Fluidized beds density distributions

Fluidized-bed design procedures requite an understanding of particle properties. The most important properties for fluidization are particle size distribution, particle density, and sphericity. 

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

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. 

Subsequently, simulations are performed for the air Paratherm solid fluidized bed system with solid particles of 0.08 cm in diameter and 0.896 g/cm3 in density. The solid particle density is very close to the liquid density (0.868 g/ cm3). The boundary condition for the gas phase is inflow and outflow for the bottom and the top walls, respectively. Particles are initially distributed in the liquid medium in which no flows for the liquid and particles are allowed through the bottom and top walls. Free slip boundary conditions are imposed on the four side walls. Specific simulation conditions for the particles are given as follows Case (b) 2,000 particles randomly placed in a 4 x 4 x 8 cm3 column Case (c) 8,000 particles randomly placed in a 4 x 4 x 8 cm3 column and Case (d) 8,000 particles randomly placed in the lower half of the 4x4x8 cm3 column. The solids volume fractions are 0.42, 1.68, and 3.35%, respectively for Cases (b), (c), and (d). 

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

Consider a fluidized bed operated at an elevated temperature, e.g. 800°C, and under atmospheric pressure with ah. The scale model is to be operated with air at ambient temperature and pressure. The fluid density and viscosity will be significantly different for these two conditions, e.g. the gas density of the cold bed is 3.5 times the density of the hot bed. In order to maintain a constant ratio of particle-to-fluid density, the density of the solid particles in the cold bed must be 3.5 times that in the hot bed. As long as the solid density is set, the Archimedes number and the Froude number are used to determine the particle diameter and the superficial velocity of the model, respectively. It is important to note at this point that the rale of similarity requires the two beds to be geometrically similar in construction with identical normalized size distributions and sphericity. It is easy to prove that the length scales (Z, D) of the ambient temperature model are much lower than those in the hot bed. Thus, an ambient bed of modest size can simulate a rather large hot bed under atmospheric pressure. 

The density of the prills is reduced substantially when much evaporation occurs with 0.2-0.5% water in the feed, ammonium nitrate prills have a specific gravity of 0.95, but with 3-5% water it falls to 0.75. Prilled granules usually are less dense than those made by layering growth in drum or fluidized bed granulators. The latter processes also can make larger prills economically. To make large prills, a tall tower is needed to ensure solidification before the bottom is reached. The size distribution depends very much on the character of the atomization but can be made moderately uniform. Some commercial data of cumulative % less than size are ... 

In principle, the experimental protocol of fluidized bed adsorption does not deviate from packed bed operations, the main difference being the direction of liquid flow. The standard sequence of frontal chromatography, equilibration, sample application, wash, elution, and cleaning (CIP) is performed with an upward direction of flow as shown in Fig. 3. During equilibration of the matrix the stabilization of the fluidized bed occurs, in case of size and/or density distribution of the adsorbent particles the classification within the bed may be detected by visual observation of the bed. As discussed below, bed stability may... 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

In industrial fluidized bed reactors, the bed height is commonly fixed by an overflow weir. Thus, as the gas velocity, U, increases from Umf, the apparent bed density decreases. An important design principle for the gas distributor is to ensure its sufficient pressure drop for a uniform gas distribution, i.e., without gas channeling, and stable bed operation. Specifically, the total pressure drop across both the distributor and the bed should be in an increasing trend with an increase in the gas velocity. Suppose that the pressure drop across a perforated distributor, Apdistnbuior, with a total orifice area of Ao can be expressed by... 

Finally, fluidized-bed mixers are rapid mixers, but cannot, of course, deal with cohesive powders or a very wide distribution of particulate sizes neither are they suitable for powder mixtures with pronounced size, density, and shape variations because of segregation problems. They generate small static electric charges. 

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