation of small bubbles. In the next part, the interfacial area, which is one of key parameters in the gas–liquid mass transfer study, was determined from bubble sizes obtained experimentally.

### 3.3. Interfacial Area (a)

_{B}values obtained by Grace and Wairegi [14]. The bubble velocity (U

_{B}) of 0.15–0.25 m/sec were obtained from the diameters of 1.6–6.2 mm. Small bubbles in the large column tended to have lower rising velocity than in the small column due to effects of power dissipated in the liquid resulting in the break-up of bubbles. Bubbles then obstructed movement of each other out of the column. Moreover, it can be stated that small bubbles (low U

_{B}values) can enhance the retention time of bubble in column, thus increasing the bubble specific interfacial area (a).

_{B}) at different gas superficial velocities can be calculated. The local interfacial area (a) can then be determined. Fig. 9 presents the relation between the interfacial area (a) and the superficial gas velocity for different diffusers (F1, Fo1, F2, F3, F4, R1 and R2) and bubble column dimensions (small, medium and large) used in this work.

^{−1}while superficial gas velocities were between 0.0002 and 0.0015 mL/sec as shown in Fig. 9(a). Whatever the orifice type, the values of a were linearly increased with the superficial gas velocities. The values obtained from Fo1 were obviously greater than those of F1 and R1, which corresponded to the lowest d

_{B}and U

_{B}as aforementioned. However, the physical property of diffuser (Fo1) in terms of elasticity and shear stress should be well considered in practical operation, especially at higher superficial gas velocity.

_{g}as shown Fig. 9(b), (c) for the medium and large columns, respectively. Moreover, the increase of the cross-sectional area of column also played a role since the gas flow rate was enhanced as a result. The a values obtained from the rigid diffuser (R2) were clearly greater than those of flexible diffusers (F2, F3 and F4). Small bubbles with low rising velocity from the rigid orifice (R2) were responsible for this result. Moreover, the results of the R2 diffuser were validated in the medium and the large columns as increased with V

_{g}depicting in Fig. 9(d). This result conformed to those obtained with the k

_{L}a coefficient as in Fig. 4(d). Note that the difference in a can be clearly observed from the Fo1 diffuser in the small column whereas the related k

_{L}a coefficients were close to those obtained from different diffusers (F1 and R1) as shown in Fig. 4(a). For a better understanding of the gas-liquid transfer phenomena, the liquid-side mass transfer coefficient (k

_{L}) was considered in the next part.

### 3.4. Liquid-side Mass Transfer Coefficient (k_{L})

_{L}coefficient can be calculated from the experimental values of the volumetric mass transfer coefficient (Fig. 4) and the interfacial area (Fig. 9) by Eq. (5). The values of k

_{L}were scatter since the calculation of k

_{L}could possess errors from the measurements of both k

_{L}a and a. The average and maximum experimental errors for determining the k

_{L}were estimated at 10% and 15%, respectively [10]. Fig. 10 shows the variation of the liquid-side mass transfer coefficient (k

_{L}) with the superficial gas velocity (V

_{g}) for different gas diffusers and bubble column types.

_{L}varied between 1 × 10

^{−4}and 4 × 10

^{−4}m/sec for V

_{g}in the range of 0.0002–0.03 m/sec. At every operating condition, the k

_{L}values tended to be constant for the gas flow rates greater than 0.0004 m/sec. On the contrary, k

_{L}was increased with V

_{g}at lower velocities. Fig. 11 displays the variation of k

_{L}with the bubble diameter (D

_{B}) for the different gas diffusers and bubble columns. This plot was applied for analyzing and comparing the results in this study with the three zones of k

_{L}coefficients proposed by Painmanakul et al. [10] and Sardeing et al. [15].

_{L}coefficient was roughly constant at D

_{B}larger than 3.5 mm and then slightly decreased up to the D

_{B}of 1.5 mm before remaining constant until 1.5 mm. The dimension of bubble columns cannot affect the k

_{L}coefficient. The coefficient k

_{L}only depend on bubble sizes due to a modification of the gas-liquid interface nature (size and shape of generated bubbles) coupled with local hydrodynamic changes (terminal rising bubble velocity and drag coefficient of bubbles). Three zone of the variation between k

_{L}and D

_{B}can be observed in Fig. 11 as follows.

**Zone A (d**_{B}**< 1.5mm):**k_{L}are low for small bubbles (about 1 × 10^{−4}m/sec) [16] corresponded with the results obtained from the flexible diffuser (Fo1).**Zone B (1.5 < d**_{B}**< 3.5mm):**k_{L}values were increased (1 × 10^{−4}to 4 × 10^{−4}m/sec) with the bubble diameter. The modification of the bubble shape (from sphere to ellipsoid) as well as the bubble interface should be responsible for these result [15]. The diffusers (R2, F2, F3, and F4) can provide the bubble sizes and the k_{L}coefficient in this zone.**Zone C (d**_{B}**> 3.5mm):**k_{L}values were independent on bubble diameters conforming with the results of Higbie [17]. The k_{L}were constant for larger bubble size behaving as fluid particles with a mobile surface. This zone can be related with the results obtained from the diffusers (F1 and R1).

_{L}). Note that, the value of surface coverage ratio at equilibrium (s

_{e}) in case of clean liquid phase, used in this work. In Fig. 12, the comparison between the experimental results and the predicted values from the existing models is presented.

_{L}coefficients was obtained (average difference of ±15%), especially for Zone A and Zone C. However, more experimental data are necessary for more accurate predicting and validating the Zone B correlation (average difference of ±40%). These zone related with the diffusers (R2, F2, F3 and F4) operated at high superficial gas velocities in medium and large columns. The bubble break-up and coalescence phenomena due to the power dissipated in the liquid phase should be responsible for these results. Moreover, this can possibly affect the k

_{L}a prediction model (average difference about ±35%) as shown in Fig. 5. In the future, effects of the geometrical transition from the sphere to ellipsoid of bubbles on the k

_{L}coefficient should be focused, especially for Zone B in order to propose more precision model for mass transfer parameters (k

_{L}a and k

_{L}).

_{L}in Zone A, it can be stated that the generation of tiny bubbles (D

_{B}< 1mm) was unnecessary to increase the mass transfer capacity. The increase of interfacial area from generated fine bubbles can be compromised by the great decrease of the k

_{L}coefficient. These results conformed to the case of diffuser (Fo1) in the small bubble column. Even the increase of a can be clearly observed, the related k

_{L}a coefficients were close to those observed form the different diffusers (F1 and R1). Therefore, within the range of bubble sizes (1.5–2.3 mm) generated by the R2 diffuser, high interfacial area and moderate k

_{L}coefficient can be obtained. These can provide the maximum k

_{L}a coefficient for gas-liquid mass transfer. In the case of a gas–liquid reactor equipped with gas diffuser, the total specific power consumption (P

_{g}/V

_{Total}) for mixing condition could be related to the total gas pressure drop as in Eq. (7).

##### (7)

$$\frac{{P}_{G}}{{V}_{Total}}=Q\times \frac{\mathit{\Delta}{P}_{Total}}{{V}_{Total}}=Q\times \frac{({\rho}_{L}.g.{H}_{L}+\mathit{\Delta}P)}{{V}_{Total}}$$_{Total}) is a function of the liquid height (r·g·H

_{L}) and the specific sparger pressure drop (ΔP), which is increased with the gas velocity through the orifice (V

_{g}= Q

_{g}/A

_{OR}). From Painmanakul et al. [4], the value of ΔP increases with the gas flow rate as well as the decrease of hole area or orifice size for small bubble generation. The drawback in term of energy consumption for small bubble size has to be taken into account as the important consequences for using the bubble column in real operating condition.

_{L}a coefficient, small orifice size should be used for generating the small bubbles. Form the obtained results, the advantage of rigid diffuser operated at high superficial gas velocity in the large bubble column can be found. However, the clogging problem of a diffuser must be taken into account. For flexible diffuser, the control of superficial gas velocity and orifice size should be well considered in order to maintain a small bubble generation in the reactor. Moreover, it was unnecessary to generate numerous fine bubbles at high superficial gas velocity for enhancing the k

_{L}a coefficient and absorption efficiency in the bubble column. The increase of values can be withdrawn by the great decrease of the k

_{L}coefficients as well as the increase of related power consumption.

### 4. Conclusions

_{g}) on bubble column performance in terms of bubble hydrodynamic and mass transfer parameters. For this purpose, the methods for determining the volumetric mass transfer coefficient (k

_{L}a), bubble size (D

_{B}), interfacial area (a), and liquid-film mass transfer coefficient (k

_{L}) were applied to enable the absorption efficiency in a bubble column. The following results were obtained:

The k

_{L}a coefficients increased with the superficial gas velocity (V_{g}) and the bubble column size. The prediction model was proposed with the average difference between the experimental and predicted k_{L}of ± 35%:

For single orifice gas diffuser, physical property of gas orifice can clearly influence the generated bubble size, especially at low superficial gas velocity. Less effect was found at higher V

_{g}due to the power dissipated in the liquid resulting in the bubble break-up and coalescence phenomena;In the case of gas diffuser with multiple orifices, effects of orifice size, diffuser thickness, and superficial gas velocity were noticed on the modification of generated bubble size presence in bubble column;

At highest interfacial area, the advantage of rigid diffuser can be obtained for high V

_{g}operation in large bubble column due to the generation of small bubbles with low rising velocity;Three zones of k

_{L}coefficients with different bubble sizes (1×10^{−4}m/sec in Zone A, 1×10^{−4}– 4×10^{−4}m/sec in Zone B, and 4×10^{−4}m/sec in Zone C) can be found. The result was validated with different bubble column configurations and operating conditions;To enhance the k

_{L}a coefficient and absorption efficiency in bubble column, it was unnecessary to generate numerous fine bubbles at high superficial gas velocity for highest interfacial area as this a can be cancelled out by the great decrease of the k_{L}coefficients as well as the increase of power consumption.

_{L}a and k

_{L}coefficients), more experimental data are required, especially for the gas diffuser or bubble size ranging within Zone B (1.5 < d

_{B}< 3.5 mm). Finally, the industrial-scale bubble column (larger column dimension and higher superficial gas velocity) should be studied for extending the lab-scale results into the practical operating condition.

### Notation

*C*_{L}^{*}

^{−3}

*D*

^{2}·sec

^{−1}

*k*_{L}

^{−1}

*k*_{L}^{rigid}

^{−1}

*k*_{L}^{ZoneA}

^{−1}

*k*_{L}^{zoneB}

^{−1}

*k*_{L}^{zoneC}

^{−1}

*a*

^{−1}

*k*_{L}*a*

^{−1}

*Sc*

Re

*Se*

*d*_{B}

*d*_{B}^{0}

*d*_{B}^{1}

*d*_{OR}

*t*_{e}

*V*_{B}

^{3}

*U*_{B}

^{−1}

*V*_{L}

^{3}

*V*_{total}

^{3}

*Vg*

^{−1}

*f*_{B}

^{−1}

*h*

*H*_{L}

*g*

^{−2}

Δ*P*