Influence of Different Parameters on the TDH:

Superficial Gas velocity

Zenz and Weil (1958) concluded that the increase of entrainment rate is related to the instability of the gas velocity distribution, due increase of bubble frequency. The increase in TDH (F) results from the violent bursting of the large bubbles, which are less frequent in the bed.
Fournol et al., (1973) concluded that the entrainment rate decreases rapidly with the declining of fluidization velocity and with the increasing height above the bed.
Baron et al. (1988) e Geldart et al. (1995) established that the gas velocity strongly influences the TDH (F) height.
Sciazko et al. (1988, 1991) based their TDH(C) study on the Pemberton and Davidson's (1984) ghost bubbles theory. The particles movement in a moving state can be described by force balances. The authors proved that excess velocity is the most important parameter for the TDH..

Pinto et al., (1999) analyzed the influence of three factors on the entrainment of particles: fraction of open area in the distributor, solid mass and superficial gas velocity. The material used was sand with mean diameters between 268 and 711mm.

Regarding the influence of gas velocity on the homogeneous particles, the authors observed an increase in the TDH(C) only for the low velocities.

More recently, Cipolato et al., (2004) studied  in heterogeneous beds of large particles (dp=400mm), the influence of four parameters: fraction of open area in the distributor; solid mass; dispersion index and gas velocity on the entrainment of large particles through a factorial design. For a fraction of open area of 1.4%, and two velocities of 0.46 m/s and 1.60m/s, the TDH(C) is practically equal, leading to the conclusion that the velocity parameter did not affect this parameter.

Mass/Height of Solid

Hamdullahpur et al., (1986) conducted their experiments in a rectangular fluidized bed of 0.319m ´ 0.176m ´ 4m. The entrainment gas was at atmospheric pressure and room temperature. The material used was sand with mean diameter of 300mm (Geldart's group B). In addition to, the experiments were realized for six different velocities using the LDV (Laser Doppler Velocimeter) system.

The axial velocity and turbulence intensity were measured by the central axis and crossing the freeboard.The experiments were performed at 5.2 and 12 cm of fixed-bed, by applying velocities between 0.20 and 0.40 m/s. The authors noted that at 0.2 m/s, the gas velocity in the center of the bed increased with the bed height; however, for the other velocities, the intensity was lower. The variation of turbulent magnitude increased 35% with the bed height. This confirms that the freeboard turbulence is induced by the bubbles eruption in the center of the bed, and the level is highly dependent on the bubble size.

Fournol et al., (1973) used FCC with mean diameter of 58 mm as entrained material and gas superficial velocity ranging from 0.11 to 0.22 m/s. The authors concluded that the entrainment rate rapidly decreases with the rise in bed height; moreover, it depends on the reduction in the fluidization velocity.

Pinto et al. (1999) worked experimentaly using homogeneous particles with mean diameter between 268 and 711mm, a solid mass from 1.0 to 3.0 kg, bed height from 0.10 to 0.30, and both of a perforated plate (1.4, 3.4 and 5.9% of free area) and a Tuyere distributor(1.4% of free area). From the results, they observed that the solid mass is the most influential variable to the TDH (C). Figure 7 shows their final conclusions.

Sand, dp = 268mm, Ms = 2kg, H0 = 0,20m,                    Sand dp = 400mm, n = 1.5, v = 1,6m/s,
FALD=5,98%, Uq = 1,25m/s, Dc = 0,092m                       FALD=5,9%, Dc = 0,092m

Figuras 7 e 8 - Apparent Density as a function of  height above the distributor

In accordance with Pinto et al., (1999), Cipolato et al., (2004) demonstrated that for mixtures of heterogeneous particles with an mean diameter of 400mm, solid masses from 1.0 to 2.0 kg, that the solid mass is the most influential variable to the TDH(C). Figure 8 shows the conclusion drawn by the authors.

Freeboard Height

Wen and Chen (1982) proposed a model that describes the entrainment of solid particles in the freeboardregion of a fluidized bed. They concluded that the entrainment of the particles rate decreased exponentially with the increasing height of the freeboard. The elutriation rate of the fine particles was virtually independent of the fluid dynamics of the bed, and both the entrainment and the elutriation rates were affected by the column size. The elutriation rate was especially affected by the column wall; where the solid velocity is low.

Fraction of Open Area in the Distributor

Pinto et al., (1999) showed that the fraction of open area in the distributor is not relevant to the TDH(C) determination. They used both types of distributor; a perforated plate one with 1.4, 3.4 and 5.9% open area and a Tuyere with 1.4% open area, and the results were substantial for the homogeneous particles averaging from 268 and 711mm.

Cipolato et al., (2004) showed that the fraction of open area in the distributor is not relevant to the TDH(C) determination. In this paper, the authors used perforated plate distributor with fraction of open areas of 1.4 and 5.9%, obtaining a significant result for the heterogeneous particles of mean diameter of 4000mm.

Column diameter

Zenz and Weil (1958) analyzed the effect of column diameter on the TDH for diameters ranging from 0.051 to 0.61 m. Being noticeable in all cases a decrease in TDH, caused by the walls effect (small diameters) as well as by the poor distribution of the gas phase (large diameters).