Spherical pellets

In this section three miscellaneous topics in the area of agglomeration shall be discussed, namely, dry pelletization, spherical agglomeration in liquid suspension, and spontaneous or inadvertent agglomeration of fine particles. 

Example 7.5 Cooling nuclear pellets Spherical nuclear fuel pellets generate heat at a rate per unit volume, q, and being cooled at the boundary by convection heat transfer. For a single pellet on start up, we have... 

E21.1 Hydrogenation of particular oil is performed in a liquid phase catalytic reactor (plug flow reactor (PFR)) containing catalytic particles (pellets—spherical diameters) of 1 cm. The external concentration is 1 kmol/L and on the particle surface is 0.1 kmol/L at a superficial velocity of 0.1 m/s. Verify if there are mass effects. There will be a change if the particle diameter is equal to 0.5 cm Neglect the effects in diffusive pores (Fogler, 2000). Additional data ... 

In place of the earlier cylindrical catalyst pellets, spherical pellets with smooth or porous surfaces made from porcelain, magnesium silicate, quartz and silicon carbide are used to obtain higher space velocities. A very thin layer of V205/T102 is applied to the carrier to manufacture the catalyst a ratio of Ti02 to V2O5 with 2 to 15% V2O5 in the active mass has been found to be very efficient. Contact time is between 0.15 to 0.6 sec. Current service life of the catalyst is of the order of 2 to 4 years. 

Molecular sieves are generally available as cylindrical pellets, spherical beads, and powder. Pellets and beads are most commonly used for dehydration and gas purification applications. The pellets are formed by extrusion and usually have a fixed diameter of At, or A in., and a variable length equal to 1 to 4 times the diameter. The bead size is characterized by screen cut, which identifies the Tyler screen size through which all of the beads pass and the size that retains all of the beads, in that order, with the two sizes separated by an x. The two most commonly used screen cuts are 4 x 8 and 8 x 12. 

Let us compare computations of the effectiveness factor, using each of the three approximations we have described, with exact values from the complete dusty gas model. The calculations are performed for a first order reaction of the form A lOB in a spherical pellet. The stoichiometric coefficient 10 for the product is unrealistically large, but is chosen to emphasize any differences between the different approaches. 

In these definitions the suffix zero refers to conditions at the surface of the pellet and a is a characteristic dimension, for example the radius in Che case of a spherical pellet. In terms of these variables equations (12.29)-(12.31) take the following form... 

Apart from this simple result, comparison of stability predictions for the two limiting situations can be made only by direct numerical computation, and for this purpose a specific algebraic form must be assumed for the reaction rate function, and a specific shape for che catalyst pellet. In particular, Lee and Luss considered a spherical pellet and a first order... 

A successful variation of oil agglomeration was used for removal and dewatering of soot from a 1—3% soflds suspension consisting of <5 — fim particles in refinery process waters (Fig. 8). Heavy oil was added to the dilute slurry and intensely agitated in a multistage mixer. The soot agglomerated with the oil to form 3—5 mm pellets that were easily screened from the water (95). The pellets contained only 5—10% water. The process was modified to recover very fine clean coal, and it produced highly uniform, hard, spherical pellets 1—2 mm in diameter. 

Use of the peUetted converter, developed and used by General Motors starting in 1975, has declined since 1980. The advantage of the peUetted converter, which consists of a packed bed of small spherical beads about 3 mm in diameter, is that the pellets were less cosdy to manufacture than the monolithic honeycomb. Disadvantages were the peUetted converter had 2 to 3 times more weight and volume, took longer to heat up, and was more susceptible to attrition and loss of catalyst in use. The monolithic honeycomb can be mounted in any orientation, whereas the peUetted converter had to be downflow. AdditionaUy, the pressure drop of the monolithic honeycomb is one-half to one-quarter that of a similar function peUetted converter. 

Effectiveness As a reac tant diffuses into a pore, it undergoes a falling concentration gradient and a falling rate of reaction. The concentration depends on the radial position in the pores of a spherical pellet according to... 

The analytical result for a first-order reaction in a spherical pellet is ... 

Catalysts may be porous pellets, usually cylindrical or spherical in shape, ranging from 0.16 to 1.27 cm (Ma to V2 in) in diameter. Small... 

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x ... 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

With no resistance to mass transfer, the concentration is Cm throughout the whole spherical pellet, and the reaction rate, which must be equal to the mass transfer rate in a steady-state process, is ... 

A hydrocarbon is cracked using a silica-alumina catalyst in the form of spherical pellets of mean diameter 2.0 mm. When the reactant concentration is 0.011 kmol/m3, the reaction rate is 8.2 x 10"2 kmol/(m3 catalyst) s. If the reaction is of first-order and the effective diffusivity De is 7.5 x 10 s m2/s, calculate the value of the effectiveness factor r). It may be assumed that the effect of mass transfer resistance in the. fluid external Lo the particles may be neglected. 

FIGURE 10.3 Nonisothermal effectiveness factors for first-order reactions in spherical pellets. (Adapted from Weisz, P. B. and Hicks, J. S., Chem. Eng. Sci., 17, 265 (1962).)... 

J. J. Fitzgibbon. Sintered, spherical, composite pellets prepared from clay as a major ingredient useful for oil and gas well proppants. Patent CA 1232751, 1988. 

Fig. 3.3.5 Propagators for water flow at 2.93 mm3 s-1 through the fixed-bed reactor (a) spherical glass beads, pore diameter dp = 2 mm and (b) cylindrical pellets with average equivalent diameter of 2.2 mm.

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