Catalyst state gradient

As mentioned in the previous discussions of deactivation, catalyst aging is very composition dependent. Thus, catalyst state at a given time on stream will vary with axial distance in a plug flow reactor. This is shown in Fig. 22. Benzene and methylcyclopentane compositions as a function of time on stream are shown at 20% through the catalyst bed and at the end of the bed. KINPTR predicts the catalyst state gradient in the reactor. 

Fig. 22. Evidence for catalyst state veclor gradient, isothermal pilot plant data, with methylcyclopentane-hexane feed (B, benzene M, methylcyclopentane).

So far we have considered an infinite value of the gas-to-particle heat and mass transfer coefficients. One may encounter, however, an imperfect access of heat and mass by convection to the outer geometrical surface of a catalyst. Stated in other terms, the surface conditions differ from those in the bulk flow because external temperature and concentration gradients are established. In consequence, the multiple steady-state phenomena as well as oscillatory activity depend also on the Sherwood and Nusselt numbers. The magnitudes of the Nusselt and Sherwood numbers for some strongly exothermic reactions are reported in Table III (77). We may infer from this table that the range of Sh/Nu is roughly Sh/Nu (1.0, 104). 

If catalytic performance is to be correlated with spectroscopic data, the analyzed volume must be representative of the working catalyst. Impurities from the feed that may accumulate in the first layers of a catalyst bed can be a problem (Groothaert et al., 2003). Furthermore, high conversions will lead to large composition gradients in the fluid phase, resulting in catalyst states and surface species that differ from position to position. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Unsteady-State Direct Oxidation Process. Periodic iatermption of the feeds can be used to reduce the sharp temperature gradients associated with the conventional oxidation of ethylene over a silver catalyst (209). Steady and periodic operation of a packed-bed reactor has been iavestigated for the production of ethylene oxide (210). By periodically varyiag the inlet feed concentration of ethylene or oxygen, or both, considerable improvements ia the selectivity to ethylene oxide were claimed. 

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

Temperature gradients within the porous catalyst could not be very large, due to the low concentration of combustibles in the exhaust gas. Assuming a concentration of 5% CO, a diffusion coefficient in the porous structure of 0.01 cms/sec, and a thermal conductivity of 4 X 10-4 caI/sec°C cm, one can calculate a Prater temperature of 1.0°C—the maximum possible temperature gradient in the porous structure (107). The simultaneous heat and mass diffusion is not likely to lead to multiple steady states and instability, since the value of the 0 parameter in the Weisz and Hicks theory would be much less than 0.02 (108). 

EfiBdent hydrogen supply iiom decalin was only accomplished by the si terheated liquid-film-type catalysis under reactive distillation conditions at modaate heating tempaatures of 210-240°C. Caibcm-supported nano-size platinum-based catalysts in the si ietheated liquid-film states accelerated product desorption fixjm file catalyst surface due to its temperature gradient under boiling conditions, so that both hi reaction rates and conversions were obtained simultaneously. 

Steady-state reactors with ideal flow pattern. In an ideal isothermal tubular pZi/g-yZovv reactor (PFR) there is no axial mixing and there are no radial concentration or velocity gradients (see also Section 5.4.3). The tubular PFR can be operated as an integral reactor or as a differential reactor. The terms integral and differential concern the observed conversions and yields. The differential mode of reactor operation can be achieved by using a shallow bed of catalyst particles. The mass-balance equation (see Table 5.4-3) can then be replaced with finite differences ... 

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. 

At steady state, the rates of each of the individual steps will be the same, and this equality is used to develop an expression for the global reaction rate in terms of bulk-fluid properties. Actually, we have already employed a relation of this sort in the development of equation 12.4.28 where we examined the influence of external mass transfer limitations on observed reaction rates. Generally, we must worry not only about concentration differences between the bulk fluid and the external surface of the catalyst, but also about temperature differences between these points and intraparticle gradients in temperature and composition. 

In the suspended state, however, no temperature gradient arises at the catalyst surface since the active site temperature is the same as the boiling point of the solution. Only small magnitudes of reaction rates and conversions were obtained in the suspended state because of diminished rate constant k and enlarged retardation constant K (Table 13.2). 

In the adequate case (1.0 or 2.0 mL tetralin), the catalyst appeared to be wet differently from dry sand-bath or suspension states. As in the case of decalin dehydrogenation under the superheated liquid-film conditions, the catalyst temperature is higher than the boiling point, exhibiting a temperature gradient, and the substrate liquid is limited in amount to... 

A log-log plot using K Km, /ccat and Acuncat data from the 18 separate cases of antibody catalysis exhibited a linear, albeit scattered, correlation over four orders of magnitude and with a gradient of 0.86 (Fig. 16).4 Considering the assumptions made, this value is sufficiently close to unity to suggest that the antibodies do stabilize the transition state for their respective reactions. However, even the highest A cat/A uncat value of 106 in this series (Tramontano et al., 1988) barely compares with enhancement ratios seen for weaker enzyme catalysts (Lienhard, 1973). 

When a catalytic reaction occurs on the surfaces within a catalyst pellet in a packed bed, there are inevitably concentration gradients around and within the pellet. We have thus far considered only the overaU variation in concentrations as a function of distance along the direction of flow J in the reactor. However, in order to account for the variations around and within catalyst peUets, we now need to find Cj x, y, z) rather than just Cj z). Stated... 

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