Voidage profile

J. N. Papageorgiou, G. F. Froment 1995, (Simulation models accounting for radial voidage profiles in fixed-bed reactors), Chem. Eng. Sci. 50, 3043. 

Figure 18. Comparison of radial voidage profiles calculated by correlation with experimental data in the three different beds used (FCC/air). (From Zhang et al., 1991.)...

Zhang, W., Tung, Y., and Johnsson, F., Radial Voidage Profiles in Fast Fluidized Beds of Different Diameters, Chem. Eng. Sci., 46(12) 3045 (1991)... 

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 ... 

Tung, Y., Li, J., and Kwauk, M., Radial Voidage Profiles in a Fast Fluidized Bed, Proc. of Third China-Jpn. Symp. on Fluidization, p. 139, Beijing, China (1988)... 

Wang, N., Li, Y., Zheng, X., and Kwauk, M., Voidage Profiling for Fast Fluidization, First Intern. Conf. Circulating Fluidized Beds, Halifax, Canada (1985)... 

For glass beads in the ETH riser, the macro-scale structures seem to be similar for different approaches, as the predicted voidage profiles... 

Figure 20 Predicted flow regime diagram of the industrial MIP reactor, with solids flux as a function of the imposed total pressure drop at fixed gas flow rate. The snapshots of voidage profile refer to the transition, from left to right, the dilute transport, choking transition in between with different solids inventory, to the dense fluidization (Lu et al., 2007).

Figure 10.10. Typical axial voidage profiles for Group A particles (after Li and Kwauk, 1980 Yang, 1992).

Figure 10.11. Effects of gas and solids flow rates on the axial profile of the cross-sectional averaged voidage in a riser with an abrupt exit (from Brereton and Grace, 1993b) (a) Abrupt exit geometry (b) Voidage profiles.

Fig. 5. Types of apparatus and their respective effects on axial voidage profile. 1, fast fluidized bed 2, intermediate hopper 3, cyclone 4, slow fluidized bed 5, downcomer 6, solids rate controlling device 7, solids rate measurement device 8, suspension section.

As Fig. 5b (Li et ai, 1984) shows, there is no intermediate solids hopper as for type A, and the solids rate device is used only for measurement rather than for control. In operation, solids circulation rate is determined essentially by gas velocity. Therefore, gas velocity and solids circulation rate could not be adjusted independently. Solids circulation rate follows what an operating velocity produces at whatever solids inventory the system was initially filled with. Owing to the absence of an intermediate hopper, the initial solids inventory could influence directly axial voidage profile, that is, the position of the inflection point changes with the initial solids inventory in the system. 

Voidage profiles represent one of the most important aspects of the flow structure of fast fluidization, which play an important role in gas and solids mixing, mass and heat transfer, and conversion in a chemical reactor. Considerable efforts have been given to studying the axial and radial variation of solids concentration axially, dilute at the top and dense at the bottom, and radially, dilute in the center and dense in the vicinity of the wall. As already mentioned in Section II, these variations depend mainly on gas velocity and solids circulation rate and are also influenced by the configuration of the apparatus. 

Figure 15 shows typical results of axial voidage profile measurements (Li and Kwauk, 1980 Li et al, 1981). Experiments were conducted by using different solids materials in a Type A apparatus, 90 mm i.d. and 8 m high. Voidages were calculated from pressure gradient measurements. Solids circulation rate was controlled by a pneumatically actuated pulse feeder (see Section III in Chapter 7). 

It can be seen from Fig. 15 that for any given solids circulation rate, most of the voidage profiles display a sigmoidal distribution, and the position of the inflection point becomes lower as gas velocity increases, indicating that solids inventory in the fast column diminishes with increasing gas velocity. 

Fig. 15. Axial voidage profile Tor four powders in a Type A fast fluidized bed (after Li and...

Fig. 16. Axial voidage profile for different inventories of pulverized coal in a Type B fast fluidized bed (after Li et al., 1984).

As regards Type C apparatus, typical of CCNY s setup (Yerushalmi et al, 1976), when the solid rate controlling valve opens but slightly, and the initial solids inventory is high, the voidage profile will be close to that for Type A apparatus, while when this valve is mostly open, the voidage profile will be similar to that for Type B apparatus. In most casts, its axial voidage variation will be affected by the initial solids inventory. The effect of solids inventory is reflected in what Weinstein et al. (1984) called imposed pressure drop across the fast bed. ... 

To describe the axial voidage profile, a one-dimensional model for steady-state operation has been developed as follows. 

When the inlet and outlet effects are minimal to the extent of being negligible, a set of correlations of the state parameters on the axial voidage profiles, as... 

The S-shaped axial voidage profile can be described by using the diffusion-segregation model (Li and Kwauk, 1980) as follows ... 

For single-region voidage profiles, as can be seen in Fig. 16, the inflection point may be understood to lie beyond the top or the bottom of the fast column. In this case, the voidage profile would be described by Eq. (35) or Eq. (32) alone. 

Local voidages for FCC catalyst at various radial positions were measured with an optical fiber probe in a Type A apparatus, from which radial volidage profiles and their probability density functions were computed by Li et al. (1980b), as shown in Figs 20 and 21. When gas velocity is less than the incipient fast fluidization velocity of 1.25 m/s, the radial voidage profile is relatively flat when gas velocity increases further, this profile becomes steeper high in the center. As flow is transformed into pneumatic transport, the... 

Fig. 20. Radial voidage profile for fast fluidized beds (after Li et aU 1980, 1985).

The preceding equation shows that as long as the cross-sectional average voidage E is known, then the three-dimensional voidage profile could be calculated. 

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