Catalyst pellet behavior

The final chapters, 11 and 12, are concerned with the particular application of transport theory to which this monograph is principally directed, namely the modeling of porous catalyst pellets. The behavior of a porous catalyst is described by differencial equations obtained from material and... 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

Despite the very restricted circumstances In which these equations properly describe the dynamical behavior, they are the starting point for almost all the extensive literature on the stability of steady states in catalyst pellets. It is therefore Interesting to examine the case of a binary mixture at the opposite limit, where bulk diffusion controls, to see what form the dynamical equations should take in a coarsely porous pellet. 

This section discusses the techniques used to characterize the physical properties of solid catalysts. In industrial practice, the chemical engineer who anticipates the use of these catalysts in developing new or improved processes must effectively combine theoretical models, physical measurements, and empirical information on the behavior of catalysts manufactured in similar ways in order to be able to predict how these materials will behave. The complex models are beyond the scope of this text, but the principles involved are readily illustrated by the simplest model. This model requires the specific surface area, the void volume per gram, and the gross geometric properties of the catalyst pellet as input. 

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

How do changes in catalyst pellet size affect system behavior ... 

For porous catalyst pellets with practical loadings, this quantity is typically much larger than the pellet void fraction e, indicating that the dynamic behavior of supported catalysts il dominated by the relaxation of surface phenomena (e.g., 35, 36). This implies that a quasi-static approximation for Equation (1) (i.e., e = 0) can often be safely invoked in the transient modeling of porous catalyst pellets. The calculations showed that the quasi-static approximation is indeed valid in our case the model predicted virtually the same step responses, even when the value of tp was reduced by a factor of 10. 

The manner in which Ni and V sulfide deposits accumulate on individual catalyst pellets depends on the kinetics of the HDM reactions as influenced by catalyst properties, feed characteristics, and operating conditions. The dynamic course of deactivation of catalytic reactor beds is also determined by the kinetics of the HDM reaction. The lifetime and activity of a reactor bed are directly related to the details of the metal deposit distribution within individual pellets. This section will review deactivation behavior of reactor beds in light of our understanding of the reaction and diffusion phenomena occurring in independent catalyst pellets. Unfortunately, this is an area of research which remains mostly proprietary with too little information published. What has been published is generally lacking in detail for the same reason. 

Fig. 51. Effect of catalyst pellet size on deactivation behavior for an Iranian Heavy atmospheric residuum desulfurized to 0.5 wt. % product sulfur (Tamm el at., 1981). 

This review will only focus on the modeling efforts in pore diffusion and reaction in single-catalyst pellets which have incorporated pore plugging as a deactivation mechanism. A broad literature exists on the deactivation of catalysts by active site poisoning, and it has been reviewed by Froment and Bischoff (1979). The behavior of catalytic beds undergoing deactivation is... 

Steam reformers are used industrially to produce syngas, i.e., synthetic gas formed of CO, CO2, 11-2, and/or hydrogen. In this section we present models for both top-fired and side-fired industrial steam reformers by using three different diffusion-reaction models for the catalyst pellet. The dusty gas model gives the simplest effective method to describe the intermediate region of diffusion and reaction in the reformer, where all modes of transport are significant. This model can predict the behavior of the catalyst pellet in difficult circumstances. Two simplified models (A) and (B) can also be used, as well as a kinetic model for both steam reforming and methanation. The results obtained for these models are compared with industrial results near the thermodynamic equilibrium as well as far from it. 

Figures 13 and 14 refer to the situation where only intraparticlc transport effects influence the observable reaction rate. However, a similar behavior is observed if, besides intraparticle heat and mass transport processes, the heat and mass transfer between the catalyst pellet and the bulk fluid phase is also considered. More information about this situation can be found, for example, in the works of Cresswell [26], McGreavy and...

Effectiveness factors for a first-order reaction in a spherical, nonisothermal catalysts pellet. (Reprinted from R B. Weisz and J. S. Hicks, The Behavior of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chem. Eng. Sci., 17 (1962) 265, copyright 1962, with permission from Elsevier Science.)... 

The abstract models can be divided into two categories, each of which can be further subdivided into three classes (Fig. 5). Some of the models consist of coverage equations only, and these models will be called surface reaction models. The remaining models use additional mass and/or heat balance equations that include assumptions about the nature of the reactor in which the catalytic reaction takes place (the reactor could be simply a catalyst pellet). These models will be called reactor-reaction models. Some of the models mentioned under the heading surface reaction models also incorporate balance equations for the reactor. However, these models need only the coverage equations to predict oscillatory behavior reactor heat and mass balances are just added to make the models more realistic [e.g., the extension of the Sales-Turner-Maple model (272) given in Aluko and Chang (273)]. Such models are therefore included under surface reaction models, which will be discussed first. 

At the root of these behaviors is the phenomenon of synchronization of a macroscopic oscillating system. This topic has been discussed occasionally in the literature but has rarely been explicitly treated. In principle there are several stages or hierarchical levels on which oscillations can occur (1) the single-crystal plane, (2) the catalytically active metal crystallite, (3) the catalyst pellet, (4) arrangements of several pellets in one layer of a flow reactor or a CSTR, and finally (5) the catalytic packed-bed reactor (327). On each of these levels, different types of oscillations may exist, but to become observable on the next level oscillations on the respective sublevels must be synchronized. For example, if oscillations of the CO/O2 reaction on a Pt(lOO) face of a Pt crystallite supported on a pelletized support material in a packed-bed reactor occur, the reaction on the (100) facet as a whole must oscillate in synchrony, other (100) facets of the crystallite have to synchronize, other crystallites in the pellet must couple to the first crystallite, and, finally, all pellets in one layer of the bed must display oscillations in synchrony. If the synchronization on one of these levels fails, different oscillators will superimpose and their effects will cancel. One would then only observe a possible increased level of noise in the measured conversion. On the other hand, if synchronization occurs independently over several regions of a system, then it might exhibit apparently chaotic behavior caused by incomplete coupling. 

Oscillations are possible on all levels in a catalytic reactor, from the single-crystal plane to the crystallite to the catalyst pellet to the packed-bed reactor, and each level adds another degree of complexity. Thus it is necessary to isolate the major influences at each level and to separate the characteristics of the oscillations on one level from the effects caused by coupling with other levels. Only when each level is well understood is it possible to fully understand the overall oscillatory behavior. Oscillations in heterogeneous catalysis will therefore remain an intriguing and demanding problem for many years to come. 

Diffusive and convective transport processes introduce flexibility in the design of catalyst pellets and in the control of FT synthesis selectivity. Transport restrictions lead to the observed effects of pellet size, site density, bed residence time, and hydrocarbon chain size on chain growth probability and olefin content. The restricted removal of reactive olefins also allows the introduction of other intrapellet catalytic functions that convert olefins to other valuable products by exploiting high intrapellet olefin fugacities. Our proposed model also describes the catalytic behavior of more complex Fe-... 

In industrial heterogeneous catalytic processes catalysts inevitable lose activity over a period of time. Quantitative study of the activity-time relation is important in determining the optimum reactor design and operation. The first step in treating the problem is to analyze the behavior of a single catalyst pellet. 

In the laboratory either integral or differential (see Sec. 4-3) tubular units or stirred-tank reactors may be used. There are advantages in using stirred-tank reactors for kinetic studies. Steady-state operation with well-defined residence-time conditions and uniform concentrations in the fluid and on the solid catalyst are achieved. Isothermal behavior in the fluid phase is attainable. Stirred tanks have long been used for homogeneous liquid-phase reactors and slurry reactors, and recently reactors of this type have been developed for large catalyst pellets. Some of these are described in Sec. 12-3. When either a stirred-tank or a differential reactor is employed, the global rate is obtained directly, and the analysis procedure described above can be initiated immediately. 

The same catalyst pellets will be employed in both reactors. Laboratory studies have shown that external resistances are negligible for this system. The heat of reaction is small, so that isothermal operation is achievable. Assume plug-flow behavior and that the density of the reaction liquid does not change with conversion. The bulk density of catalyst in either reactor is 1.0 g/cm. ... 

The curve of Cj, versus for an infinitely long cylinder normal to the flow is much like that for a sphere, but at low Reynolds numbers, does not vary inversely with because of the two-dimensional character of the flow around the cylinder. For short cylinders, such as catalyst pellets, the drag coefficient falls between the values for spheres and long cylinders and varies inversely with the Reynolds number at very low Reynolds numbers. Disks do not show the drop in drag coefficient at a critical Reynolds number, because once the separation occurs at the edge of the disk, the separated stream does not return to the back of the disk and the wake does not shrink when the boundary layer becomes turbulent. Bodies that show this type of behavior are called bluff bodies. For a disk the drag coefficient Cj, is approximately unity at Reynolds numbers above 2000. 

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