Fluidized beds coefficients

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

Bed-to-Surface Heat Transfer. Bed-to-surface heat-transfer coefficients in fluidized beds are high. In a fast-fluidized bed combustor containing mostly Group B limestone particles, the dense bed-to-boiling water heat-transfer coefficient is on the order of 250 W/(m -K). For an FCC catalyst cooler (Group A particles), this heat-transfer coefficient is around 600 W/(600 -K). 

Particle-to-fluid heat-transfer coefficients in gas fluidized beds are predicted by the relation (Zenz and Othmer, op. cit.)... 

Heat transfer between gas and sohds is exceedingly hard to measure because it is so rapid. Although the coefficient is low, the available surface area and the relative specific heat of solid to gas are so large that temperature equilibration occurs almost instantaneously. Experiments on injection of argon plasmas into fluidized beds have shown quenching rates of up to fifty million degrees Kelvin per second. Thus, in a properly designed bed, gas to solids heat transfer is not normally a matter of concern. 

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. 

Ostergaard (02) measured the wall-to-bed heat-transfer coefficient in a bed of 3-in. diameter. The media were air, water, and glass ballotini of0.5-mm diameter. It was observed that the heat-transfer coefficient for a liquid fluidized bed near the point of incipient fluidization could be approximately... 

Measurements of heat-transfer coefficients and effective thermal conductivity for gas-liquid fluidized beds have also been carried out by Manchanda (M2). 

Hajek et al. [173] have reported a detailed kinetic study of the solid phase decomposition of the ammonium salts of terephthalic and iso-phthalic acids in an inert-gas fluidized bed (373—473 K). Simultaneous release of both NH3 molecules occurred in the diammonium salts, without dehydration or amide formation. Reactant crystallites maintained their external shape and size during decomposition, the rate obeying the contracting volume equation [eqn. (7), n = 3]. For reaction at 423 K of material having particle sizes 0.25—0.40 mm, the rate coefficients for decompositions of diammonium terephthalate, monoammonium tere-phthalate and diammonium isophthalate were in the ratio 7.4 1.0 134 and values of E (in the same sequence) were 87,108 and 99 kJ mole-1. 

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

To provide the pr equisite knowledge for designing the three-phase fluidized-bed reactors with new modes, the hydrodynamics such as phase holdup, mixing and bubble properties and heat and mass transfer characteristics in the reactors have to be determined. Thus, in this study, the hydrodynamics and heat and mass transfer characteristics in the inverse and circulating three-phase fluidized-bed reactors for wastewater treatment in the present and previous studies have been summarized. Correlations for the hydrod3aiamics as well as mass and heat transfer coefficients are proposed. The areas wherein future research should be undertaken to improve... 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

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. 

Measurements at the wall of fluidized beds were made by Krishna et al. ( K7,K11), who used an annular cell with varying radial ratios to test the influence of inner tubes on fluidization. Only at low r jr0 values is the inner wall coefficient appreciably higher than the outer wall coefficient (which is itself somewhat lower than in a pipe bed of the same radius). 

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... 

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

The effect of pressure on the heat transfer coefficient is influenced primarily by hgc (Botterill and Desai, 1972 Xavier etal., 1980). This component of h transfers heat from the interstitial gas flow in the dense phase of the fluidized bed to the heat transfer surface. For Group A and small Group B particles, the interstitial gas flow in the dense phase can be assumed to be approximately equal to Um ed. 6/i s extremely small for... 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

Figure 1. Average heat transfer coefficients at surface of horizontal tube in bubbling fluidized bed. (From Chandran, Chen and Staub, 1980.)...

In contrast to the strong effect of gas properties, it has been found that the thermal properties of the solid particles have relatively small effect on the heat transfer coefficient in bubbling fluidized beds. This appears to be counter-intuitive since much of the thermal transport process at the submerged heat transfer surface is presumed to be associated with contact between solid particles and the heat transfer surface. Nevertheless, experimental measurements such as those of Ziegler et al. (1964) indicate that the heat transfer coefficient was essentially independent of particle thermal conductivity and varied only mildly with particle heat capacity. These investigators measured heat transfer coefficients in bubbling fluidized beds of different metallic particles which had essentially the same solid density but varied in thermal conductivity by a factor of nine and in heat capacity by a factor of two. 

Temperature of the fluidized bed is another parameter that could influence the heat transfer coefficient. Increasing bed temperature affects not only the physical properties of the gas and solid phases, but also increases radiative heat transfer. Yoshida et al. (1974) obtained measurements up to 1100°C for bubbling beds of aluminum oxide particles with 180 pm diameter. Their results, shown in Fig. 6, indicate an increase of over 100% in the heat transfer coefficient as the bed temperature increased from 500 to 1000°C. Very similar results were reported by Ozkaynak et al. (1983) who obtained measurements for bubbling beds of sand particles (dp = 1030 pm) at temperatures up to 800°C. 

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