Entrainment above the tdh

Entrainment Above TDH. A relatively simple procedure to calculate the amount of entrainment above the TDH is given hereia. A more detailed treatment can be found ia Reference 21. 

The flux of the solids entrained above the TDH can be measured either by isokinetic sampling or by catching the solids recovered by the cyclones. For the flux of solids entrained below the TDH, isokinetic sampling or a movable gas exit connected to a cyclone can be used (54). 

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 ... 

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. 

For each particle size, the flux of solids entrained above the TDH is limited by choking, i.e. it cannot be larger than the fraction of the total choking load which is attributed to that particle size when the coltnnn above the TDH is assumed to behave as a pneumatic transport line. 

The Briens-Bergougnou model demonstrates that three approaches can be used to reduce the amount of solids entrained above the TDH ... 

Minute changes in the size distribution of the bed solids can sometimes result in large reductions of the flux of solids entrained above the TDH [54]. Special attention should thus be given to the size distribution of fresh solids, attrition of bed solids and cut-points of the cyclones. 

The total solids entrainment flux, A. at a given axial distance above the bed surface, h, can be correlated to the solid entrainment flux on the bed surface, Jo, and that above the TDH, J0o, by [Wen and Chen, 1982]... 

In designing an FBD for solids drying, it is important to take note about the occurrence of entrainment of fine particles, especially if the solids are polydispersed (i.e., has wide particle size distribution). The gas exit should be placed at a height above the TDH to minimize elutriation of fines. 

The height from the bed surface to the top of the disengagement zone is known as the transport disengagement height (TDH). Above TDH the entrainment flux and concentration of particles is constant. Thus, from the design point of view, in order to gain maximum benefit from the effect of gravity in the freeboard, the gas exit should be placed above the TDH. Many empirical correlations for TDH are available in the literature those of Horio et al. (1980) presented in Equation (7.37)... 

Figure 8 Effect of the bed height on the entrainment flux (a) above the TDH and (b) just above the bed surface. ( >, = 0.61 m, silica sand, dp = 61 pm, data measured by Baron et al., 1990.)...

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, ... 

Models that focus more on the entrainment of the particles from the dense bed to the freeboard are given by George and Grace (1978) and by Smolders and Baeyens (1997). Both models first calculate the entrainment flux EiQ at the bed surface based on such bubble properties as size, frequency, and velocity. For the flux above the TDH, it is simply assumed that only particles with a terminal velocity less than the gas velocity in the freeboard are entrained, the mass flux of these particles being the same as at the bed surface ... 

These two models will give the same entrainment flux at the bed surface as above the TDH for fluidized beds operated with solids having all terminal velocities less than the superficial velocity. This latter finding is in contradiction with empirical findings which show a decay in the entrainment with height even for such fluidized beds of fines. 

As solids recovery equipment such as cyclones and electrostatic separators is expensive, the flux of solids entrained into the recovery train must be minimized. The column exhaust must thus be located above the TDH. On the other hand, the column must be kept as short as possible to minimize capital costs. In practice, when internal cyclones are used, the exact position above the TDH of the column exhaust to the cyclones will be set by the dipleg pressure balance. 

Briens and Bergougnou [52] tested this model with available experimental data and found that in most cases, the predicted entrainment flux was within one order of magnitude of the actual experimental flux. This model could not accurately predict the size of entrained particles above the TDH. 

The distance above the catalyst bed in which the flue gas velocity has stabilized is refened to as the transport disengaging height (TDH). At this distance, there is no further gravitation of catalyst. The center-line of the first-stage cyclone inlets should be at TDH or higher otherwise, excessive catalyst entrainment will cause extreme catalyst losses. 

Cyclones. According to the model presented above, Eq. (24), a minimum loss rate due to cyclone attrition requires to avoid both high inlet velocities Ue and high solids mass fluxes mc m at the cyclone inlet. The latter requirement can be fulfilled by locating the cyclone inlet above the transport disengaging height (TDH) (Kunii and Levenspiel, 1991). In addition, an enlargement of the freeboard section will reduce the amount of particles that are entrained and thus the mass flux, mc in. 

Freeboard. Under normal operating conditions gas rates somewhat in excess of those for minimum fluidization are employed. As a result particles are thrown into the space above the bed. Many of them fall back, but beyond a certain height called the transport disengaging height (TDH), the entrainment remains essentially constant. Recovery of that entrainment must be accomplished in auxiliary equipment. The TDH is shown as a function of excess velocity and the diameter of the vessel in Figure 6.10(i). This correlation was developed for cracking catalyst particles up to 400 pm dia but tends to be somewhat conservative at the larger sizes and for other materials. 

Assume that the process exit is positioned above TDH and that none of the entrained solids are returned to the bed. 

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