Fluidized beds, transport coefficients

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. 

One of the strengths of the KTGF, although still under development, is that it can offer a very clear physical picture with respect to the key parameters (e.g., particle pressure, particle viscosity, and other transport coefficients) that are used in the TFMs. The TFMs based on KTGF requires less ad hoc adjustments compared to the other two types of models. Therefore, it is the most promising framework for modeling engineering-scale fluidized beds. 

Due to the fact that protein adsorption in fluidized beds is accomplished by binding of macromolecules to the internal surface of porous particles, the primary mass transport limitations found in packed beds of porous matrices remain valid. Protein transport takes place from the bulk fluid to the outer adsorbent surface commonly described by a film diffusion model, and within the pores to the internal surface known as pore diffusion. The diffusion coefficient D of proteins may be estimated by the semi-empirical correlation of Poison [65] from the absolute temperature T, the solution viscosity rj, and the molecular weight of the protein MA as denoted in Eq. (16). 

Obviously liquid residence time is not an appropriate parameter to describe pore diffusion effects in fluidized bed adsorption. This may be elucidated by assessing particle side transport by a dimensionless analysis. Hall et al. [73] described pore diffusion during adsorption by a dimensionless transport number Np according to Eq. (17), De denoting the effective pore diffusion coefficient in case of hindered transport in the adsorbent pores and Ue the... 

An extremely effective means of enhancing heat removal from a reactor is to make use of fluidized-bed technology (3). Heat transfer coefficients for gaseous systems are increased to values of around 600 W/m2K or more by virtue of the very efficient convective-regenerative particle transport mechanism of heat transfer. Further... 

Evaluation of the Average Transport Coefficient and Bubble Size. A constant bubble size is used when evaluating the properties of the fluidized bed, and since bubbles in real beds vary in size, it is important to ask what bubble size should be used. 

Spray (indirect convection) residence time 3 to 30 s gas velocity 0.2 m/s thermal efficiency 50% adiabatic efficiency 100% solid temperatnre = adiabatic satnration temperatnre volnmetric heat transfer coefficient 0.13 to 0.18 kW/m K 1.8 to 2.7 kg steam/kg water evaporated. Ap = 1.5 to 5 kPa. See size redaction sprays, Section 16.11.8.2 spray reactor, Section 16.11.6.12 heat exchange. Section 16.11.3.12 and size enlargement. Section 16.11.9.4. Flash/transported (indirect convection) 175 to 630°C, gas velocity 3 to 30 m/s or 2.5 to 3 times the terminal velocity of the particles gas reqnirement 1 to 5 Nm /kg solid or 1 to 10 kg air/kg solid exit air temperatnre 20°C greater than exit dry solid temperatnre 4000 to 10,000 kJ/kg water evaporated. See transported slnrry, transfer Une reactors. Section 16.11.6.9. Heat transfer coefficient for gas drying h = 0.2 kW/m -K. Flnidized bed (indirect convection) residence time 30 to 60 s for surface fluid vaporization 15 to 30 min for internal diffnsion 3500 to 4500 kJ/kg water evaporated. See fluidized bed reactors. Section 16.11.6.27 heat transfer. Sections 16.11.3.4 and 16.11.3.8 size enlargement. Section 16.11.9.5 and mixing. Section 16.11.7.1. Tray/gas flow through the bed 0.24 to 3.3 g water evaporated/s m tray area. Residence time 2 to 8.5 h superficial air velocity 0.2 to 1 m/s steam 2 to 6.8 kg steam/kg water evaporated. Fan power 1.6 to... 

Wall-to-Bed Heat Transfer. The wall-to-bed heat transfer coefficient increases with an increase in liquid flow rate, or equivalently, bed voidage. This behavior is due to the reduction in the limiting boundary layer thickness that controls the heat transport as the liquid velocity increases. Patel and Simpson [94] studied the dependence of heat transfer coefficient on particle size and bed voidage for particulate and aggregative fluidized beds. They found that the heat transfer increased with increasing particle size, confirming that particle convection was relatively unimportant and eddy convection was the principal mechanism of heat transfer. They observed characteristic maxima in heat transfer coefficients at voidages near 0.7 for both the systems. 

The interphase momentum transfer term can be derived from correlation developed to model fluidization processes since the range of solids concentrations experienced in pneumatic transport systems is similar. This form has been employed by Patel and Cross [46] for modeling gas-solids fluidized beds. For solid concentrations greater than 0.2, the interphase friction coefficient, K, may be computed by using the Ergun [47] equation ... 

While the lower order models described in Section 6.3 are useful for the quick prediction of the overall performance of a reactor, these models often rely on simplified flow approximations and often fail to account for change in the local fluid dynamics or transport processes during the presence of internal hardware or changes in flow regimes. Moreover, these models are also based on empirical knowledge (as discussed in Section 6.4) of several parameters such as interfacial area, dispersion coefficients, and mass transfer coefficients. Some of these limitations may be avoided by using CFD models for simulations of gas-liquid-solid flows in three-phase slurry and fluidized bed. 

An industrial DMTO fluidized bed catalyst pellet is basically composed of SAPO-34 zeofite particles and catalyst support (or matrix). The pores of zeolite particles and matrix are interconnected as a complex network. The pores inside zeofite particles are typically micropores (less than 2 nm) and the matrix normally has either mesopores (2-50 nm) or macropores (>50 nm), or both (Krishna and Wesselingh, 1997). The bulk diffusion coefficients in the meso- and macropores might be several orders of magnitude larger than surface diffusion coefficients in the micropores. Kortunov et al. (2005) found that the diffusion in macro- and mesopores also plays a crucial part in the transport in catalyst pellets. Therefore, other than a model for SAPO-34 zeofite particles, a modeling approach for diffusion and reaction in MTO catalyst pellets, which are composed of SAPO-34 zeofite particles and catalyst support, is needed. 

Since in the macroscale model, the reaction rate and diffusion coefficient are effective ones that are obtained on an ensemble-averaged basis, the internal diffusion will not appear in the controlling equations explicitly. The effective reaction rate already includes the influence of internal diffusion inside catalyst pellets. The external mass transfer term, which mainly accounts for the species transport outside catalyst pellets, is used in the controlling equations in macroscale models. So, the diffusion mentioned in macroscale model normally represents species diffusion outside catalyst pellets. In fluidized bed, species diffusion is closely related to the flow regime in the reactor (Abba et al., 2003). Abba et al. (2003) summarized the formulae for calculating diffusion coefficients in different flow regimes in fluidized bed. 

Provided particle transport conditions are not approached, a thin cushion of air will form at the underside of an object immersed in an air fluidized bed, while a defluidized region of solid particles will rest on the topside. Especially when a tube diameter is fairly large, because of these effects, horizontal tubes or cylindrical obstacles do not have particularly good particle-surface contact except at the obstacle surface near the ends of the horizontal diameter of the obstacle. The relatively poor heat transfer coefficients at the top and bottom of horizontal tubes are partly compensated for by good heat exchange at the tube sides where bubbles may sometimes be formed. At fluidizing flow rates... 

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