Bubbles, mass transfer

FIG. 17-15 Bubbling-bed model of Kunii and Levenspiel. db = effective bubble diameter, Cab = concentration of A in bubble, CAc = concentration of A in cloud, CM = concentration of A in emulsion, q = volumetric gas flow into or out of bubble, = mass-transfer coefficient between bubble and cloud, and kce = mass-transfer coefficient between cloud and emulsion. (From Kunii and Levenr spiel, Fluidization Engineering, Wiley, New York, 1969, and Krieger, Malabar, Fla., 1977.)... 

Figure 9.9. Characterization of the bubble mass transfer coefficients for Tank tests. Coarse bubble (CB) j6i = 1/36, and fine bubble (FB) = 1/6. The 95% confidence interval is included (Cl) (Schierholz et al. 2006).

The particle capacitance effect in bubble mass transfer was shown earlier (see Section VI,C) for the streaming emulsion outside a bubble, so that m is included in the emulsion-side film coefficient k. Chiba and Kobayashi (C3) and Drinkenburg and Rietema (D17) introduce the same effect. Yokota et al. (Y13), in studies of mass transfer from submerged surfaces in a gas fludized bed, find that the rate is strongly enhanced by adsorption of the transferring gas component on fluidized particles. The role of the particle capacitance effect in heat transfer has been discussed by Mickley and Fairbanks (M14), Mickley et al. (M16), Drinkenburg (D16), Yoshida et al. (Y18), and Kunii and Levenspiel (K24). 

In the bubbling bed model of Kunii and Levenspiel (K24), there are two transfer steps for the bubble mass transfer, namely, the transfer between bubble void and cloud-particle overlap region kbOb and that between the cloud-particle overlap region and the emulsion phase keOr,. They further assume that the cloud-particle overlap region and the bubble wake are mixed perfectly, and contact freely with the cloud gas. Their basic equations in the present notation are (for their case 2) ... 

Obviously, model identification is not possible under this condition. Another extreme is k much larger than the bubble mass-transfer coefficient. The extremes differ from (me another, as follows ... 

As explained in Section VI, the bubble mass-transfer coefficient /tob b is given by... 

The properties of point P2 are more clearly observed from Fig. 70, for the experimental apparent HTU by van Swaay and Zwiderweg (V7, V8). The HTU decreases as A r increases beyond about 1.5 sec", showing an apparent enhancement of bubble mass transfer due to ek (M28). This k corresponds to point P2. The full curves are calculated by Eqs. (7-29) and (7-30) from the use of numerical values given in Fig. 70. The equations give two extremes ... 

When = 0 in Eq. (7-35), the above model is reduced to the direct ccmtact model (VUE) of Lewis et al. This relation is also obtained by combining Eqs. (7-34) and (7-9). In an essentially similar manner the other models are reduced to the form of Eq. (7-35) and these are summarized in Table VII. Various extreme cases of chemical reacticm, bubble mass transfer, or directly contacting catalyst being controlling are easily obtained from this table. 

Bubbles. Mass transfer between gas bubbles and a liquid phase is oF importance in a variety of operations—gas-liquid reactions in agitated vessels, aerobic reimamaiions, aed absorption or distillation in tray columns. As in liquid-liquid transfer, dispersion of a phase into small units greatly increases tha avtalable area for transfer. If the fractional holdup (volume gas/total volume) of the gas in a gas-liquid mixture is Hs, the imerfacial area par unit volume for bubbles of diameter dB is given by... 

The effect of surface active materials on bubble mass transfer must also be important. There is little doubt that small bubbles become coated with surface active matter and rise and exchange gases at rates below those for bubbles that are clean [81-84]. Johnson and Slauenwhite (unpublished data) found that mass transfer of gases from bubbles in a diatom culture medium occurred at rates substantially below those for bubbles in water that had been treated to remove most organic matter. In some cases, measured rates of dissolution of bubbles rising in the culture medium were less than rates predicted for pure diffusion alone. 

As the lower limit for Sh. we will sec that this value usually vanishes for bubble mass transfer, but it may become significant when applied to small light particles, e.g.. microbial cells. Fseudostagnant liquid environments can exist in viscous fermentations and/or with well dispersed single cells as illustrated in case (a)of Figure 3. 

All the models proposed for fluidized bed membrane reactors have the same limitations. These models are phenomenological models that make use of closure equations originally derived for fluidized bed without internals. Although it is known that the presence of internals (membranes and permeation of gas through them) may vary the behavior of bubbles, mass transfer and solid circulation inside the bed, reliable closure equations for membrane assisted fluidized bed are not yet available. A way to solve this problem is to use a so-called multi-scale modeling of dense gas-solid systems, where low level... 

An important finding that is consistently reported in the literature is explained by CFD simulations the impact of holdup is limited. If a liquid slug is completely saturated with the gas-phase component and if the film thickness can be assumed to be the same for the slug and the bubble, mass transfer is indeed completely independent of the holdup. 

Moo-Young, M. and T. Hirose, Bubble mass transfer in creeping flow of viscoelastic fluids, Can. J. Chem. Eng. 50 128 (1972). 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

M ass Transfer. Mass transfer in a fluidized bed can occur in several ways. Bed-to-surface mass transfer is important in plating appHcations. Transfer from the soHd surface to the gas phase is important in drying, sublimation, and desorption processes. Mass transfer can be the limiting step in a chemical reaction system. In most instances, gas from bubbles, gas voids, or the conveying gas reacts with a soHd reactant or catalyst. In catalytic systems, the surface area of a catalyst can be enormous. Eor Group A particles, surface areas of 5 to over 1000 m /g are possible. 

This equation predicts that the height of a theoretical diffusion stage increases, ie, mass-transfer resistance increases, both with bed height and bed diameter. The diffusion resistance for Group B particles where the maximum stable bubble size and the bed height are critical parameters may also be calculated (21). 

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. 

The boiling mechanism can conveniently be divided into macroscopic and microscopic mechanisms. The macroscopic mechanism is associated with the heat transfer affected by the bulk movement of the vapor and Hquid. The microscopic mechanism is that involved in the nucleation, growth, and departure of gas bubbles from the vaporization site. Both of these mechanistic steps are affected by mass transfer. 

Direct Chlorination of Ethylene. Direct chlorination of ethylene is generally conducted in Hquid EDC in a bubble column reactor. Ethylene and chlorine dissolve in the Hquid phase and combine in a homogeneous catalytic reaction to form EDC. Under typical process conditions, the reaction rate is controlled by mass transfer, with absorption of ethylene as the limiting factor (77). Ferric chloride is a highly selective and efficient catalyst for this reaction, and is widely used commercially (78). Ferric chloride and sodium chloride [7647-14-5] mixtures have also been utilized for the catalyst (79), as have tetrachloroferrate compounds, eg, ammonium tetrachloroferrate [24411-12-9] NH FeCl (80). The reaction most likely proceeds through an electrophilic addition mechanism, in which the catalyst first polarizes chlorine, as shown in equation 5. The polarized chlorine molecule then acts as an electrophilic reagent to attack the double bond of ethylene, thereby faciHtating chlorine addition (eq. 6) ... 

Ozone is only slightly soluble in water. Thus, factors that affect the mass transfer between the gas and Hquid phases are important and include temperature, pressure, contact time, contact surface area (bubble size), and pH. 

Gas Handling. The reactants are often gaseous under ambient conditions. To maximize the rate of the catalytic reaction, it is often necessary to minimize the resistance to gas—Uquid mass transfer, and the gases are therefore introduced as swarms of bubbles into a weU-stirred Hquid or into devices such as packed columns that faciHtate gas—Hquid mixing and gas absorption. 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

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