Within the Catalyst Pellet

Little resistance to heat transfer exists within the eatalyst pellet (Reference 4, page 69). Consequently, the catalyst temperature is assumed to be uniform, at the catalyst surface temperature. 

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However, before extrapolating the arguments from the gross patterns through the reactor for homogeneous reactions to solid-catalyzed reactions, it must be recognized that in catalytic reactions the fluid in the interior of catalyst pellets may diSer from the main body of fluid. The local inhomogeneities caused by lowered reactant concentration within the catalyst pellets result in a product distribution different from that which would otherwise be observed. 

Our very first experiments with the reactor depicted in Figure 5.4.1 were carried out with a 15% Pt-Y-Al203 single cylindrical catalyst pellet [10-12], The acquisition time of 2D images of an axial slice at that time was about 260 s. Despite this, the first direct MRI visualization of the operation of a model gas-liquid-solid reactor has revealed the existence of large gradients of the liquid phase content within the catalyst pellet upon imbibition of liquid a-methylstyrene (AMS) under conditions... 

The existence of pulsating motion of the liquid phase within the catalyst pellet indicates that under certain conditions a steady-state regime of reaction progress can become unstable due to the exothermicity of the reaction under study. Further... 

For supported layered catalysts, optimizing the location of the active sites within the catalyst pellets maximizes the effectiveness or the selectivity or reactor yield. 

The packing itself may consist of spherical, cylindrical, or randomly shaped pellets, wire screens or gauzes, crushed particles, or a variety of other physical configurations. The particles usually are 0.25 to 1.0 cm in diameter. The structure of the catalyst pellets is such that the internal surface area far exceeds the superficial (external) surface area, so that the contact area is, in principle, independent of pellet size. To make effective use of the internal surface area, one must use a pellet size that minimizes diffusional resistance within the catalyst pellet but that also gives rise to an appropriate pressure drop across the catalyst bed. Some considerations which are important in the handling and use of catalysts for fixed bed operation in industrial situations are discussed in the Catalyst Handbook (1). 

We would be remiss in our obligations if we did not point out that the regions of multiple solutions are seldom encountered in industrial practice, because of the large values of / and y required to enter this regime. The conditions under which a unique steady state will occur have been described in a number of publications, and the interested student should consult the literature for additional details. It should also be stressed that it is possible to obtain effectiveness factors greatly exceeding unity at relatively low values of the Thiele modulus. An analysis that presumed isothermal operation would indicate that the effectiveness factor would be close to unity at the low moduli involved. Consequently, failure to allow for temperature gradients within the catalyst pellet could lead to major errors. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

In the preceding example we assumed that reaction occurred on the external surface so we did not have to be concerned with diffusion within the catalyst pellet. Now we consider the effect of pore diffusion on the overall rate. We have to do considerable mathematical manipulation to find the proper expressions to handle this, and before we begin, it is worthwhile to consider where we are going. As before, we want the rate as a function of bulk concentration Ca >i and we need to know the rate coefficient for various approximations (Figure 7-1 1). 

Complete characterization of poisoned catalysts, of course, requires much more than chemical analysis. For example, the interaction of poisons with catalyst constituents and with each other has been studied by X-ray diffraction and by electron microscopy, the morphology of the poison deposits by optical methods, the distribution within the catalyst pellets and washcoats by the microprobe, and the distribution of poison on the surface of the active metals by Auger spectroscopy. 

The fact that the effective heat conduction within the catalyst pellet normally is not the crucial process in determining the excess temperature of the catalyst pellet can be illustrated by analyzing the contribution of the interphase temperature gradient to the total excess temperature. To demonstrate this, we first eliminate the common reaction term occurring in the mass and enthalpy balances (eqs 32 and 33) ... 

Reverse-flow operation for Sulfur Production over Bauxite Catalysts by the Claus Reaction has been considered in Refs 9 and 31. The rate of H2S oxidation by SO2 on bauxite catalysts is very high even at ambient gas inlet temperature, but sulfur condensing at low temperatures blocks the active catalyst surface, and the reaction stops because of catalyst deactivation. In a reverse-flow reactor the periodic evaporation of condensed sulfur from the outlet parts of the catalyst bed occurs. Although it is difficult to remove all the sulfur condensed within the catalyst pellets at the bed edges, after a certain time a balance between the amount of sulfur condensed and evaporated is attained. Using a reverse-flow reactor instead of the two-bed stationary Claus process provides an equal or better degree of... 

Consider, by way of example, an irreversible first-order reaction, A B, occurring in a pellet with slab geometry. As a result of the concentration profile, the reaction rate depends on the position within the catalyst pellet. Hence, a mass balance for the reactant has to be taken over an infinitesimal slice of the slab. At the steady state this leads to ... 

Figure 4. Distribution profile of vanadium within the catalyst pellets for catalysts with different pore size distributions...

The modeling equations contain two key dimensionless parameters a Thiele modulus ( o) and a Peclet number (Peo) they characterize reaction/diffusion processes within the catalyst pellets and convection effects within the interpellet voids, respectively (81). Accordingly, both quantities depend on catalyst properties and reactor conditions. 

Particulate catalyst can be arranged in arrays of any geometric configuration. In such arrays, three levels of porosity (TLP) can be distinguished. The fraction of the reaction zone that is free to the gas flow is the first level of porosity. The void fraction within arrays is the second level of porosity. The fraction of pores within the catalyst pellets is referred as the third level of porosity. Parallel-passage and lateral-flow reactors... 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

In gas-solid reactors when solid particles are held stationary (so-called fixed bed reactor), gas flows through a porous medium comprising macropores existing between pellets or packed solid particles and micropores within the catalyst pellets (or other porous solids). Issues such as isotropy of the porous medium, initial distribution of gases, characteristics of solid particles, ratio of characteristic length scale of solid particles and that of the reactor and so on, influence the flow within fixed bed reactors. Support screens are often used to cover the bed of solid particles to avoid fluidization and carry-over of bed particles. These reactors are extensively used in process industries. Some examples and illustrative flow simulations are discussed in Chapter 13. 

In contrast, the two metals show higher penetration into the pellet for the presulfided catalysts. This provides clear indication that diflusion of feedstock molecules within the catalyst pellets is somehow more restricted for the unsulfided catalyst in comparison with the presulfided one. 

The most difficult step to include within the scheme of physical and chemical steps is that of diffusion within the catalyst pellet. To show what kind of... 

This example also shows the effects of mass- and enei y-transfer resistances within the catalyst pellet. The temperature increases toward the center of the pellet and increases the rate, but the oxygen concentration goes down, tending to reduce the rate. The global value of 49.8 x 10" is the resultant balance of both factors. Hence the net error in using the bulk conditions to evaluate the rate would be [(49.8 — 43.6)/49.8] (100), 12.5%. In this case the rate increase due to external and internal thermal effects more than balances the adverse effect of internal mass-transfer resistance. The procedure for calculating the effects of internal gradients on the rate is presented in Chap. 11. 

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