Heterogeneous catalytic reactions approximation

It should be noted that the detailed modelling of heterogeneous catalytic reactions faces some specific difficulties. Compared with homogeneous systems, the limits of the field wherein the law of mass action analog (the surface-action law) can be correctly applied are less distinct. Still less reliable are the elementary step constants. Nevertheless, we believe that, despite the complexity of "real kinetics , the importance of studying the models fitting the law of mass action cannot be undervalued. These models describe the chemical components of a complex catalytic process properly and, on the other hand, they are a necessary step that can be treated as a first approximation. Our study is devoted to the analysis of just these models. 

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

To conclude this section, it should be noted that the calculations of the potential energy surfaces for heterogeneous catalytic reactions, even by semiempirical methods, still remain a matter for the future. Insufficient accuracy of the semiempirical methods, the approximate nature of cluster modeling, the large volume of a configurational space, a variety of possible reaction paths, etc., considerably restrict the utility of quantum chemistry as applied to this field. There is, however, no doubt that these difficulties will be successfully overcome. The value of conclusive quantum-chemical calculations can hardly be overestimated. They are able to answer questions which the most sophisticated and refined experiments would fail to answer. 

Based on the above considerations, the types of reactions that are amenable to inorganic membrane reactors in the first wave of industrial implementation will probably be as follows (1) The reactions are heterogeneous catalytic reactions, particularly dehydrogenation processes (2) The reaction temperature exceeds approximately 200°C (3) When the reactions call for high-purity reactant(s) or produces) and the volume demand is relatively small, dense membrane reactors (e.g., Pd-based) can be used. On the other hand, if high productivity is critical for the process involved, porous membrane reactors are necessary to make the process economically viable. 

There is now a great deal of interest in utilizing the microkinetic approach in modeling rates of catalytic reactions despite the lack so r of reliable rate constants of elementary reactions on different catalytic materials. However, the alternative approaches diat provide a simple means of understanding, explaining and predicting the kinetic behavior of complex heterogeneous catalytic reactions continue to be invaluable. The main approximations that are conventionally used to simpUfy the detailed kinetics are [1] ... 

This approximation will be considered for a heterogeneous catalytic reaction, although a similar treatment can be done for homogeneous and enzymatic reactions, as will be illustrated in the respected chapters. 

The study of catalytic polymerization of olefins performed up to the present time is certain to hold a particular influence over the progress of the concepts of the coordination mechanism of heterogeneous catalysis. With such an approach the elementary acts of catalytic reaction are considered to proceed in the coordination sphere of one ion of the transition element and, to a first approximation, the collective features of solids are not taken into account. It is not surprising that polymerization by Ziegler-Natta catalysts is often considered together with the processes of homogeneous catalysis. 

For a molecule characterised by a AH value of 40 k.I mol 1 and undergoing facile surface diffusion, i.e. a A/ dir value close to zero, then each molecule will visit, during its surface lifetime (10 r s), approximately 107 surface sites. Since the surface concentration a is given by a = NtSUIf, then for a AH value of 40 kJ mol-1 and zsurf= 10-6 s at 295 K, the value of a is 109 molecules cm-2. These model calculations are illustrative but it is obvious that no conventional spectroscopic method is available that could monitor molecules present at a concentration 10-6 monolayers. These molecules may, however, contribute, if highly reactive, to the mechanism of a heterogeneously catalysed reaction we shall return to this important concept in discussing the role of transient states in catalytic reactions. 

The organic polymer membranes have an upper operating limit of approximately 200 C due to their thermal stability. Below this temperature, there exist organic polymer membranes suitable for homogeneous catalytic reactions in some compatible solvents. This temperature also represents the lower limit for most heterogeneously catalyzed reactions [Armor, 1992]. 

A heterogeneously catalyzed reaction takes place at the surface of a catalyst. Catalysts, their properties, and the nature of catalytic surfaces are discussed in Chapter 7. For this discussion, we approximate the surface as a single crystal with a known surface order. The density of atoms at the low-index planes of transition metals is on the order of. 10 cm 2. Figure 5.16 presents the atomic arrangement of low-index surfaces for various metals. This figure illustrates the packing arrange-... 

Heterogeneous catalytic oxidation is a well studied and industrially useful process. Industrial catalytic oxidation of vapors and gases is a very broad field and is dealt with in several texts and review articles. Catalytic oxidation, both partial and complete, is an important process for such reactions as the partial oxidation of ethene and propene, ammoxidation of propene to acrylonitrile, maleic anhydride production, production of sulfuric acid, and oxidation of hydrocarbons in automotive exhaust catalysts. By far, the majority of oxidation catalysts and catalytic oxidation processes have been developed for these industrially important partially oxidized products. However, there are important differences between the commercial processes and the complete catalytic oxidation of VOCs at trace concentrations in air. For instance, in partial oxidation, complete oxidation to CO2 and H2O is an undesirable reaction occurring in parallel or in series to the one of interest. Other differences include the reactant concentration and temperature, the type of catalyst used, and the chemical nature of the oxidizable compound. Approximate ranges of the major independent variables of interest in this review are shown in Table 1. 

Although many useful strategies have been developed to model heterogeneous catalytic and electrocatalytic reactions, the approach that has been most successful in computational catalyst screening involves the development and use of descriptors, which are simple thermodynamic or kinetic parameters that are directly related to the catalytic properties of the material and that can be rapidly evaluated with electronic structure (primarily. Density Functional Theory— DFT) calculations. In a typical descriptor-based catalyst search, an approximate functional relationship between the... 

The heterogeneous catalytic reforming reactions are supposed to take place on the gas-solid interface. In heterogeneous catalysis no species enter into the solid phase, hence for this process the species mass balance are solved only in the gas phase. For the adsorption process the reaction actually takes place within the solid adsorbent material. However, in the modeling approach employed by Wang et al. [161] a pseudo-homogeneous reaction model was adopted so that the CO2 capture reaction was approximated by a particle surface reaction thus the overall diffusion... 

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