Mass transfer coefficients fluidized beds

Knto et al.11 and Davidson and Harrison 4 have reviewed available correlations for both heat and mass transfer coefficients in gas-solid fluidized beds. Some investigated have proposed dial the same correlation can be applied 1 3 for both fized and fluidized beds by proper choice of the fluid velocity teres. Further disen salons of mass transfer in fluidized beds can he found in Davidsou and Harrison " aed Kunii and Lavenspiel, 5 Because of the difficulty of operating small laboratory fluidized beds under conditions comparable to those of a full-scale unit, the applicability of many of theae studies may he quesiioanble. 

Table 12.2 is a summary of useful correlations for jp and jfj that have been proposed by various investigators. The indicated correlations are quite consistent with one another in the regions where they overlap. Although the mass transfer coefficients determined from these correlations are not particularly large, they lead to high mass transfer rates when they are multiplied by the external surface area of the bed. For more detailed treatments of mass transfer in fluidized beds, see the text of Kunii and Levenspiel (83) and the review by Beek (84). 

Heat and mass transfer in fluidized beds have been discussed in Refs. [6,138-141], The latter reviewed the most important correlations and proposed Equations T9.11 and T9.12 of Table 4.9 for the calculation of heat and mass transfer coefficients, respectively. Further information for fluidized bed drying can be found in Ref. [142]. 

From the point of view of mass transfer, a fluidized bed without bubbles is very effective, since the volumetric mass transfer coefficient is as a rule very high (this is the product of the mass transfer coefficient at the particle surface, and the surface area of the particles in the bed). On the other hand, in bubbling beds the mass transfer between the fluid and the solid is usually limited by the mass transfer between the bubbles and the dense phase. This process can be described by another volumetric mass transfer coefficient, that is the product of the specific area of the bubbles, which is quite small due to the relatively large bubble diameters, and the mass transfer coefficient between the bubbles and the dense phase, which is relatively large, due to the effective interchange of gas in the bubbles and gas in the dense phase. The bubbles also contribute to a large residence time distribution of the fluid phase (compare section 7.2.4) and this reduces further the effectivity of the mass transfer between the fluid phase and the solid. In bubbling beds the fluid is usually a gas. 

In a quiescent fluid, the dimensionless mass-transfer coefficient, or the Nusselt number, djkj for a sphere is two. In fluidized beds the Nusselt... 

The results of Massimilla et al., 0stergaard, and Adlington and Thompson are in substantial agreement on the fact that gas-liquid fluidized beds are characterized by higher rates of bubble coalescence and, as a consequence, lower gas-liquid interfacial areas than those observed in equivalent gas-liquid systems with no solid particles present. This supports the observations of gas absorption rate by Massimilla et al. It may be assumed that the absorption rate depends upon the interfacial area, the gas residence-time, and a mass-transfer coefficient. The last of these factors is probably higher in a gas-liquid fluidized bed because the bubble Reynolds number is higher, but the interfacial area is lower and the gas residence-time is also lower, as will be further discussed in Section V,E,3. 

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

Fluidized-bed driers are also widely used due to their large heat- and mass-transfer coefficients. However, materials of even moderate adherence and cohesiveness cannot be dried in a fluid bed. The same applies to materials that are sensitive to oxygen, especially at elevated temperatures. Vacuum drying is often necessary for oxygen sensitive materials and this is not easy to realize in fluid-bed driers, although there are systems to deal with this problem. Fluid-bed driers are not as easy to clean as shelf driers or rotary driers. 

It is instructive to consider the relative rates of mass transfer in fixed and fluidized bed reactors. The rapid rate in the fluidized bed is due not so much to the high mass transfer coefficients involved, but to the very large... 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

The use of floating bubble breakers has been used to increase the volumetric mass transfer coefficient in a three-phase fluidized bed of glass beads (Kang et al., 1991) perhaps a similar strategy would prove effective for a bed of low density beads. Static mixers have been shown to increase kxa for otherwise constant process conditions by increasing the gas holdup and, therefore, the interfacial area (Potthoff and Bohnet, 1993). 

Understanding the effect of reactor diameter on the volumetric mass transfer coefficient is critical to successful scale up. In studies of a three-phase fluidized bed bioreactor using soft polyurethane particles, Karamanev et al. (1992) found that for a classical fluidized bed bioreactor, kxa could either increase or decrease with a change in reactor diameter, depending on solids holdup, but for a draft tube fluidized bed bioreactor, kxa always increased with increased reactor diameter. 

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.)... 

The experimental mass transfer coefficients for gas-particle mass transfer in a fluidized bed (Figure 2.2), as summarised by Kunii and... 

Equation (12.71) provides a means to quantify kf on the basis of experimentally measured inlet and outlet concentrations of species A in the bed under low gas velocity conditions. Wen and Fane (1982) proposed the following empirical correlations for overall mass transfer coefficients in gas-solid fluidized beds, using the experimental data of Kato et al. (1970) based on Eq. (12.71) ... 

For gas-solid fluidized beds, Wen and Fane (1982) suggested that the determination of the bed-to-surface mass transfer coefficient can be conducted by using the corresponding heat transfer correlations, replacing the Nusselt number with the Sherwood number, and replacing the Prandtl number by Sc(cpp)/(cpp)/(l — a). Few experimental results on bed-to-surface mass transfer are available, especially for gas-solid fluidized beds operated at relatively high gas velocities. 

The mass transfer coefficient between a bubble and its cloud due to diffusion, k, given in Eq. (12.82) for a gas-solid fluidized bed can be derived on the basis of the mass... 

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