Shaped catalysts

The oxychlorination reaction is very exothermic and the catalyst is very active, which makes it necessary to mix the catalyst with an inert diluent to avoid overheating in a fixed-bed reactor. A low surface area, spherically- or ring-shaped alumina or chemical porcelain body can be used as a diluent with the ring-shaped catalyst. The density of the inert material should be similar to the catalyst to avoid segregation during loading, and the size should be slightly different to allow separation of the inert material from the spent catalyst. 

The next level is that of shaped catalysts, in the form of extrudates, spheres, or monoliths on length scales varying from millimeters to centimeters, and occasionally even larger. Such matters are to a large extent the province of materials science. Typical issues of interest are porosity, strength, and attrition resistance such that catalysts are able to survive the conditions inside industrial reactors. This area of catalysis is mainly (though not exclusively) dealt with by industry, in particular by catalyst manufacturers. Consequently, much of the knowledge is covered by patents. 

The characteristic times on which catalytic events occur vary more or less in parallel with the different length scales discussed above. The activation and breaking of a chemical bond inside a molecule occurs in the picosecond regime, completion of an entire reaction cycle from complexation between catalyst and reactants through separation from the product may take anywhere between microseconds for the fastest enzymatic reactions to minutes for complicated reactions on surfaces. On the mesoscopic level, diffusion in and outside pores, and through shaped catalyst particles may take between seconds and minutes, and the residence times of molecules inside entire reactors may be from seconds to, effectively, infinity if the reactants end up in unwanted byproducts such as coke, which stay on the catalyst. 

Figure 5.25. Examples of the various forms of shaped catalysts. (Courtesy of Haldor Tops0e A/S).

A fraction ( of the active surface of some porous slab-shaped catalyst pellets becomes poisoned. The pellets are used to catalyse a first-order isothermal chemical reaction. Find an expression for the ratio of the activity of the poisoned catalyst to the original activity of the unpoisoned catalyst when (a) homogeneous poisoning occurs, (b) selective poisoning occurs. 

The catalyst support may either be inert or play a role in catalysis. Supports typically have a high internal surface area. Special shapes (e.g., trilobed particles) are often used to maximize the geometric surface area of the catalyst per reactor volume (and thereby increase the reaction rate per unit volume for diffusion-limited reactions) or to minimize pressure drop. Smaller particles may be used instead of shaped catalysts however, the pressure drop increases and compressor costs become an issue. For fixed beds, the catalyst size range is 1 to 5 mm (0.04 to 0.197 in). In reactors where pressure drop is not an issue, such as fluidized and transport reactors, particle diameters can average less than 0.1 mm (0.0039 in). Smaller particles improve fluidization however, they are entrained and have to be recovered. In slurry beds the diameters can be from about 1.0 mm (0.039 in) down to 10 Jim or less. 

The concept requires that for reversible reactions equilibrium be attained in the center of the catalyst. A numerical simulation of the set of continuity equations for CH4 and CO2 inside a ring-shaped catalyst particle used in an industrial reformer confirmed the presumption that equilibrium is indeed attained within a very thin layer close to the surface. 

The factors that influence catalyst performance are numerous and only partially understood. What follows is a discussion of key catalyst design issues, starting with the catalytic surface and progressing through supported catalysts to shaped catalyst particles, successively incorporating new phenomena and variables as the complexity of the system increases. 

Figure 2. Regularly shaped catalyst islands on an adsorptive support. Reprinted with permission from Chem. Eng. Sci., vol. 38, p. 719, D.-Y. Kuan, H. T. Davis, and R. Aris, Effectiveness of Catalytic Archipelagos. I. Regular Arrays of Regular Islands, copyright 1983 [8], Pergamon Press PLC.

Figure 3. Irregularly shaped catalyst particles represented via Voronoi tessellation.

Figure 8. Illustration from an early patent on shaped catalysts. From Foster [27].

Figure 5. Local mass-transfer distribution at the surface of individual cylindrical or ring-shaped catalyst pellets in a fixed-bed packing.

Density grading is flexible in that it can be applied to any size or shape catalyst particle. The number of fractions produced... 

Finally, 1 and A tie down the catalyst geometry of the ring-shaped catalyst pellet (Figure 6.9) ... 

Thus for < = 0 the ring-shaped catalyst pellet becomes a cylindrical catalyst pellet. Equation 6.41 is illustrated in Figure 6.10. In this diagram 1 is plotted versus A lines with a constant geometry factor T are drawn. The four comers of the diagram represent... 

Figure 6.9 Geometry of a ring-shaped catalyst pellet.

For any ring-shaped catalyst pellet with known values of and A the value of T can be obtained from Figure 6.10. The value of the first Aris number An can then be calculated with Equation 6.38. 

Figure 6.10. Dimensionless inner radius i versus dimensionless height X for a ring-shaped catalyst pellet.

Figure 6.17 Dimensionless inner radius i versus dimensionless height X for a ring-shaped catalyst pellet. Lines of constant maximum relative error are drawn for first-order kinetics using the approximation 1...

This anisotropy can be accounted for in the Aris numbers. Considering a ring-shaped catalyst pellet, the material balance on a micro scale, for simple reactions, reads as (Appendix C)... 

Differential equation 7.120 describes the concentration profile in an isotropic ring-shaped catalyst pellet with an effective diffusion coefficient DeAH, a height H, and an inner radius... 

Comparison of Equations 7.126 and 7.127 with 7.124 and 7.125 shows that for ring-shaped catalyst pellets the modified effective diffusion coefficient Dj follows from... 

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