Voidage profile radial

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)... 

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. 

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).

Fig. 22. Effect of solids flow rate on radial voidage profile (after Tung et a/., 1988).

Fig. 30. Effect of average voidage on radial gas velocity profile (after Zhang, 1990).

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. 

Tung, Y., Zhang, W., Wang, Z., Tiu, X., and Ching, X. Further study of radial voidage profiles in fast fluidized beds, Eng. Chemistry and Metallurgy 10(2), 18-23 (1989). 

Fig. 32. Radial voidage profiles with and without ring internals. ug = 1.75 m/s, Gs = 18.6 kg/(m2s) (O, without ring internals , with ring internals) (Zheng et at, 1992).

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. 

Radial voidage profile displays the structure of dilute at the center and dense near the wall. 

A more rigorous analysis of the problem has recently been made by Lefroy and Davidson (L2). This analysis takes into account the vertical gas velocity and voidage profiles in the spout, as well as the effect of particle cross-flow from the annulus. Disregarding the radial variations across any horizontal section of the spout, the following equation can be written for continuity of gas flow and solids flow, respectively ... 

Fig. 26. Radial voidage profile in a conical spouted bed (Groltsiker s results, G7, quoted in R4).

Haidegger et al, 1989, have studied the total oxidation of ethane in a fixed-bed reactor and found a better agreement between experiment and simulation with the A (r)-model, compared to the model using a wall resistance (l/ w)-Simulation results for models with and without the radial porosity profile will be compared below. In the model neglecting the influence of the voidage profile, constant mass and heat dispersion and a wall resistance (I/Kw 0) will be applied. The effects of the radial voidage profile will be studied using the same correlation as used in Kiirten, 2003, for the mass and the A(r)-model for the heat dispersion. 

In contrast to this simple approach, Cohen and Metzner [1981] have made use of the detailed voidage profiles in the radial direction and have treated wall effects in a rigorous manner for both Newtonian and power-law fluids in streamline flow. From a practical standpoint, this analysis suggests the effect to be negligible in beds with (D/d) > 30 for inelastic fluids. 

Using the correlation of radial voidage profiles developed by Zhang et al. (1991),... 

Zhang W, Tung Y, Johnsson F. Radial voidage profiles in fast fluidized beds of different diameters. Chem Eng Sci 46(12) 3045-3052, 1991. 

Tung Y, Li Y, Kwauk M. Radial voidage profiles in a fast fluidized bed. In Kwauk M, Kunii D, eds. Fluidization 88 Science and Technology. Beijing Science Press, 1988, pp 139-145. 

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