Bubble emulsion 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.)... 

Tliis model is simpler that the Kunii-Levenspiel model and eliminates the unsubstantiated expression for cloud-to-emulsion transfer employed by Kunii and Levenspiel (Grace, 1984). Furthermore, compared to the previous models, the introduction of the parameter yb in the model leads to better results as the assumption that there is no solids in the bubble phase may lead to the underestimation of conversion in fast reactions. For slow reactions, the value of yb is of minor importance. However, for fast reactions the model may become sensitive to this parameter and the actual conversion should be bounded between the predicted ones using the upper and lower limits of yh, i.e. 0.01 and 0.001, respectively (Grace, 1984). 

Kunii and Levelspiel (19) again use Equation (2) to describe bubble/cloud transfer. Based on the penetration theory, they propose the following expression for cloud/emulsion transfer ... 

For most practical conditions, a comparison of k and k from Equations (4) and (5) would suggest that the principal resistance to transfer resides at the outer cloud boundary. However, when (a), (b) and (c) are taken into account, this is no longer the case. In fact, experimental evidence (e.g. 30,31,32) indicates strongly that the principal resistance is at the bubble/ cloud interface. With this in mind, it is probably more sensible to include the cloud with the dense phase (as in the Orcutt (23, 27) models) rather than with the bubbles (as in the Partridge and Rowe (37) model) if a two-phase representation is to be adopted (see Figure 1). If three-phase models are used, then Equations (2) and (5) appear to be a poor basis for prediction. Fortunately the errors go in opposite directions. Equation (2) overpredicting the bubble/cloud transfer coefficient, while Equation (5) underestimates the cloud/emulsion transfer coefficient. This probably accounts for the fact that the Kunii and Levenspiel model (19) can give reasonable predictions in specific instances (e.g.20),... 

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) ... 

An important feature of fluidized-bed reactors is mass transfer between bubble and emulsion. Several models have been proposed for this exchange. The Davidson model assumes no cloud, so that only one mass transfer coefficient be (for direct bubble-emulsion exchange) is involved. On the other hand, the... 

Kunii and Levenspiel (1969, 1991) considered the vaporization or sublimation of A from all particles in the bed. They assumed that fresh gas enters the bed only as bubbles, and that at steady state the measure of sublimation of A is given by the increase in Ca with height in the bubble phase. They further assumed that the equilibrium is rapidly established between Ca at the gas-particle interphase and its surroundings. The above assumptions lead to a mass transfer equation in terms of a bubble-emulsion mass transfer coefficient, GB-... 

Bubble diameter just above the distributor Maximum bubble diameter Bubble diameter Mass transfer coefficient (bubble emulsion phase)... 

In addition to this convective cross flow of gas from the bubble into the emulsion phase of the cloud, mass transfer also occurs by diffusion into the emulsion. 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

The bubbles play the role of the gas phase. The role of the liquid is played by an emulsion phase that consists of solid particles and suspending gas in a configuration similar to that at incipient fluidization. The quasi-phases are in cocurrent flow, with mass transfer between the phases and with a solid-catalyzed reaction occurring only in the emulsion phase. The downward flow of solids that occurs near the walls is not explicitly considered in this simplified model. 

Values for the various parameters in these equations can be estimated from published correlations. See Suggestions for Further Reading. It turns out, however, that bubbling fluidized beds do not perform particularly well as chemical reactors. At or near incipient fluidization, the reactor approximates piston flow. The small catalyst particles give effectiveness factors near 1, and the pressure drop—equal to the weight of the catalyst—is moderate. However, the catalyst particles are essentially quiescent so that heat transfer to the vessel walls is poor. At higher flow rates, the bubbles promote mixing in the emulsion phase and enhance heat transfer, but at the cost of increased axial dispersion. 

The emulsion phase approaches the performance of a CSTR with its inherent lower yield for most reactions. To make matters worse, mass transfer between the emulsion and bubble phases becomes limiting to the point that some of the entering gas completely bypasses the catalytic emulsion phase. The system behaves like the reactor in Example 11.5. 

Mass transfer coefficient between the emulsion and bubble phases in a gas fluidized bed 11.45... 

The performance equation for the model is obtained from the continuity (material-balanoe) equations for A over the three main regions (bubble, cloud + wake, and emulsion), as illustrated schematically in Figure 23.7. Since the bed is isothermal, we need use only the continuity equation, which is then uncoupled from the energy equation. The latter is required only to establish the heat transfer aspects (internally and externally) to achieve the desired value of T. 

Note that the continuity equations for product B reflect the fact that B, formed in the cloud + wake and emulsion regions, transfers to the bubble region. This is in contrast to reactant A, which transfers from the bubble region to the other regions. 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-15) assumes constant-sized bubbles (effective bubble size db) rising through the suspension phase. Gas is transferred from the bubble void to the cloud and wake at mass-transfer coefficient /v, and from the mantle and wake to the emulsion... 

It is cavitation in a heterogeneous medium which is the most studied by sonoche-mists. When produced next to a phase interface, cavitation bubbles are strongly deformed. A liquid jet propagates across the bubble towards the interface at a velocity estimated to hundreds of metres per second. At a liquid-liquid interface, the intense movement produces a mutual injection of droplets of one liquid into the other one, i. e. an emulsion (Fig. 3.3). Such emulsions, generated through sonication, are smaller in size and more stable than those obtained conventionally and often require little or no surfactant to maintain stability. It can be anticipated therefore that Phase Transfer Catalysed (PTC) reactions will be improved by sonication. Examples are provided later in this chapter. 

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