On the design of bubble columns equipped with a fine pore sparger : Effect of gas properties

In our previous works we have proposed design equations that can predict with reasonable accuracy the transition point from homogeneous to heterogeneous regime as well as the gas holdup and the mean Sauter diameter at the homogeneous regime. The validity of the proposed correlations was checked with data obtained using different geometrical configurations and several Newtonian and non-Newtonian liquids as well as the addition of surfactants. However, in all the experiments the gas phase was atmospheric air. This work investigates the effect of gas phase properties by conducting experiments employing various gases (i.e., air, CO2, He) that cover a wide range of physical property values. Experiments revealed that only the use of low-density gas (He) has a measurable effect on bubble column performance. More precisely, when the low-density gas (He) is employed, the transition point shifts to higher gas flow rates and the gas holdup decreases, a fact attributed to the lower momentum force exerted by the gas. In view of the new data, the proposed correlations have been slightly modified to include the effect of gas phase properties and it is found that they can predict the aforementioned quantities with an accuracy of ±15%. It has been also proved that CFD simulations are an accurate means for assessing the flow characteristics inside a bubble column.


Introduction
Bubble columns are gas-liquid contactors that are used in many industrial gas-liquid operations (e.g.gas/liquid reactions, agitation by gas injection, fermentations, waste water treatment, etc.) in chemical and biochemical industries.In all these processes, gas holdup and bubble size distribution are important design parameters, since they define the gas-liquid interfacial area available for mass transfer.In turn, these parameters depend on the operating conditions, the physico-chemical properties of the two phases, the gas sparger type and the column geometry [1,2].Two main flow regimes are encountered in bubble columns, namely the homogeneous bubbly flow regime, which is encountered for low gas velocities and is characterized by discrete and uniformly dispersed bubbles and the heterogeneous regime, which corresponds to higher gas velocities.In the homogeneous regime the bubbles are smaller and thus the interfacial contact area per unit mass of air is larger and thus it is most desirable for practical applications, where a low shear rate environment is desirable (e.g.bioreactors, blood oxygenators).The mechanism of bubble formation, presented in Figure 1 and Table 1, is of crucial importance to bubble column hydrodynamics.A bubble is detached, when the sum of the upward forces outweighs the sum of the downward ones.

Upward Forces Downward Forces
Buoyancy ( ) Gas momentum Surface tension In previous works [2,[3][4][5] the effect of the sparger characteristics (i.e.diameter, pore size), the liquid physical properties and the gas flow rate on the performance of a bubble column equipped with a fine pore sparger has been experimentally studied, using Newtonian and non-Newtonian liquids as well as liquids containing surfactants.Based on the data design correlations, which can predict with reasonable uncertainty (better than ±15%) the transition point between the homogeneous and the heterogeneous regime as well as the gas hold-up and the bubble size distribution at the homogeneous regime, were formulated.All these correlations are based on data where the gas phase is air.The purpose of this work is to check the validity of previously proposed correlations, by conducting experiments with several gases and, if necessary, to modify them to incorporate the effect of gas type.

Experimental set-up and procedure
The experimental set-up (Figure 2) consists of a cylindrical bubble column, equipped with a fine pore sparger for the injection and the uniform distribution of the gas phase, an appropriate flowmeter for gas flow control, a high speed digital video camera (Redlake MotioScope PCI ® 1000S) for bubble size and gas holdup measurements and a computer for acquiring and processing the data.A Plexiglas ® rectangular box, filled with the same fluid as the one used at the corresponding experiment was placed around the bubble column to eliminate image distortion caused by light refraction.
The gas phase is introduced to the column through a fine pore sparger, namely a 316 L SS porous disk (Mott Corp.®) with a nominal pore size of 40 μm, that covers the whole bottom plate.The effect of the sparger to column diameter ratio on the bubble column performance has been investigated and discussed in a previous paper [4].To ensure that the gas phase is evenly distributed over the whole sparger area the gas phase was injected through a 1 cm nozzle to a vessel of 35 cm height placed beneath the bubble column, following the design proposed in a previous paper [4].A record-ing rate of 125 frames per second (fps) was used for the measurement of gas holdup, while a speed of 500 fps was selected for measuring the bubble size.
The geometrical characteristics of the bubble columns studied are given in Table 2.The liquid phase was either de-ionized water or an aqueous glycerin solution, while three gases, namely air, CO 2 and He, covering a sufficiently wide range of density values were individually employed.The mentioned fluids and their properties are all given in Table 3.All the experiments were performed with no liquid throughput, at atmospheric pressure and ambient temperature conditions (i.e.around 20 o C).The average gas holdup (εG) is estimated by calculating the bed expansion as follows: where Ηο and Η is the liquid level before and after gas injection respectively, ΔΗ is the liquid level difference and n is the number of recurrent measurements for each gas flow rate (in this case n=50).
The estimated maximum uncertainty of the measurements is less than 15%.
From bubble images taken by the video camera the diameter of a sample of 100 bubbles was measured and the Sauter mean diameter (d32), was calculated: The minimum number of classes required for the construction of the size distributions,  was estimated by the Sturges' rule: k=1+log2S.The number of classes used for the construction of the distributions in the present work is 10 equal intervals.Aiming to avoid possible random errors that may be involved in the measuring procedure, we were repeating the same experiment 5 times and we were calculating d32 for each experiment.

Bubble size distribution
Figure 3 illustrates typical bubble size distributions with the 40 μm sparger (dC=9 cm), for all gases studied and for a constant U GS value.As expected [2], the distributions are log-normal while regardless of the liquid phase only the low density He gas exhibits an observable effect on the bubble distribution curve, due to the lower momentum force exerted by the low density He gas (Table 1).
However, the value of mean Sauter diameter is not considerably affected by the type of gas but is mainly affected by the type of liquid phase employed (Table 5).In previous works in our lab [2,4] a correlation for predicting the Sauter mean diameter (d32) based on dimensionless numbers was proposed.The same correlation can be used for predicting the mean Sauter diameter when different gases are employed provided that the constants of the correlation are suitably adjusted (Eq.9).
where dimensionless numbers are defined as: Fr d g The proposed correlation (Eq.9) can be used for predicting d 32 values with reasonable accuracy (i.e.±15%) for all the gases employed.

Regime transition
The transition point from homogeneous to heterogeneous regime is estimated by applying the drift flux analysis, which considers the relative motion of the two phases.The basic quantity is the drift flux, j, is given by: , where ε G is the gas holdup and U GS is the superficial gas velocity defined as . When the drift flux is plotted versus the gas holdup, the change in the slope of the curve indicates the transition from homogeneous to heterogeneous regime [6].
The effect of the type of gas on regime transition is illustrated in Figure 4.It is obvious that, only when the lower density gas, He, is employed, the homogeneous regime is extended to higher j or equally U GS values.
In previous papers [4,7] a correlation was proposed for predicting the transition point that is based on dimensionless numbers and incorporates the physical properties of the liquid phase as well as the geometrical characteristics of the column and the porous sparger.This correlation has the general form: In view of the new results to incorporate the effect of type of gas, the ratio of gas density to that of air density is added.The new correlation is as follows: The predicted UGS, trans values are in very good agreement, i.e. better than 15%, with the corresponding experimental data.The proposed correlation is suitable for predicting the transition point from homogeneous to heterogeneous regime.

Gas holdup
In this section the effect of the various parameter on the gas hold-up values is investigated.As it is expected, gas holdup increases with the gas velocity.The first part of the curve corresponds to the homogeneous regime, which is followed by a transition regime where the gas holdup slightly decreases.Finally, at the heterogeneous regime the gas holdup continues to increase, but with a lower slope than the homogeneous regime [3].
Figure 5 shows the dependence of gas holdup on corresponding gas superficial velocity for the two bubble columns used.It is obvious from that by increasing the column diameter the gas holdup increases, especially for higher gas flow rates.However, the literature results concerning the effect of column diameter on gas holdup are contradictory.Some researchers report that the column diameter has no effect on gas holdup.The above works concern bubble columns with diameter larger than 10 cm, where the gas distributor is a perforated plate.
Ruzicka et al. [8] also state that the gas holdup is independent of column dimensions provided that the column diameter is larger than 10 cm, the column height is larger than 15 cm and the column height to diameter ratio is more than 5. On the other hand, some works report that the column diameter affects the gas holdup.The gas holdup increases when the column diameter decreases, whereas Kumar et al. [9] who conducted experiments in bubble columns with diameters larger than 10 cm, state that there is a continuous increase in the gas holdup with increasing column diameter.
To the best of our knowledge, there are no experimental results concerning bubble columns with diameter less than 10 cm, equipped with fine porous sparger.Dhotre et al. [10], who have numerically studied the effect of sparger type and height to diameter ratio on radial gas holdup profiles, report that for multipoint spargers, an increase of the column height to column diameter ratio results into marginal decrease of gas holdup.Obviously, when the column diameter decreases the wall effects become more intense.ure 5. Effect of column diameter on gas holdup for the water-air system.
Figure 6 presents typical effect of the type of gas on gas holdup.With increasing gas density gas holdup increases, e.g.helium that has a lower density exhibits lower values of gas holdup than air and CO 2 .This behavior is attributed to the fact that, the lower density gas exerts a lower momentum force to an under-formation bubble (Eq.2).This observation agrees with other researchers who also reported that gases of higher density produce higher gas holdup values, attributing this behavior on phenomena occurring during bubbles formation on the sparger.However, it is worth noticing that, even though the density of CO 2 is 50% higher than that of atmospheric air, for the lower gas superficial velocities both air and CO 2 exhibit almost the same behavior and only when the density decreases by more than 80% (i.e. for He)) a noticeable change is observed (Figure 6) In previous studies conducted in our lab [3,4,7] a correlation for predicting the average gas holdup, εG, was proposed based on dimensionless numbers.The equation has the general form: where Fr, Ar and Eo are respectively defined by: The values of constants c 1 to c 7 depend on the of liquid phase.It was also proved [3][4][5]7] that the proposed correlations can predict hold up with reasonable accuracy, i.e. better than 15%.However, in the ε G prediction the type of gas is not taken into account, although the gas momentum affects bubble evolution (Table 1).From Figure 6, where the effect of gas type is presented, it is apparent that only the very low density gas He has has a measurable effect on gas hold-up value.In case that the gas phase is other than air, it is necessary to introduce a term that incorporates the properties of the gas phase.
Based on the above, we have modified Eq. 12 by introducing in the gas Reynolds number Re G defined as: The modified form of the proposed correlation is as follows: where the constants of the correlation are given in Table 6.Furthermore, Figure 7 shows that the ε G values predicted by Eq. 12 are in very good agreement (±15%) with the corresponding experimental data. .

Concluding remarks
In this work, we have experimentally investigated in what extent the type of gas phase influences the performance of a bubble column reactor by employing gases that cover a wide range of physical properties; namely atmospheric air and CO 2 exhibit almost the same behavior, while the low density He shows a measurable effect on bubble column design quantities.This can be attributed to the fact that the low density He gas exhibits a lower momentum force.Thus, the previously proposed correlations for predicting the transition point from the homogeneous to the heterogeneous regime, the gas holdup and the Sauter mean diameter are slightly modified to include the effect of the type of gas employed.The new correlations can predict the aforementioned quantities with reasonable accuracy (better than 15%).

Figure 3 .
Figure 3.Effect of type of gas on bubble size distribution (U GS =0.01 m/s.)

1 where
Fr trans and Eo based on d 32 are difined as :

Figure 4 .
Figure 4. Effect of type of gas on regime transition for water.

Figure 7 .
Figure 7.Comparison of the proposed correlation with the experimental data.