Voidage distribution

Horio s scaling law derivation was based on the requirement that two similar circulating fluidized beds have equal values of voidage distribution, dimensionless core radius, gas splitting to core and annulus, solid splitting to core and annulus, and cluster voidage. The CAFM equations were then examined to determine how these requirements could be met. 

Figure 22. Vertical voidage distribution in fast fluidization. (Li and Kwauk, 1980.)...

The voidage distribution model permits the derivation of analytical expressions for the integrated average voidage taken through the whole height, defined as... 

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. 

Thus, 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. 

The three-dimensional voidage distribution provides the basic correlation for building a reactor model for fast fluidization, given data on particle-fluid transfer coefficients and intrinsic particle reaction kinetics. 

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)... 

The fu st term is a modified Archimedes number, while the second one is the Froude number based on particle size. Alternatively, the first term can be substituted by the Reynolds number. To attain complete similar behavior between a hot bed and a model at ambient conditions, the value of each nondimensional parameter must be the same for the two beds. When all the independent nondimensional parameters are set, the dependent parameters of the bed are fixed. The dependent parameters include the fluid and particle velocities throughout the bed, pressure distribution, voidage distribution of the bed, and the bubble size and distribution (Glicksman, 1984). In the region of low Reynolds number, where viscous forces dominate over inertial forces, the ratio of gas-to-solid density does not need to be matched, except for beds operating near the slugging regime. 

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... 

The axial voidage distribution resulting from mixing of dissimilar particles, as shown in Fig. 26, will now be examined in the light of the dynamics of these particles at the interfacial boundary between the properly juxtaposed phases of a binary particle mixture (Lou, 1964 Kwauk, 1973). Both the lighter particles at the top and the heavier particles at the bottom share the same tendency of invading the region occupied by the other. This behavior conforms to the concept of random walk, for which Fick s law can be adapted to describe the macroscopic diffusion flux of the smaller particles 2 ... 

Typical voidage distribution curves computed by using Eq. (9.3) for four kinds of solid materials are shown in Fig. 57 and compared against experimentally determined values. 

The simplest case is called the one-fluid model, that is, k — 1, assuming that particles are distributed in the fluid discretely. It was used for modeling voidage distributions in fast fluidized beds (Li and Kwauk, 1980 Bai et al., 1988 Zhang et al., 1990). 

According to Li and Kwauk s model, Zhang and Xie derived C/i = 1-4), resulting in the final correlations for spatial voidage distribution (Zhang et al., 1991) ... 

Zhang, H, Xie, Y. S., and Hasatani, M. A new two dimensional correlation for voidage distribution of fast fluidized beds, in Proc. of 4th China-Japan Symposium Fluidization, Beijing, China, p. 21. 1991. 

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. 

Fic. 12. Comparison of measured axial voidage distribution with mathematical model of... 

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. 

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