Dense phase voidage

Figure 6. The effect of pressure on dense phase voidage. (Weimer Quarderer.)...

Flow Distribution between Phases. One of the principal assumptions underlying many of the models of fluidized bed reactors is the two-phase theory of fluidization. This theory, really no more than a postulate, holds that the flow beyond that required for minimum fluidization passes through the bed as translating void units. Although not included in what the originators of this postulate (38) appeared to have in mind, the two phase theory is often held to imply, in addition, that the dense phase voidage remains constant and equal to e - for all U > U. ... 

Rowe PN. The dense phase voidage of fine powders fluidized by gas and its variation with temperature, pressure and particle size. In Fluidization (JR Grace, LW Sheimlt, MA Bergougnou, eds.). Engineering Foundation, New York, 1989, pp 195-202. 

Weimer AW, Quarderer GJ. On dense phase voidage and bubble size in high pressure fluidized beds of fine powders. AIChE J 31 1019-1028, 1985. 

Almost all of the models proposed to date are based on the two phase theory of fluidization originally proposed by Toomey and Johnstone (97) and later modified by Davidson and Harrison (98). According to the theory, the fliiidized bed is assumed to consist of two phases, viz., l) a continuous, dense particulate phase (emulsion phase) and 2) a discontinuous, lean gas phase (bubble phase) with exchange of gas between the bubble phase and emiilsion phase. The gas flow rate through the emulsion phase is assumed to be at minimum fluidization and that in excess of the minimum fluidization velocity passes throu the bubble phase. This formulation of the two phase theory is based on the ass mq)tion that the voidage of the emulsion phase remains constant. However, as pointed out by Rowe (22) and Horio and Wen (lOO) this assumption may be an over-simplification. In particular, experiments with fine powders (dp < 60 ym) conducted by Rowe show that the dense phase voidage changes with gas velocity, and as much as 30 percent of the gas flow occurs interstitially. This effect can be... 

For cracker catalyst (d = 55 (im, density = 950 kg/m3) fluidised by air, values of umb/umf of up to 2.8 have been found by Davies and Richardson(45). During the course of this work it was found that there is a minimum size of bubble which is stable. Small bubbles injected into a non-bubbling bed tend to become assimilated in the dense phase, whilst, on the other hand, larger bubbles tend to grow at the expense of the gas flow in the dense phase. If a bubble larger than the critical size is injected into an expanded bed, the bed will initially expand by an amount equal to the volume of the injected bubble. When, however, the bubble breaks the surface, the bed will fall back below the level existing before injection and will therefore have acquired a reduced voidage. 

It is far from certain that such a high-voidage spray zone can exist within a fluidized bed a spray zone, with a submerged nozzle, would require a jet to be blown in the dense phase by the atomising air. Work by Rowe et al. (1979) and by Smith and Nienow (1982), using X-ray... 

II. Voidage of the Dense Phase in Bubbling Beds. Powder Tech., 26,47. 

Consider a riser where the voidage in the bottom dense region is uniform and the top dilute region behaves as the freeboard of a dense-phase fluidized bed. The axial profile of the voidage in the top dilute region can be expressed by [Kunii and Levenspiel, 1990] (see 10.4.1)... 

The preceding model successfully explains the role played by the particles in the heat transfer processes occurring in the dense-phase fluidized bed at voidage a < 0.7. But it predicts very large values when the contact time of particles with the heating surface decreases because the nonuniformity of the solids concentration near the wall is not taken into account in this model. 

As opposed to the relatively uniform bed structure in dense-phase fluidization, the radial and axial distributions of voidage, particle velocity, and gas velocity in the circulating fluidized bed are very nonuniform (see Chapter 10) as a result the profile for the heat transfer coefficient in the circulating fluidized bed is nonuniform. 

When two units of the ring internals were installed at H — 2.25 m and H = 4.75 m, the dense-phase region was cut into three layers with a dilute influence zones in between and was thereby itself extended upward, while the solids inventory remained the same. Voidages e for the dilute-phase region and ea for the dense-phase region remain essentially the same, as shown in Fig. 31. In the influence zone of the internals, the radial voidage distribution is considerably flattened, as shown in Fig. 32. Reduced solid concentration in an influence zone is instrumental in suppression of solids mixing between adjacent dense-phase layers. 

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