Effectiveness factor interpretation

A few details have been reported on the slow reductions of 8303 by As(ni) and T1(I) . In the anaerobic reductions by As(III) the reaction is first-order in 820 and although As(III) certainly catalyses decomposition, the dependence of the rate on [As(III)] is small. Aeration leaves the rate of spontaneous decomposition of 820g unaffected, but the As(III)-catalysed route is accelerated by a factor of ten, the kinetic law remaining unchanged. The oxygen effect is interpreted in terms of the chain reaction... 

In the laboratory, the measured rate constant for the first-order reaction would have to equal the product rjk if this constant were expressed per unit area of catalyst. This relationship then gives us an alternative interpretation of the effectiveness factor in terms of our model... 

The starting points for the continuity and energy equations are again 21.5-1 and 21.5-6 (adiabatic operation), respectively, but the rate quantity7 (—rA) must be properly interpreted. In 21.5-1 and 21.5-6, the implication is that the rate is the intrinsic surface reaction rate, ( rA)int. For a heterogeneous model, we interpret it as an overall observed rate, (—rA)obs, incorporating the transport effects responsible for the gradients in concentration and temperature. As developed in Section 8.5, these effects are lumped into a particle effectiveness factor, 77, or an overall effectiveness factor, r]0. Thus, equations 21.5-1 and 21.5-6 are rewritten as... 

The main aim of this part of the book is to demonstrate the advantages of using multivariate statistical computations. The application of chemometric methods to the results of routine environmental monitoring and their relevant interpretation facilitates asserta-tions concerning the identification of effective factors in the environment and the objective assessment of pollutant loading. These factors and loading states are either not accessible or are of only very restricted accessibility in current environmental monitoring. 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

A summary of reactor models used by various authors to interpret trickle-bed reactor data mainly from liquid-limiting petroleum hydrodesulfurization reactions (19-21) is given in Table I of reference (37). These models are based upon i) plug-flow of the liquid-phase, ii) the apparent rate of reaction is controlled by either internal diffusion or intrinsic kinetics, iii) the reactor operates isothermally, and iv) the intrinsic reaction rate is first-order with respect to the nonvolatile liquid-limiting reactant. Model 4 in this table accounts for both incomplete external and internal catalyst wetting by introduction of the effectiveness factor r)Tg developed especially for this situation (37 ). 

Both classical and quantum mechanical treatments of Raman scattering are based on Eq. (2.1), and such treatments are very valuable in understanding the effect and interpreting spectra (1-5). One of the more analytically important results of Raman theory is the Raman scattering cross section, aj, which will be discussed at some length below. Before considering the factors that affect CT, it is useful to review several aspects of Raman theory. 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

In contrast to cyanine dyes and Ru complexes, fairly concentrated chlorophyl monolayers could be deposited on Sn02- In the latter case, the quantum yield of the photocurrent was determined as a function of the molar ration of chlorophyl and stearic acid (concerning the definition of quantum yield see Section 10.2.5). An optimum was obtained for a 1 1 ratio, whereas the quantum yield dropped by a factor of nearly 3 for a pure chlorophyl layer [35]. This effect was interpreted as concentration quenching which cannot be further discussed here. The same authors have also investigated chlorophyl multilayers, all of which were deposited using the Langmuir-... 

Although some sex-specific differences have been observed, the mechanism by which this occurs is unknown. These differences could be a result of differences in sex steroid levels as seen with the rat, but proof in humans is lacking. Basically, because of the confounding effects of age, diet, and physiological factors, interpretation of the sex-dependent differences in drug pharmacokinetics in humans is very complex and the role of metabolism remains to be clarified. 

The location of the absorption bands due to chromophores depends markedly on environmental factors. By studying the displacements of the Amax of the chromophores by the introduction of other groups, one can understand the nature of substituent effects. The interpretation of the spectra of organic molecules often becomes difficult because of the presence of more than one chromophore. Typical examples of such complex chromophores would be dienes, ajS-unsaturated ketones, substituted benzenes etc. However, by a study of the electronic spectra of a large number of different types of molecules, it has generally been possible to correlate the spectroscopic data with the structure of molecules. 

By definition the first-order rate constant measured per unit area of catalyst must be equal to the product (r k ). Hence, an alternative interpretation of the effectiveness factor is... 

Under strong diffusion effects, the effectiveness factor is inversely proportional to Thiele modulus. When the reaction has a generic n-order, one should take care in interpreting the experimental results, since, according to Equation 18.29, the reaction order is not the same as the intrinsic rate. The observed rate is as follows ... 

The SFR with catalytically coated plates is an easy setup to investigate heterogeneously catalyzed gas-phase reactions. In situ invasive capillary techniques can be used to determine the gas-phase concentration in the one-dimensional boundary layer on top of the catalyst. The measurement species profiles can be compared with numerically predicted profiles to test surface reaction mechanisms, diffusion models but also gas-phase reaction schemes, CVD processes, and others (not discussed here). However, internal difiiision inside the catalytic disc has to be taken into account when thicker catalyst layers are used. Then, the choice of an adequate diffusion model can be crucial for a correct interpretation of the measured data. The computer code DETCHEM offers simulations with the following models to account for internal diffusion in stagnation flows on porous plates with reactions inside effectiveness factor model, ID reaction diffusion model (RD-approach), and DGM (not discussed here). While the RD-approach may even play a role in simple cases as discussed here, it is the model of choice when parallel reactions occur (e.g., catalytic partial oxidation, three-way... 

The purpose of this paper is to summarize previous interpretations of the effect of incomplete catalyst wetting on trickle-bed performance and to develop a model for the effectiveness factor for partially wetted catalyst pellets. In the case of a reaction... 

---