Yang Fluidization, Solids Handling, and Processing

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An Example of Modeling Coalescence in Granulation Processes.

Growth by coalescence in granulation processes may be modeled by the population balance, as mentioned. It is necessary, however, to determine both the mechanism and kernels which describe growth. For fine powders within the non-inertial regime of growth where granule deformation can be neglected, all collisions result in successful coalescence provided that binder is present. Therefore, coalescence occurs via a random, or size independent kernel which is only a function of liquid loading y, or

The dependence of growth on liquid loading represented by fn(y) strongly depends on wetting properties. For random growth, it may be shown that the average granule size is given by

where a0 is the initial nuclei size, and kt is the extent of granulation. Random growth will occur until the inertial regime of granulation is reached, at which point an additional relationship exists to determine the largest granule size possible, or

Combining the previous two relationships allows us to estimate the extent of granulation as a function of the governing group of the Stokes number, or

Hence, the extent of non-inertial growth depends logarithmically on binder viscosity and the inverse of agitation velocity (Adetayo et al., 1995). Maximum granule size depends linearly on these variables. Also, the extent of growth has been observed to depend linearly on liquid loading y and,

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3.7Unwanted Aggregation in Fluidized Beds

Industrial fluidized beds are operated with particles which usually contain impurities or are themselves a mixture of many components. Upon heating, some of these components soften, melt or react with each other, generating stickiness. In fluid bed reactors, the fluidizing gas as well as the solid particles can react chemically producing new components and, during this process, particle cohesion and stickiness can occur. In all these cases, the fluidization behavior of the bed changes dramatically as temperature is increased and unwanted agglomerates form. Such characteristics as the minimum fluidization and bubbling velocity, the bubble size and bubble frequency, all undergo a significant change and, in the limit, total defluidization of the bed can take place. Like in granulation, stickiness generated by surface softening or due to the presence of a sticky chemical species results in agglomerate formation and growth. However, unlike granulation, this growth is usually unintended and it proceeds in the noninertial regime where, as long as stickiness is present, coalescence takes place and can, in some cases, become uncontrollable.

It was shown (Siegell, 1984; Compo et al., 1984; Tardos et al., 1985a,b; and Compo et al., 1987) that cohesiveness and subsequent agglomeration and sintering of fluidized particles occurs if fluid beds are operated at temperatures at or above the so-called minimum sintering temperature (point), Ts, of the particles. It was also shown that for pure materials fluidized in inert gases, the sintering temperature is an intrinsic property of the solid particle surface which can be estimated using constant heating rate dilatometry (Tardos et al., 1984). This temperature is usually a fraction of the melting point of the solid material and depends on structure and chemical composition; Table 9 gives a few examples for materials used by Compo et al. (1987). As can be seen from the table, the ratio of the sintering point to the melting temperature varies a great deal and can take values from approximately 0.5 to 0.95. These results show that “the rule of thumb” employed in industry for the ratio Ts/TM to be approximately 0.8 is correct for some compounds but not for others.

Using the “dilatometer” technique, a small sample of powder (about 1– 2 grams) is heated at constant rate in the apparatus depicted schematically in Fig. 43. Dilatation of the sample is measured by a linear voltage transducer (LVDT); contraction of the sample indicates particle-particle surface flattening and defines the minimum softening point or sintering temperature, Ts. In

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Table 9. Dependency of Minimum Sintering Temperature on the Electronic Structure of Crystalline Material

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It was also shown both theoretically and experimentally (Tardos et al., 1985a,b) that there is a strong correlation between the excess temperature above the minimum sintering point, T-Ts, and the excess gas velocity above minimum fluidization conditions (measured below the sintering point) U-Umf, required to maintain fluidization. A general correlation was developed between the excess temperature and the excess gas velocity, which takes the form

where DB and dp = 2a are the bed and particle diameters, and K and n are material dependent coefficients. These take different values for amorphous and crystalline materials and are given in Table 10.

Table 10. Values of Coefficients K and n

There is a significant difference in the form of Eq. (46) for amorphous and crystalline materials (Compo et al., 1987 and 1990); for the first group, a slight increase in temperature above minimum sintering results in a significant increase in excess gas velocity as can be seen in both, the value of the

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constant K as well as the value of the exponent (n = 2, in this case). For crystalline materials, on the other hand, the correlation is weaker and the exponent is significantly smaller (n = 0.4–0.5).

The determination of sintering temperatures was extended to more complex materials such as coal ashes (Ladesma et al., 1987) and beneficiated ilmenite ores (Compo et al., 1987). Although these experiments were also performed in an inert atmosphere, different components within these materials reacted and sintered at different temperatures. It was again found that sintering and softening detected in the dilatometer predicted very closely the agglomeration and defluidization observed in the experimental fluid bed in accordance with the results given in Eq. (46).

During more recent work (Tardos and Pfeffer, 1995) several systems were studied where fluidizing gas actually reacted with fluidized particles and either a solid or a gaseous product was formed. The influence of product formation on fluidization was studied in both an isothermal fluidized bed and in the dilatometer. The following reactions were studied: reduction of calcium sulfate (phosphogypsum) to calcium sulfide (CaS) in hydrogen, oxidation of coke and magnesium in air and production of aluminum nitride (AlN) from a solid precursor containing aluminum and carbon by carbothermal nitridation (Nicolaescu et al., 1994).

In one case, the product was a gas (CO2) while in others it was a solid (calcium sulfide, aluminum nitride and magnesium oxide). One of the products was a fine, extremely cohesive material (CaS) while the others were stable, free flowing materials which exhibit no cohesiveness (MgO and AlN). It was shown that in the case of the gaseous product, the bed was easily fluidizable as long as the temperature did not exceed the sintering point of the solid reactant. When the product was a noncohesive, solid powder, steady fluidization could be maintained until total conversion was achieved by keeping the temperature below the sintering point of both the reactant and the product. Production of the cohesive powder, calcium sulfide, was only possible in a fluid bed diluted with heavy inert particles (sand) which acted as fluidization media and promoted the removal of the product from the surface of the reactant powder. In the case of the aluminum nitride production, even though carbon (coke) is not readily fluidizable at temperatures above 1200– 1300°C, the formation of a fluidizable product (AlN) ensured good fluidization to temperatures as high as 1500–1600°C.

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ACKNOWLEDGMENT

The authors would like to acknowledge that the section dealing with population balance modeling of granulation processes is an abbreviated version of material prepared by Dr. J. D. Litster, University of Queensland, for a joint short course given by Dr. B. J. Ennis and Dr. J. D. Litster.