Bubble gas holdup

Figure 2. Total and Small Bubble Gas Holdups for CO -NaOH System.

This equation is solved with respect to u under the simplifying assumptions (M31, U5) that is constant in the turbulent flow region, and that bubble gas holdup b is distributed radially according to the relation ... 

Pressure. Within limits, pressure may have Htfle effect in air-sparged LPO reactors. Consider the case where the pressure is high enough to supply oxygen to the Hquid at a reasonable rate and to maintain the gas holdup relatively low. If pressure is doubled, the concentration of oxygen in the bubbles is approximately doubled and the rate of oxygen deHvery from each bubble is also approximately doubled in the mass-transfer rate-limited zone. The total number of bubbles, however, is approximately halved. The overall effect, therefore, can be small. The optimum pressure is likely to be determined by the permissible maximum gas holdup and/or the desirable maximum vapor load in the vent gas. 

Z. 5-25-Y, large huhhles = AA = 0.42 (NG..) Wi dy > 0.25 cm Dr luterfacial area 6 fig volume dy [E] Use with arithmetic concentration difference, ffg = fractional gas holdup, volume gas/total volume. For large huhhles, k is independent of bubble size aud independent of agitation or liquid velocity. Resistance is entirely in liquid phase for most gas-liquid mass transfer. [79][91] p. 452 [109] p. 119 [114] p. 249... 

Gas Holdup (e) in Bubble Columns With coalescing systems, holdup may be estimated from a correlation by Hughmark [Ind. Eng... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Some data on gas holdup are also reported by Stemerding (SI6). Hoogendoorn and Lips (H10) have reported gas-holdup data for counter-current bubble flow in the experimental system described in Section V,A,4. Gas holdup was not influenced by changes of liquid flow rate, but increased with nominal gas velocity in the range from 0.03 ft/sec to 0.3 ft/sec. The results are somewhat lower than those obtained by Weber, the difference being explained as due to the difference in gas distributor. Weber used a porous plate and Hoogendoorn and Lips a set of parallel nozzles. 

Measurements for water containing 0.2% ethanol, the addition of which was found to influence markedly the gas holdup (see Section V,B,3), indicate that variation of surface tension has no significant effect upon axial mixing. The results for 2-mm spheres could not be correlated by a similar expression. It is proposed in that work that the flow mechanism in this case is significantly different because of the higher ratio between bubble size and particle size. 

Information on gas holdup and axial dispersion in bubble-columns containing suspended solid particles is scarce reference will therefore also be made to significant studies of bubble-columns with no particles present, results obtained for these systems being probably of some relevance to the understanding of bubble-column slurry operations. 

Verschoor (V5) studied the motion of swarms of gas bubbles formed at a porous glass gas distributor. Gas holdup was observed to increase approximately linearly with nominal gas velocity up to a critical point (corresponding to a nominal gas velocity of about 4 cm/sec), whereupon it decreased to a minimum and then increased again on further increase of the gas velocity. Higher holdup was observed for a water-glycerine mixture than for water. 

Houghton et al. (HI3) have reported data on the size, number, and size-distribution of bubbles. Distinction is made between bubble beds, in which bubble diameter and gas holdup tend to become constant as the gas velocity is increased (these observations being in agreement with those of other workers previously referred to), and foam beds, in which bubble diameter increases and bubble number per unit volume decreases for increasing gas velocity. Pore characteristics of the gas distributor affect the properties of foam beds, but not of bubble beds. Whether a bubble bed or a foam bed is formed depends on the properties of the liquid, in particular on the stability of bubbles at the liquid surface, foam beds being more likely to form in solutions than in pure liquids. 

The results reported for beds of small particles (1 mm diameter and less) are in substantial agreement on the fact that the presence of solid particles tends to decrease the gas holdup and, as a consequence, the gas residencetime. This fact may also support the observations of gas absorption rate by Massimilla et al. (Section V,E,1) if it is assumed that a decrease of absorption rate caused by a decrease of residence time outweighs the increase of absorption rate caused by increase of mass-transfer coefficient arising from the increase in bubble Reynolds number. These results on gas holdup are in... 

Based on the same assumption, the results by Viswanathan et al. on gas holdup in beds of larger particles are in agreement with the results of Lee (L3) on bubble breakup in beds of larger particles (05). No work on the residencetime distribution of the gas phase in gas-liquid fluidized beds has come to the author s attention. 

Gas holdup may be of the same magnitude in the various operations, although for bubble-columns, the presence of electrolytes or surface-active agents appears to be a condition for high gas holdup. The gas residence-time distribution resembles that of a perfect mixer in the stirred-slurry operation, and comes close to piston flow in the others. 

This brief discussion of some of the many effects and interrelations involved in changing only one of the operating variables points up quite clearly the reasons why no exact analysis of the dispersion of gases in a liquid phase has been possible. However, some of the interrelationships can be estimated by using mathematical models for example, the effects of bubble-size distribution, gas holdup, and contact times on the instantaneous and average mass-transfer fluxes have recently been reported elsewhere (G5, G9). 

Yoshida and Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

Calderbank et al. (C1-C4), who worked with systems quite similar geometrically to that of Yoshida and Miura, found that the average bubble diameter for air in water at 15°C ranged from 3 to 5 mm. Westerterp et al. (W2-W4) found the range to be 1-5 mm for air in sodium sulfite solution at 30°C. In addition, they noted that any increase in interfacial area between the bubbles and the liquid was due primarily to the increase in gas holdup, and the average bubble diameter was essentially unaffected by the impeller speed and was approximately 4.5 mm (W3). 

Under constant operating conditions, the number of bubbles in the vessel is constant, and their total volume or gas holdup is equal to Q0, where 0 is the average residence-time of the bubbles and Q is the volumetric gas flow rate. The number of bubbles in the vessel at any instant is then given by... 

For chemical reaction-rate constants greater than 10 sec-1, NT increases linearly with the total bubble surface area, i.e., linearly with the gas holdup. In other words, the agitation rate only affects the total bubble surface area and has almost no effect on the rate of absorption per unit area. This result is in accordance with the work of Calderbank and Moo-Young (C4), discussed in Section II. 

Fig. 17. Influence of bubble size on NAj as affected by interaction between bubbles (as a function of a in subreactors and for constant gas holdup), chemical reaction rates, and contact times. NAJ was calculated from Eq. (176) with c, = 1.46 x 10-7 gr-mole/cm3 D= 2.3 x 10"5 cm2/sec G> =0.064 d = 0.1 cm 0 = 2.85 sec [after Gal-Or and Hoel-scher (G5)].

Mass transfer in the continuous phase is less of a problem for liquid-liquid systems unless the drops are very small or the velocity difference between the phases is small. In gas-liquid systems, the resistance is always on the liquid side, unless the reaction is very fast and occurs at the interface. The Sherwood number for mass transfer in a system with dispersed bubbles tends to be almost constant and mass transfer is mainly a function of diffusivity, bubble size, and local gas holdup. 

The diffusivity in gases is about 4 orders of magnitude higher than that in liquids, and in gas-liquid reactions the mass transfer resistance is almost exclusively on the liquid side. High solubility of the gas-phase component in the liquid or very fast chemical reaction at the interface can change that somewhat. The Sh-number does not change very much with reactor design, and the gas-liquid contact area determines the mass transfer rate, that is, bubble size and gas holdup will determine reactor efficiency. 

The low density of gases makes it more difficult to keep the bubbles dispersed. The bubbles will move to the low-pressure areas, that is, behind the impellers, in the trailing vortices close to the impeller, behind the baffles, and at the inner side after a bend. The bubbles will coalesce in these areas with high gas holdup. It is very difficult to design reactors without low-pressure regions where the low-density fluid will accumulate. One such reactor is the monolith reactor for multiphase flow [32, 33]. 

Gas holdup and liquid circulation velocity are the most important parameters to determinate the conversion and selectivity of airlift reactors. Most of the reported works are focused on the global hydrodynamic behavior, while studies on the measurements of local parameters are much more limited [20]. In recent years, studies on the hydrodynamic behavior in ALRs have focused on local behaviors [20-23], such as the gas holdup, bubble size and bubble rise velocity. These studies give us a much better understanding on ALRs. 

The bubble size distribution is closely related to the hydrodynamics and mass transfer behavior. Therefore, the gas distributor should be properly designed to give a good performance of distributing gas bubbles. Lin et al. [21] studied the influence of different gas distributor, i.e., porous sinter-plate (case 1) and perforated plate (case 2) in an external-loop ALR. Figure 3 compares the bubble sizes in the two cases. The bubble sizes are much smaller in case 1 than in case 2, indicating a better distribution performance of the porous sinter-plate. Their results also show the radial profile of the gas holdup in case 1 is much flatter than that in case 2 at the superficial gas velocities in their work. 

Fig. 3. Radial profiles of the bubble size with Fig. 4. Influence of internals on the gas holdup different gas distributors (air-water system) [22]. (air-water-solid slurry system) [23].

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