Slip velocity fluidized beds

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,... 

The results of an example calculation for a recirculating fluidized bed coal devolatilizer of 0.51 m in diameter handling coal of average size 1200 pm at 870°C and 1550 kPa are presented in Fig. 11. The calculation is based on operating the fluidized bed above the draft tube at 4 times the minimum fluidization velocity. It is also based on the selection of a distributor plate to maintain the downcomer at the minimum fluidization condition. If the two-phase theory applies, this means that the slip velocity between the gas and the particles in the downcomer must equal to the interstitial minimum fluidizing velocity as shown below. 

Owing to the rapid formation and dissolution of particle clusters which contribute to high slip velocities and solid backmixing but preserve a limited extent of gas backmixing, the fast fluidized bed regenerator exhibits unique axial and radial profiles for voidage, temperature and carbon concentration (see Figs. 9 and 11 and Table VIII). 

Imafuku et al.46 measured the gas holdup in a batch (i.e., no liquid flow) three-phase fluidized-bed column. They found that the presence of solids caused significant coalescence of bubbles. They correlated the gas holdup with the slip velocity between the gas and liquid. They found that the gas holdup does not depend upon the type of gas distributor or the shape of the bottom of the column when solid particles are completely suspended. Kato et al.53 found that the gas holdup in an air-water-glass sphere system was somewhat less than that of the air-water system and that the larger solid particles showed a somewhat smaller... 

Various model parameters involved in the derivation of the stability criterion need to be specified in order to use the stability criterion for quantitative predictions. Model parameters essential for this purpose include the slip velocity, the virtual mass coefficient, and the dispersion coefficient. The procedure for estimation of these parameters is given for gas-solid (and solid-liquid) fluidized beds and bubble columns. 

It is important to note that the fluidized bed does not conform to Stokes law a dense phase can be maintained at an upward gas velocity at which entrainment of most of the particles would be predicted (207). The upward velocity of fluidized solids is always less than the superficial gas velocity the difference is known as slip velocity (197). 

The mean bubble size in a fluidized bed has been discussed in Section II,B. As discussed, for a fluidized catalyst bed of good fluidity may be taken as approximately 5.0 cm [cf. Figs. 10 and 11, and Eq. (2-11)] for Uc, > 10 cm/sec. With Eq. (3-33), this (I32 gives = 49.5 cm/sec, which is shown in Fig. 34 as a dashed line. It is interesting that the mean slip velocity is essentially the same as for a bubble column, when Uq > 20 cm/sec. As noted in Section II,B, and Mg are very sensitive to change in particle size, size distribution, shape, and density. 

The averaged volume fraction Cb. calculated by Eq. (3-25), is shown in Fig. 36, for bubble columns and also for FCC-catalyst beds (M40). The mean slip velocity of bubbles is again taken as ii , = 49.5 cm/sec. Also, Vi is calculated by Eq. (3-31a) for curve FQF and by Eq. (3-31) for curve FQP, while curve EE is an empirical fit of the data. As in the case of a bubble column, curve FQP matches better with curve EE, although FQP is consistently higher. Curve EE tends to decrease the slope for Uq s 7-8 cm/sec, perhaps due to the decrease in Ms the scatter of data makes the behavior unclear. This is explained by the difference in the region of Uc < 20 cm/sec. The bubble column shows higher 6b values than those for the fluidized bed, which is due to the bubble column s lower Us (cf. Fig. 34). 

III,D,5). In this chapter, the equation is further examined in relation to bed performance, since the turbulence properties of the bed result from interaction between bubbles and the continuous phase. As shown in Fig. 34, the mean slip velocity of bubbles in a fluidized catalyst bed of good fluidity is essentially the same as that for a bubble column when Uq > 20 cm/sec. A criterion under which bubble size approaches a dynamic equilibrium is obviously needed for predicting or evaluating the performance of scaled-up beds. 

The mean slip velocity Us has been shown in Fig. 34 for the bubbles observed in bubble columns or in fluidized FCC beds. Here the mean... 

It is clear, in this case, that the suppressant impurity poisons the growth surface, presumably by adsorption (CSTR with suppressant versus no suppressant). A higher growth rate in the fluidized bed versus the CSTR implies considerable diffusional resistance (higher fluid slip velocities in the fluidized bed result in improved growth rate). 

It is possible to determine overall crystal growth rates by adding a known mass of sized seeds to a supersaturated solution in an agitated vessel, following a similar procedure to that outlined above for the fluidized bed method. To correlate the data, however, it is necessary to estimate the particle-fluid slip velocity as a function of impeller speed in the agitated vessel using relationships of the type described in section 9.4.1. 

An expression for this random collisional force can be derived by taking into account that 1) it must be linear in w since the fluctuations are assumed to be sufficiently weak, and 2) it may contain only those components directed along unit vectors marking preferable directions, at a given physical point of the suspension under study. There are usually two such directions, and these directions are determined by acceleration g of external body forces and by mean fluid slip velocity u). When these directions are essentially different, the corresponding general expression for the collisional force is presented in reference [23]. If vectors g and (u) are collinear, as is specific to fluidized beds and to other vertical flows of suspensions, this expression takes the form ... 

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