# Transport Disengaging Height (TDH)

TDH Definitions

The literature presents some definitions about TDH which show different results, causing difficulty to compare them.

Zenz e Weil (1958), e Fournol et al. (1973) defined the TDH as a height, and above it, the entrainment rate and the particle average diameter become constant.

In Figure 2, Zenz and Weil (1958) illustrate the particles movement in the bed. It also shows a theoretical model of particles ejection from the bed surface, and these particles would have the same velocity as the bubble velocity when leaning against the bed surface. With each particle ejected by the gas and affected by the inertia, the gravitational and the entrainment forces. Some particles are continuously carried out; while others only reach a certain height, where they fall back to the bed. Figure 2: Illustration of the fluidization model proposed by Zenz and Weil (1958)

Figure 2b shows an empirical approach which the bed contains a saturated feed, so that from a sufficient height above the bed surface, with the velocity stabilized,  the vessel can be considered as a pneumatic conveying and the entrainment as a transport phenomenon. Thus, considering that the air bubbles, when colliding with the bed surface may correspond to an intermittent jet with irregular high velocity. The jet's velocity dissipates in the superficial gas velocity at an equilibrium height, and this height is the definition asTDH. In the TDH each particle having a velocity greater than the superficial gas velocity, would have already fallen back into the bed, and the other particles will be entrained.

In the study by Wen and Chen (1982), the TDH is considered to be the distance between the end of the fluidized region and the height at which the particles no longer exist. It has also been defined as the region in which the entrainment rate becomes constant (Figure 3). Figure 3: Entrainment of particles according to Wen and Chen (1982).

Geldart (1986) defined the TDH as the region where the fluidized solids fall back in the bottom of the bed, and being specific to fine (F) and large (C) particles:

1. (i) TDH (F): is the height at which the solid concentration (especially fines), above the bed surface, reaches a constant or a slight variation.
2. TDH (C): is the height where the large particles (or clusters) are released to the freeboard, and return to the bed.

Horio et al., (1983) have distinguished characteristics of the three freeboard regions, shown in Figure 5. From it, the splash's height is differentiated from the TDH's: the TDH would be the sum of the splash's and the diffusion zone heights. Figure 5: Zones of Freeboard (Sciazko et al., 1988).

According to Baron et al., (1988), the TDH was defined as the height at which the concentration of solids approaches an asymptotic value; since this one decreases with the height above the bed , and the TDH was determined by the trajectory of the clusters ejected into the freeboard by the gas bubbles.

Sciazko et al., (1991) repeated the same working conditions of their experiment conducted in 1988, to define the TDH, as follows:

1. TDH (F) - height above the fluidized bed in which the conservation of the entrainment rate of particles or the clusters, remains constant or slight variation.
2. TDH (C) - height above the fluidized bed needed to separate the solid particles, with terminal velocity (Ut) greater than the superficial gas velocity (Ug) in the gas phase. Above the critical height there are only the particles for which Ut < Ug;