Reynolds particle, fluidization

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

FIG. 17-2 Schematic phase diagram in the region of upward gas flow. W = mass flow solids, lh/(h fr) E = fraction voids Pp = particle density, Ih/ft Py= fluid density, Ih/ft Cd = drag coefficient Re = modified Reynolds uum-her. (Zenz and Othmei Fluidization and Fluid Particle Systems, Reinhold, New York, 1960. )... 

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. 

For most purposes, the correlations for jD presented in Tables 12.1 and 12.2 also suffice for estimating jH. There is, however, one additional correlation for fluidized beds that is worth noting. On the basis of data for the fluidization of 20 to 40 mesh silica and alumina gel particles in air at Reynolds number values (DpG/fi) ranging from 9 to 55, Kettenring et al. (92) suggest that... 

Finally, consider the case when the magnitude of the slip velocity between the particles and the gas is close to umf/e everywhere in the fluidized bed. With the vertical pressure drop equal to the particle weight, the following holds for any value of the particle Reynolds number,... 

Reynolds number at minimum fluidization, dp UmfPjF = Particle Reynolds number, dp U pjjl = Modified Reynolds number ... 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

However, for Re < 10 the experimental values of Nu fall sharply with decreasing Reynolds number, well below the theoretical minimum of Nu = 2. This is attributable in part to experimental difficulties, for example fhe problem of measuring particle temperature, and in part to the theoretical interpretation of the data. Botterill (1975) posed the question of what exactly is measured by a bare wire thermocouple inserted in a fluidized bed. Despite the uncertainties in the experimental evidence, Botterill concluded that it probably does indeed measure the particle temperature. This was the assumption of Smith and Nienow (1982) who used bare wire thermocouples to measure bed particle temperatures during fluidized bed granulation. In the region Re < 10, as Kunii and Levenspiel (1991) indicate, the data can be represented by an expression due to Kothari... 

Equation 3.7 is valid only for particle Reynolds numbers below 100 and the Reynolds number of, say, a pea in a fluidized bed freezer is of the order of 1000 and thus the correlation tends to overestimate the heat transfer coefficient considerably. Kelly (1965) proposed, specifically for the fluidization of peas. 

The exponent m is a function of particle Reynolds number based on the minimum fluidization velocity. It can be estimated by the following correlation ... 

In this equation, Re is tlie particle Reynolds number based on the minimum superficial velocity for fluidization. Moreover, for fixed-beds, we can set = 1 and sf = s. The correlation is applicable for void fractions between 0.4 and 0.8 with particle density up to 480 lb/ft3. Note that by changing the Rep number, the fluidized bed voidage ef is changed. 

The minimum Reynolds number for fluidization Remf as well as the minimum fluidization velocity Umf may be calculated according to the correlation of Riba et al. [20], Mv defining the ratio of particle to liquid density... 

For the fluidized bed process the bed expansion as a consequence of an increase in linear flow rate has to be considered. In a simplified picture diffusive transport takes place in a boundary layer around the matrix particle which is frequently renewed, this frequency being dependent on velocity and voidage, as long as convective effects, e.g. the movement of particles are neglected. Rowe [74] has included these considerations into his correlation for kf in fluidized beds, which is applicable for a wide range of Reynolds numbers, including the laminar flow regime where fluidized bed adsorption of proteins takes place (Eq. 19). The exponent m is set to 1 for a liquid fluidized bed, a represents the proportionality factor in the correlation for packed beds (Eq. 18) and is assumed as 1.45. 

Summarizing this short discussion it has to be stated, that up to now experiments providing absolute numbers of kf during protein adsorption in fluidized beds are not available, the interpretations are based on correlations derived for small ions. As ion exchange with fluidized resins is performed at much higher Reynolds numbers and mostly is not limited by particle side transport, the validity of the correlations for proteins has to be proven. Nevertheless, the influence of bed expansion at increased linear flow rate cannot be neglected and fluid side mass transport should be considered as a system parameter governing the sorption process in a fluidized bed under certain conditions. 

R pmf Particle Reynolds number at minimum fluidization velocity... 

The performance of a fluidized bed combustor is strongly influenced by the fluid mechanics and heat transfer in the bed, consideration of which must be part of any attempt to realistically model bed performance. The fluid mechanics and heat transfer in an AFBC must, however, be distinguished from those in fluidized catalytic reactors such as fluidized catalytic crackers (FCCs) because the particle size in an AFBC, typically about 1 mm in diameter, is more than an order of magnitude larger than that utilized in FCC s, typically about 50 ym. The consequences of this difference in particle size is illustrated in Table 1. Particle Reynolds number in an FCC is much smaller than unity so that viscous forces dominate whereas for an AFBC the particle Reynolds number is of order unity and the effect of inertial forces become noticeable. Minimum velocity of fluidization (u ) in an FCC is so low that the bubble-rise velocity exceeds the gas velocity in the dense phase (umf/cmf) over a bed s depth the FCC s operate in the so-called fast bubble regime to be elaborated on later. By contrast- the bubble-rise velocity in an AFBC may be slower or faster than the gas-phase velocity in the emulsion... 

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