Fractional gas holdup

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... 

Clark and Vermeulen (C8) later reported an extensive experimental study of power requirements in agitated gas-liquid systems. They correlated their data in dimensionless form as a function of fractional gas holdup, Weber number, and a geometrical factor. Their correlation is shown in Fig. 5. 

It is evident from Figure 3.32 that fractional gas holdup is decreased by the addition of solids and this decrease is higher for higher gas velocity, solid concentration, and solid density. 

The fractional gas holdup can be easily measured from the height of the expanded column height Zf and the settled sluny height Zs, i.e. the height of the column before aeration (liquid volume plus solids volume) (DOE, 1985 NTIS, 1983) ... 

The slope of a log-log plot of fractional gas holdup e (-) against a superficial gas velocity Uq (L T ) decreases gradually at higher gas rates. However, the gas holdup can be predicted by the following empirical dimensionless equation, which includes various liquid properties ... 

The gas-liquid interfacial area per unit volume of gas-liquid mixture a (L 1. or L ), calculated by Equation 7.26 from the measured values of the fractional gas holdup and the volume-surface mean bubble diameter d, were correlated... 

Liquid flow rate At low liquid flow rates, with nonfoaming systems, the line of demarcation between zones in Fig. 6.12a is fairly sharp (42). As liquid rate increases, so does the fractional gas holdup in the downcomer liquid. Lockett and Gharani (43) found... 

Hence, the gas phase conversion for a pseudo-first order reaction in the churn turbulent regime can be calculated if the fractional gas holdups, rise velocities, and interfacial areas for the two bubble classes as well as the physicochemical data are known. 

The key parameters in this model are the fractional gas holdups due to the large and small bubbles, the bubble rise velocities, and the bubble diameters. The fractional gas holdup structure due to different size bubbles has been determined by a number of investigators (3, 5 ) using the dynamic gas disengagement technique. This technique involves the measurement of the rate of drop in the dispersion height when the gas supply is instantly shut off ( 8 ) The following systems have been studied air-water (9 ), air-Soltrol-130 (a mixture of... 

In the above equations, AG, AL, and As are the gas-phase, liquid-phase and calalyst-surface concentrations of the reacting species, ACi is the average gas-phase concentration at the reactor inlet, Z is the axial distance from the reactor inlet, L is the total length of the reactor, m = H/RgT, where H is the Henry s law constant (cm3 atm g-mol" ), Rg is the universal gas constant, and T is the temperature of the reactor. UG is the mean gas velocity, Us is the mean settling velocity of the particles, t is the time, k is the first-order rate constant, W is the catalyst loading, zc and ZP are the axial dispersion coefficients for the gas and solid phases, respectively. Following the studies of Imafuku et al.19 and Kato et al.,21 the axial dispersion coefficient for the liquid phase was assumed to be the same as that for the solid phase, w is the concentration of the particles and hG the fractional gas holdup. Other parameters have the same meaning as described earlier. 

The above equations assume that the liquid-phase reactant C, the product of the reaction, and the solvent are nonvolatile. The effective interfacial area for mass transfer (nL) and the fractional gas holdup (ii0o) arc independent of the position of the column. The Peclet number takes into account any variations of concentration and velocity in the radial direction. We assume that Peclet numbers for both species A and C in the liquid phase are equal. For constant, 4 , Eq. (4-73) assumes that the gas-phase concentration of species A remains essentially constant throughout the reactor. This assumption is reasonable in many instances. If the gas-phase concentration does vary, a mass balance for species A in the gas phase is needed. If the gas phase is assumed to move in plug flow, a relevant equation would be... 

B Void fraction available for gas flow or fractional gas holdup mVm ftVft ... 

Figure 3. a, Fractional gas holdup of large and small bubbles (39) b, rise velocity of large and small bubbles (39)... 

Though the gas phase dispersion coefficients are large and often larger than those of the liquid phase the influence of the gas phase dispersion on conversion should not be overestimated. One has to consider that it is not the dispersion coefficient itself but the Peclet number which is the governing parameter in the model equations. The Peclet number has to be formulated under consideration of the fractional gas holdup... 

In bubble columns, since the gas bubbles are dispersed in the continuous liquid phase, fractional gas holdup (Eg) is an important design parameter, affecting column performance. The most direct and obvious effect is on the column volume, since a significant fraction of the volume is occupied by the gas. The indirect influences are also important. For instance, the possible spatial variation of Eg gives rise to pressure variation, which results in intense liquid phase motion. These secondary motions govern the rates of mixing plus heat and mass transfer. 

The fractional gas holdup is defined as the volume fraction of gas in the gas-liquid dispersion and is measured in several ways (Joshi et al., 1990a). The measurements of average gas holdup Eg and local gas holdup are both reasonably well developed. Despite the good agreement between different measuring methods, we have not yet reached a stage where holdup can be predicted for an unknown gas-liquid system, as next discussed. 

Fractional gas holdup also depends strongly on superficial gas velocity and the nature of the gas-liquid system. Column diameter and height often have some influence on Eg. The quantitative... 

Solving the above equations simultaneously yields the values of fractional gas holdup for the riser as well as the downcomer, the liquid velocity, and the height of critical location of the sparger from the bottom. The downcomer sparger is located 5.4 m from the bottom. Since //p = 15.3 m, the diameter of the downcomer and riser = Dg assumed) was found in such a way that the total gas volume in EL-ALR equals that in the bubble column of case 2 in Table CS7.3. As a result, we get Dg = Do= 1.88 m. It may be noted that the procedure has been considerably simplified. For rigorous calculations, see Lele and Joshi (1993). 

Since x = 1160 s, the average residence time (t) becomes 7830 s. The reactor volnme is obtained by taking the product of the average residence time and the average flow rate (0.00458 mVs) and is 35.88 m. This is a slurry volume. If the fractional gas holdup is 5%, and the gas space (over the dispersion) is 20%, the reactor volume is 45.2... 

Figure CS11.2a shows a comparison of fractional gas holdup under sparging conditions, with and without the use of a gas-inducing impeller. In the absence of a gas-inducing impeller, such a system behaves like a conventional mechanically agitated contactor (MAC). The comparison is made in terms of gas holdup as a function of power consumption per unit volume for different superficial velocities of sparged gas (uq = 0, 6,18, and 29 mm/s). It can be seen that the fractional...

For this value of superficial gas velocity, the gas induction rate (Qg), fractional gas holdup (Sg), and power consumption (Pg) are calcnlated, both in the presence of a gas-inducing impeller and in its absence. Hydrodynamic characteristics and the mass transfer coefficient are estimated using the correlations of Patwardhan and Joshi (1998). 

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