Gas holdup

Gas holdup is the volume fraction ofthe gas bubbles in a gassed liquid. However, it should be noted that two different bases are used for defining gas holdup (i) the total volume of the gas bubble - liquid mixture and (ii) the clear liquid volume excluding bubbles. Thus, the gas holdup defined on basis (ii) is given as 

The gas holdups can be obtained by measuring Zp and Zp, or by measuring the corresponding hydrostatic heads. Evidently, the following relationship holds. 

Although use of basis (i) is more common, basis (ii) is more convenient in some cases. 

As with the gas holdup, there are two definitions of interfacial area, namely, the interfacial area per unit volume of gas - liquid mixture a (I I. ) and the interfacial area per unit liquid volume a (L L ). 

There are at least three methods to measure the interfacial area in liquid-gas bubble systems. 

While the superficial liquid velocity is a function of riser and downcomer gas holdup, it also influences these holdups. Hence, for a given airlift reactor geometiy, the superficial liquid velocity is a function of gas holdup. The superficial liquid velocity can only be changed in this reactor through geometry modifications (which will also affect gas holdup values) or through the use of a throttling device (Popovic and Robinson, 1988). 

Local instantaneous liquid velocity measurements in bioreactors that can quantify turbulence statistics are challenging using conventional laser-based techniques because optical access is critical for effective signal acquisition. Laser Doppler anemometry (LDA) and PIV have been used to determine local liquid velocities within multiphase flows. Reviews of LDA and PIV with applications to multiphase flows have appeared in the literature (Boyer et al., 2002 Chaouki et al., 1997 Cheremisinoff, 1986). 

Liquid velocity may also be determined using hot film anemometry (Boyer et al., 2002 Magaud et al., 2001). One advantage of this technique is that it is fairly inexpensive, accurate, and relatively easy to implement. However, proper implementation requires a uniform temperature in the bioreactor as well as a limited 

Gas holdup (or gas fraction or void fraction) is defined as the volumetric fraction occupied by the gas phase in the total volume of a two- or three-phase mixture. It is one of the most important parameters characterizing gas-liquid and gas-liquid-solid hydrodynamics, because it not only gives the volume fraction of 

Gas holdup can be measured by numerous invasive or noninvasive techniques, which have been reviewed by Kumar et al. (1997) and Boyer et al. (2002), and include changes in total bed expansion upon gassing, pressure drop measurements, dynamic gas disengagement (DGD), and tomographic techniques. 

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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. 

Gas holdup with Rushton turbine can be estimated from the following correlation ... 

Static mixing of gas—Hquid systems can provide good interphase contacting for mass transfer and heat transfer. Specific interfacial area for the SMV (Koch/Sulzer) mixer is related to gas velocity and gas holdup ( ) by the following ... 

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. 

Gas holdup Inducers Specific oxygen uptake rate... 

Gas holdup Vm is the volume of carrier gas that passes through the column to elute an unretained substance, such as argon or methane. The time required is tm. 

Figure 5. Gas holdup (e0) and incremental bed porosity (eLO — eL) vs. superficial gas velocity with process development unit (PDU)...

Only a few investigations concerned with the measurement of gas holdup and residence-time distribution have been reported. The information regarding liquid holdup, which will be discussed in the following section, is considerably more abundant in some cases, values of gas holdup can be deduced from the reported data on liquid holdup and total voidage. 

Weber (Wl) has reported measurements of gas holdup for the experimental system described in Section V,B,4. The following empirical relationships can be derived from the graphical correlations ... 

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. 

Kato (K3) reported gas holdup as a function of gas velocity, particle size, amount of solids and liquid in the bed, as well as of density of solids, for the system described in Section V,C. The holdup, defined as the ratio between the gas volume and the sum of gas and liquid volumes, increased with increasing nominal gas velocity to a maximum value ranging from 0.40 to 0.75 reached for gas velocities of from 10 to 20 cm/sec. The gas holdup decreased with increasing particle size and with increasing amounts of solids in the bed. 

Various methods may be used for the determination of gas holdup—for example, displacement measurements and tracer experiments. Farley and Ray (F2) have described the use of gamma-radiation absorption measurement for the determination of gas holdup in a slurry reactor for the Fischer-Tropsch synthesis. 

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. 

Foust et al. (F4) measured gas holdup in mechanically stirred gas-liquid contactors of various diameters (from 1 to 8 ft) and various liquid contents (from 5 to 2250 gal). The nominal gas velocity varied from 1 to 5 ft/min and the power input from 0.01 to 6.5 hp. The contact time (sec/ft) could be correlated by the following expression ... 

Adlington and Thompson (Al) observed that the presence of solids had little influence on gas holdup below nominal gas velocities of about 1.5 cm/sec. At higher gas velocities, the gas holdup was depressed by the solids, particularly in beds of low porosity. The gas holdup was only little influenced by changes in particle size. 

Viswanathan et al. (V6) measured gas holdup in fluidized beds of quartz particles of 0.649- and 0.928-mm mean diameter and glass beads of 4-mm diameter. The fluid media were air and water. Holdup measurements were also carried out for air-water systems free of solids in order to evaluate the influence of the solid particles. It was found that the gas holdup of a bed of 4-mm particles was higher than that of a solids-free system, whereas the gas holdup in a bed of 0.649- or 0.928-mm particles was lower than that of a solids-free system. An attempt was made to correlate the gas holdup data for gas-liquid fluidized beds using a mathematical model for two-phase gas-liquid systems proposed by Bankoff (B4). 

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. 

Measurement of the expansion of a gas-liquid fluidized bed provides a measure of the holdup of solids or of the corresponding combined holdup of gas and liquid. From such measurements, the holdup of liquid may be calculated if the gas holdup has been determined independently. 

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). 

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