Radial Voidage Distribution

All the preceding sections were concerned with one-dimensional voidage distribution in the vertical direction. However, maldistribution of solids in the radial direction, generally dilute in the center and dense next to the wall, often causes unfavorable residence time distributions for both the solids and the fluidizing gas, thus resulting in undesirable product distribution. Although it has long been known that in vertical flow of G/S systems solids are preferentially scattered toward the wall, accurate measurement has not been easy. 

Optical fiber measurement of local solids concentrations of FCC catalyst fluidized in a 9-cm-i.d. column gave the results shown typically in Fig. 26. Analysis of these data showed that the radial voidage profile could be described solely by the cross-section-average voidage e, calculated as shown in Sec. 5.1, and the reduced radial coordinate r/R  

the three-dimensional voidage distribution in a fast fluidized bed can be determined, semi-empirically as our understanding stands at the present, from the physical properties of the solids and the gas and the operating variables. 

From a practical point of view, for improved solids distribution, the indications are for innovative design of obstructing structures next to the wall to break the falling sheet of solids in order to equalize their flow pattern across the column through repeated redistribution. 

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Figure 26. Radial voidage distribution for FCC catalyst in a 90 mm i.d. column, 2.25 m above the gas distributor.

Tung, Y., Li, J., Zhang, J., and Kwauk, M., Preliminary Experiments on Radial Voidage Distribution in Fast Fluidization, Fourth Nat. Conf. Fluidization, Lanzhou, China (1987)... 

A comprehensive account of radial voidage distribution requires a recognition of the lateral movement of solids in addition to their axial movement. One of the most important and yet least understood aspects of riser hydrodynamics is the lateral solids distribution mechanism [Kwauk, 1992]. Typical experimental findings for the radial voidage... 

Zhang et al. (1990) developed a more general diffusion model for calculating axial and radial voidage distributions in fast fluidized beds by extending Li and Kwauk s (1980) model. 

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. 

Figure 19 Radial voidage distribution in a ring-baffled fluidized bed.

Zhang et al. (1991) carried out investigations with three different fast bed systems with diameters of 32, 90, and 300 mm. They found that the radial voidage distribution, given as a ratio to the cross-sectional average, was independent of bed diameter and solids recycle rate. The similarity does not hold at transition... 

Actual data of gas concentration profiles in a pilot riser reactor are reported by Jiang et al. They studied ozone decomposition in a catalytic circulating fluidised bed. By applying an UV detection technique they were able to measure strong radial and axial ozone concentration gradients in their experimental set-up. It was concluded that the ozone concentration profiles are consistent with the trend exhibited by the voidage distribution in both axial and radial direction. 

Zhu JX, Salah M, Zhou YM. Radial and axial voidage distributions in circulating fluidized bed with ring-type internals. J Chem Eng Jpn 30(5) 928-937, 1997. 

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. 

Boundaries in fast fluidization refer mainly to the column wall as well as the inlet and outlet. Effect of the wall on pressure drop due to friction between the fluidized solids and the wall surface is minimal (Li et al, 1978), although it is the very cause of radial distribution of parameters. The configuration of the inlet and the outlet often strongly affect gas-solids flow, especially with regard to axial voidage profile. 

Figure 16 shows the radial profiles of parameters involving the solid velocity l/d(r) calculated from Model KR using the data provided by Bader et al. (1988) on radial distribution of voidage and gas throughput as shown in Fig. 16f. 

The characteristic axial and radial distributions of heat transfer coefficients computed from the preceding formula are shown in Fig. 12. In the calculation, the sectional average voidage e can be established from any of the known... 

Whether axially or radially, gas-solid flow is heterogeneous in structure. Axial voidage profile characterizes a dilute region at the top and a dense region at the bottom, i.e., an S-shaped distribution curve. 

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