Catalysts, general spherical

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. 

A kinetics or reaction model must take into account the various individual processes involved in the overall process. We picture the reaction itself taking place on solid B surface somewhere within the particle, but to arrive at the surface, reactant A must make its way from the bulk-gas phase to the interior of the particle. This suggests the possibility of gas-phase resistances similar to those in a catalyst particle (Figure 8.9) external mass-transfer resistance in the vicinity of the exterior surface of the particle, and interior diffusion resistance through pores of both product formed and unreacted reactant. The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius A at a particular instant of time, in terms of the general case and two extreme cases. These extreme cases form the bases for relatively simple models, with corresponding concentration profiles for A and B. 

The solution method, the Adomian Decomposition Method (ADM), is mechanized for solving the nonlinear models according to the principle of Parameter Decomposition .2,3 A Mathematica code of the ADM,12 for general order reactions in planar or spherical catalyst pellets, is given in more detail in the Appendix. Thus, the algebraic expressions of the approximate solutions and the computed data of results can all be easily obtained. 

By use of this technique, it is possible to prepare fine spherical catalyst particles in the 10-100/rm diameter range, as arc required for typical fluidized-bed catalytic processes. In this technique used for large-scale catalyst manufacture, the feed is generally dilute hydrogel or sol that is sprayed from the top of a tower while hot air is blown in a cocurrcnt or countercurrent direction to dry the droplets before they reach the bottom of the tower. The fine droplets arc produced or atomized by pumping the hydrogel or sol under pressure cither... 

Equation 56 can be used only for spherical catalyst pellets and first order, irreversible reactions. However, for convenience, and in analogy to the Thiele modulus, a generalized modulus ij/pn can be defined as well which applies to arbitrary pellet shape and arbitrary reaction order. This is defined as... 

In summary, wc conclude tluu particle shape control in supported metal catalysis is feasible. When a supported platinum catalyst is annealed under conditions where the platinum particles stay dean, the platinum particles assume a spherical shape with flat facets in the (100) and (111) directions. All of the particles in the catalyst assume the same general shape. In contrast, different shapes are observed when the catalyst is annealed in various udgasscs. Shi[ll] showed theoretically that only a few planes can be produced by eciuilibratiug the particles in simple adsorbates. However, w e speculate that one may be able to produce a wide distribution of panicle siiapes. with appropriate adsorbates,... 

The following discussion represents a detailed description of the mass balance for any species in a reactive mixture. In general, there are four mass transfer rate processes that must be considered accumulation, convection, diffusion, and sources or sinks due to chemical reactions. The units of each term in the integral form of the mass transfer equation are moles of component i per time. In differential form, the units of each term are moles of component i per volnme per time. This is achieved when the mass balance is divided by the finite control volume, which shrinks to a point within the region of interest in the limit when aU dimensions of the control volume become infinitesimally small. In this development, the size of the control volume V (t) is time dependent because, at each point on the surface of this volume element, the control volnme moves with velocity surface, which could be different from the local fluid velocity of component i, V,. Since there are several choices for this control volume within the region of interest, it is appropriate to consider an arbitrary volume element with the characteristics described above. For specific problems, it is advantageous to use a control volume that matches the symmetry of the macroscopic boundaries. This is illustrated in subsequent chapters for catalysts with rectangular, cylindrical, and spherical symmetry. 

The first boundary condition is equivalent to a finite value of I a at the symmetry point in spherical coordinates. This condition was invoked in Section 17.2 along the symmetry axis of long cylindrical catalysts to eliminate the modified zeroth-order Bessel function of the second kind, = 0), from the general solution given by equation (17-22). When the symmetry condition at the center of a spherical pellet is used to evaluate the integration constants, one finds that B = 0 in equation (17-28) because ... 

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