Zenz and Weil

Most entrainment rate correlations predicts that smaller particles haveahigher entrainment flux or rate than larger particles, as shown in Figure 11.1. This is especially true for the empirical correlations of Stojkovski and Kostic [18], Zenz and Weil [19], and Lin et al. [20]. The first two correlations show orders of magnitude increase in the entrainment flux for particles less than 50 microns. The correlation of Lin et al. [20] shows this same trend, but with the exponential increase in entrainment occurring at 200 microns. The correlations of Colakyan [21], Colakyan and Levenspiel [22],... 

Figure 9.20. Variation of TDH with bed diameter for FCC particles (from Zenz and Weil, 1958).

First calculate the elutriation rate constants for the three size ranges under these conditions from the Zenz and Weil correlation [Equation (7.46)]. The value of particle size X used in the correlation is the arithmetic mean of each size range ... 

After the solids have been ejected into the freeboard with a certain starting velocity, they will decelerate and either fall back to the fluidized bed or will be transported by the upflowing gas to the gas outlet. The most simple assumption for the modelling of this process is to assume that all particles behave independently of each other and to use a simple ballistic model (Zenz and Weil, 1958 Do et al., 1972). A comparison of trajectories calculated with this model and experimentally observed particle trajectories (Peters et al., 1983) is given in Fig. 3. There is a quite good agreement, but the small maximum heights between 1 and 2 cm should be noted. 

As early as 1958 Zenz and Weil (1958) introduced the idea that the freeboard above the TDH behaves like a pneumatic transport line at choking conditions. This is the assumption on which most of the models up to now are based. The differences are mainly in the calculation of the choking load and of the particle size distribution of the entrained particles. Zenz and Weil (1958) calculated for each particle size class contained in the bed the choking load Gs, (kg/m -s) for monosize particles of diameter with a correlation originally developed for pneumatic transport. The elutriation flux for these particles is then assumed to be the product of the mass fraction xb, of these particles in the bed and the choking load Gs, ... 

This choking load model has been modified by Gugnoni and Zenz (1980). They proceeded in two stages. First, they estimated the particle size distribution by using the Zenz and Weil model with a some-... 

Zenz and Weil [51] proposed a model the basic assumption of which is that the flux of solids entrained above the TDH is equal to the maximum solids flux which could be carried in a pneumatic transport line operating at the same superficial gas velocity as the fluidized bed column. Thus, for each particle size cut, the choking flux for pure monosize particles is calculated from correlations developed for pneumatic transport and the flux of particles of that size entrained above the TDH is given by ... 

Zenz, P. A., and Weil, N. A. A Theoretical-Empirical Approach to the Mechanism of Particle Entrainment from Fluidized Bed. AIChE J. 4 (1958) 472-79. 

Gugnoni and Zenz [53] proposed a model which proceeds in two steps. The first step is the calculation of the size distribution of the solids entrained above the TDH with the Zenz-Weil model. The mean diameter of the particles entrained above the TDH is then calculated. In the second step, the total flux of solids entrained above the TDH is calculated with an empirical formula. Testing of this model [52] showed that it consistently overestimated the entrained flux and that its predictions were within one order of magnitude of the experimental values. It could not accurately predict the size distribution of the entrained particles. 

Zenz, F.A., and N.A. Weil, "A theoretical-empirical approach to the mechanism of particle entrainment from fluidized beds , AIChE J., 4, (1958) 472-479. 

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