Reactivity distribution

A spectrum of metal compound reactivities in petroleum could arise for several reasons. Nickel and vanadium exist in a diversity of chemical environments. These can be categorized into porphyrinic and non-porphyrinic species vanadyl and nonvanadyl or associated with large asphaltenic groups and small, isolated metal-containing molecules. Each can be characterized by unique intrinsic reactivity. Reaction inhibition which occurs between the asphaltenes and the nonasphaltenes, as well as between Ni and V species, can also contribute to reactivity distributions. The parallel reaction interpretation of the observed reaction order discrepancy is therefore compatible with the multicomponent nature of petroleum. Data obtained at low conversion could appear as first order and only at higher conversions would higher-order effects become obvious. The... 

The methods employing selective stoppers do not allow a direct determination of the active center reactivity distribution, such as do the methods covered in Section 4.2. As shown above, the primary reason of the polymerization rate drop is a reversible plugging of the vacancy by an excess of the catalyst poison, which may eventually insert into the transition metal-carbon bond. Thus, one cannot expect an unambiguous correlation between the polymerization rate drop and the amount of the poison incorporated into the polymer. The active center reactivity distribution may, however, be obtained indirectly by correlating the length of macromolecules (after the polymer fractionation) with the content of the catalyst poison. 

A quantitative description of the active center non-uniformity is perhaps the most valuable contribution of the method covered in this Section. As noted by Tait10), the reactivity distribution of the active centers can be considered as a finger-print of a catalyst system. It is quite likely that some methods allow determination of highly... 

Later, Furusaki et al. (F17) studied the hydrogenation of ethylene by fluidized Ni catalyst to obtain the axial reactivity distribution. Here the samples of bed gas were removed by a traveling sampler placed at the center of the bed during steady reaction, so that the sample taken in the dense phase shows an average of the concentration in the bubble and emulsion phase. Figure 74 shows an example of the axial concentration profile. 

Apparently the reaction seems to have almost ended near the distributor this is because the sample has been mostly taken from the emulsion phase. The calculated concentration profile, assuming (eb)sampie = 0.2, is close to the observed profile. However, the axial reactivity distribution inside the bed is not always clear, although this kind of experiment does give useful information. A similar experimental approach has been utilized by other investigators (C7a, F12). 

The second archiving scheme, known as dissimilarity archiving, records the best solutions that are dissimilar by a specified amount. The degree of dissimilarity between two LPs, X and Y, is defined in terms of their beginning of cycle (BOC) reactivity distributions ... 

C PVCm solution in dichloroethane Insert histogram for the site reactivity distribution corresponding to curve B... 

Other useful information that can be extracted from SSITKA data using advanced mathematical analysis includes the reactivity distribution, f(k). On a heterogeneous catalyst surface, the active sites exhibit a non-uniform reactivity which can be characterised by a reactivity distribution function f(k), where k represents a measure of site activity. The determination of f(k) from the isotopic transient of P requires a numerical deconvolution technique. 

Two main methods, parametric and nonparametric, have been developed for this deconvolution. The parametric method involves development of a multi-parameter model for obtaining the value of reactivity distribution... 

The T-F method is more precise and less subjective than the ILT method on the other hand, it is more demanding from a computational point of view than the latter.The T-F method, even in the presence of small amounts of random noise, can recover significantly the reactivity distribution. 

Fig. 6(b). Reactivity distribution obtained by the T-F deconvolution method for the selective oxidation of CO on Pt/7-Al2 03 catalyst. 

It should be mentioned that the majority of the work presented here is graphically based simply because it is easier to grasp column into-actions and behavior when approached from this point of view. However, this need not be a limitation for the methods. The authors would also like to stress that it is not necessarily the specific material and problems presented in the book that are important, but more the tools that the reader should be equipped with. The concepts we present simply put tools into the designer s hand for him/her to create a unique column or separation structure that may solve his/her particular separation problem. For instance, both distributed feed and reactive distillation columns are discussed independently, although it is of course entirely possible to conceive of a reactive distributed feed system, which is not discussed. The tools in this book will thus first allow the reader understand, analyze, and design well-known and frequently encountered distillation problems. Second, the tools can be used to synthesize and develop new systems that peihaps have not even been thought of yet. This principle applies to virtually all the work in this book and the reader is urged to explore such concepts. 

Figure 2.6. Effect of the cathodic transfer coefficient, a, on the reactivity distribution within an agglomerate. For 0=1, the reactivity remains uniform throughout the agglomerate so that an effectiveness of Fa = 1 is obtained. For a = 0.5, relative reactivity drops steeply toward the agglomerate center. The corresponding effectiveness factor is strongly reduced. Fa 0.095, i.e. only 10% of the accessible catalyst is effectively used for reactions in this case.

Experiments carried out in Assembly-51 were devised to check computational models and to measure parameters related to the design and safe operation of the FTR. These included critical mass, spatial activation and small sample reactivity distributions, sodium voiding, spatial dcpendcAce of neutron spectra, central reactivity worth measurements, fuel compaction, and reactivity control worths. 

Fi(. 25. Change in quantum yidd

site reactivity distribution cone nding to Curve B... 

Sabatier s principle has an interesting consequence for the kinetics of reactions catalyzed by systems with a wide reactivity distribution of active sites. Since the rate of reaction is at maximum for those sites having interaction energies close to the optimum of Figure 6.22, the overall rate of reaction is dominated by these sites. For this reason the kinetics of the reaction can often be modeled by equations corresponding to one type of catalytically reactive site only. However, depending... 

The flavor compounds that are labeled with stable isotopes (isotopomers) differ only slightly from the analyte in terms of mass, and their physical and chemical properties—e.g., volatility, reactivity, distribution coefficient and chromatographic behavior—are the same as those of the unlabeled flavor compounds, with the exception of minor and negligible isotope effects. They are added to foods as internal standards as early as possible, namely before the first extraction, so that they undergo virtually the same losses as the flavor compounds to be studied during the isolation method and enrichment steps that are employed. For this reason, labeled compounds satisfy nearly all of the requirements for an ideal internal standard and can also tolerate workup methods with very low recovery percentages, provided that the detection sensitivity is not too low. 

Nq = n(0) is the steady-state initial neutron density. The Doppler coefficient of reactivity and the density coefficient of reactivity are considered for the reactivity feedback. The reactivity distribution in the axial direction is assumed to follow the square of the cosine distribution. 

Fig. 7.64 Local void reactivity distributions of improved 700 MWe class Super FR. (Taken from [27] and used with permission from Atomic Energy Society of Japan)...

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