Intrapellet

In the case of nonequimolal cpunterdiffusion, equation 12.2.6 suffers from the serious disadvantage that the combined diffusivity is a function of the gas composition in the pore. This functional dependence carries over to the effective diffusivity in porous catalysts (see below), and makes it difficult to integrate the combined diffusion and transport equations. As Smith (12) points out, the variation of 2C with composition (YA) is not usually strong, and it has been an almost universal practice to use a composition independent form of Q)c (12.2.8) in assessing the importance of intrapellet diffusion. In fact, the concept of a single effective diffusivity loses its engineering utility if the dependence on composition must be retained. 

In this paper we will first describe a fast-response infrared reactor system which is capable of operating at high temperatures and pressures. We will discuss the reactor cell, the feed system which allows concentration step changes or cycling, and the modifications necessary for converting a commercial infrared spectrophotometer to a high-speed instrument. This modified infrared spectroscopic reactor system was then used to study the dynamics of CO adsorption and desorption over a Pt-alumina catalyst at 723 K (450°C). The measured step responses were analyzed using a transient model which accounts for the kinetics of CO adsorption and desorption, extra- and intrapellet diffusion resistances, surface accumulation of CO, and the dynamics of the infrared cell. Finally, we will briefly discuss some of the transient response (i.e., step and cycled) characteristics of the catalyst under reaction conditions (i.e.,... 

As will be shown later, the surface coverages of CO vary with distance into the pellet during CO adsorption and desorption, as a result of intrapellet diffusion resistances. However, the infrared beam monitors the entire pellet, and thus the resulting absorption band reflects the average surface concentration of CO across the pellet s depth. Therefore, for the purpose of direct comparison between theory and experiment, the integral-averaged CO coverage in the pellet... 

Figure 8 shows how the intrapellet concentration profiles vary with time during the course of CO desorption. Both the gas-phase (solid lines) and surface (dotted lines) CO concentration profiles exhibit relatively mild gradients inside the pellet, in contrast to the steep profiles established during the adsorption process. This can be attributed to the fact that the intrinsic rate of desorption is slower than that of adsorption. 

Figure 7. Computed time variation of intrapellet concentration profiles during CO adsorption. Key ---------------------, gas phase and----> surface.

The dynamics of high-temperature CO adsorption and desorption over Pt-alumina was analyzed in detail using a transient mathematical model. The model combined the mechanism of CO adsorption and desorption (established from ultrahigh-vacuum studies over single-crystal or polycrystalline Pt surfaces) with extra- and intrapellet transport resistances. The numerical values of the parameters which characterize the surface processes were taken from the literature of clean surface studies ... 

Parametric sensitivity analysis showed that for nonreactive systems, the adsorption equilibrium assumption can be safely invoked for transient CO adsorption and desorption, and that intrapellet diffusion resistances have a strong influence on the time scale of the transients (they tend to slow down the responses). The latter observation has important implications in the analysis of transient adsorption and desorption over supported catalysts that is, the results of transient chemisorption studies should be viewed with caution, if the effects of intrapellet diffusion resistances are not properly accounted for. 

R. Madon and E. Iglesia, Hydrogen and CO intrapellet diffusion effects in ruthenium-catalyzed hydrocarbon synthesis, J. Catal., 1994, 149, 428 137. 

Intramolecular chain transfer, 20 220 Intramolecular cycloacylations, 72 177 Intramolecular self assembly, 20 482 Intramolecular stretching modes, 74 236 Intraoperative auto transfusion, 3 719 Intraparticle mass transfer, 75 729-730 Intrapellet Damkohler number, 25 294,... 

Maximum intrapellet temperatures, 25 305 effect of diffusion collision integral on, 25 301-303... 

Prandtl mixing length hypothesis, 11 779 Prandtl number, JJ 746, 809 13 246-247 Praseodymium (Pr), J4 631t, 634t electronic configuration, J 474t Praseodymium bromide, physical properties of, 4 329 Prater equation, 25 270, 299 Prater number, 25 299, 300-301, 303 effect on maximum dimensionless intrapellet temperature, 25 304, 309 effect on maximum intrapellet temperature, 25 306 Prato reaction, 12 244 Pratsinis aluminum nitride, 17 212 Pravachol, 5 143... 

Hydrodemetallation reactions are revealed to be diffusion limited by examination of metal deposition profiles in catalysts obtained from commercial hydroprocessing reactors. Intrapellet radial metal profiles measured by scanning electron x-ray microanalysis show that vanadium tends to be deposited in sharp, U-shaped profiles (Inoguchi et al, 1971 Oxenrei-ter etal., 1972 Sato et al., 1971 Todo et al., 1971) whereas nickel has been observed in both U-shaped (Inoguchi et al., 1971 Todo et al., 1971) and... 

Scrutiny of intrapellet metal concentration profiles reveals that the shapes of the profiles are a function of the axial position of the catalyst within a packed-bed reactor. Tamm et al. (1981) reported that nickel and vanadium profiles exhibit an internal maximum, termed M shaped, at the reactor inlet which shifts to the pellets edge at the bed outlet, as shown in Fig. 38. Similar internal maxima in aged catalysts have been observed elsewhere (Pazos et al., 1983 Oxenreiter et al., 1972 Hardin et al., 1978). 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

We previously proposed that intrapellet (pore) diffusion within liquid-filled catalyst pores decreases the rate of a-olefin removal. This increases the residence time and the fugacity of a-olefins within catalyst pellets and increases the probability that they will readsorb onto FT chain growth sites and initiate new chains. This occurs even for small catalyst particles ("0.1 mm pellet diameter) at normal FT conditions. Larger a-olefins remain longer within catalyst particles because diffusivity decreases markedly with increasing molecular size (carbon number). As a result, readsorption rates increase with increasing carbon number. 

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

Catalysts, prepared by impregnation of the porous support, in many cases exhibit intrapellet activity gradients, which are traditionally thought to be detrimental to catalyst performance. The effect of a deliberate nonuniform distribution of the catalytic material in the support, on the performance of a catalyst pellet received attention as early as the late 1960s [18,19]. These, as well as later studies, both experimental and theoretical, demonstrated that nonuniformly distributed catalysts can offer superior conversion, selectivity, durability, and thermal sensibility characteristics over those wherein the activity is uniform. 

We also examine the structure sensitivity of CO hydrogeneration on Co and Ru crystallites supported on various metal oxide supports at conditions that favor high selectivity (>80%) to C5+ products. We describe procedures for the synthesis of catalytic materials with high active site densities and controlled intrapellet distributions of sites. Finally, we review the extensive literature that has previously described metal dispersion, support, and transport effects on FT synthesis rate and selectivity. 

Recently, we have shown that non-Flory distributions cannot arise from the higher solubility of larger olefins because thermodynamic equilibrium between the two phases requires that the fugacity, chemical potential, and kinetic driving force for each component be the same in the two phases (4,5,14,40,41,44). Transport restrictions, however, can lead to higher intrapellet concentrations and residence times of a-olefins, a feature of FT chemistry that accounts for the non-Flory distribution of reaction products and for the increasing paraffin content of larger hydrocarbons (4,5,14,40,... 

Reactants and products must diffuse through high-molecular-weight liquid hydrocarbons during FT synthesis. The liquid phase may be confined to the mesoporous structure within catalyst pellets or extend to the outer surface and the interstitial spaces between pellets, depending on the reactor design and hydrodynamic properties. In packed-bed reactors, the characteristic diffusion distance equals the radius of the pellets plus the thickness of any liquid boundary layer surrounding them. Intrapellet diffusion usually becomes... 

The effects of diffusional restrictions on the activity and selectivity of FT synthesis processes have been widely studied (32,52,56-60). Intrapellet diffusion limitations are common in packed-bed reactors because heat transfer and pressure-drop considerations require the use of relatively large particles. Bubble columns typically use much smaller pellets, and FT synthesis rates and selectivity are more likely to be influenced by the rate of mass transfer across the gas-liquid interface as a gas bubble traverses the reactor (59,61,62). 

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