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Simplified Kinetic Models

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. [Pg.774]

Kinetic Models Used for Designs. Numerous free-radical reactions occur during cracking therefore, many simplified models have been used. For example, the reaction order for overall feed decomposition based on simple reactions for alkanes has been generalized (37). [Pg.437]

It is important to characterize FCC feeds as to their molecular structure. Once the molecular configuration is known, kinetic models can be developed to predict product yields. The simplified correlations above do a reasonable job of defining hydrocarbon type and distribution in FCC feeds. Each correlation provides satisfactory results within the range for which it was developed. Whichever correlation is used, the results should be trended and compared with unit operation. [Pg.82]

Obtaining Kinetic Samples for Reactive Extrusion. To develop and test kinetic models, homogeneous samples with a well defined temperature-time history are required. Temperature history does not necessarily need to be isothermal. In fact, well defined nonisothermal histories can provide very good test data for models. However, isothermal data is very desirable at the initial stages of model building to simplify both model selection and parameter estimation problems. [Pg.508]

Methane can be oxidatively coupled to ethylene with very high yield using the novel gas recycle electrocatalytic or catalytic reactor separator. The ethylene yield is up to 85% for batch operation and up to 50% for continuous flow operation. These promising results, which stem from the novel reactor design and from the adsorptive properties of the molecular sieve material, can be rationalized in terms of a simple macroscopic kinetic model. Such simplified models may be useful for scale up purposes. For practical applications it would be desirable to reduce the recycle ratio p to lower values (e.g. 5-8). This requires a single-pass C2 yield of the order of 15-20%. The Sr-doped La203... [Pg.396]

Eq. (122) represents a set of algebraic constraints for the vector of species concentrations expressing the fact that the fast reactions are in equilibrium. The introduction of constraints reduces the number of degrees of freedom of the problem, which now exclusively lie in the subspace of slow reactions. In such a way the fast degrees of freedom have been eliminated, and the problem is now much better suited for numerical solution methods. It has been shown that, depending on the specific problem to be solved, the use of simplified kinetic models allows one to reduce the computational time by two to three orders of magnitude [161],... [Pg.221]

Kinetic models developed for reactor scale-up are also suitable for reactor optimization. The development of detailed kinetic models accounting for all factors influencing process rates is a time-consuming task. Therefore, more empirical simplified models are often used for simulation and optimization of existing reactors. [Pg.318]

For a fixed molar ratio (ns/riAh equal to 0.05887, the temperature as applied in experiment E4, and a batch time of 347.8 dimensionless units, the feed rate of B (and thus the feed time) was optimized by computation to find tj = 323.19 dimensionless units. A run was carried out at these conditions. The data collected from this experiment were then used for re-estimation of the kinetic parameters. The new kinetic model was used to evaluate the new optimum feed rate for the same total amount of B. The optimum batch time reduced to 275.36 and the feed time to 242.75 units. Table 5.4-19 summarizes the results for three successive optimizations and re-estimations. Evidently, even a very simplified kinetic model can be successfully used in search for an optimum provided that kinetic parameters are updated based on every subsequent run carried out at the optimum conditions evaluated from the preceding set of kinetic parameters. [Pg.325]

There are two objectives of setting up a kinetic mathematical model for chiral products. The first is the elucidation of the reaction mechanism with identification of the rate-controlhng step. The second is to derive a mathematical expression for the selectivity in terms of the ratio of the major product to the minor product. Then, based upon this expression, the reaction conditions such as pressure or feed ratio are changed to increase the selectivity. However, when the enantiomeric purity is over 99%, the selectivity is extremely high hence, the reaction mechanism for the major manifold can be neglected to simplify the establishment of the kinetic model. [Pg.29]

For the interbipolycondensation the condition of quasiideality is the independence of the functional groups either in the intercomponent or in both comonomers. In the first case the sequence distribution in macromolecules will be described by the Bernoulli statistics [64] whereas, in the second case, the distribution will be characterized by a Markov chain. The latter result, as well as the parameters of the above mentioned chain, were firstly obtained within the framework of the simplified kinetic model [64] and later for its complete version [59]. If all three monomers involved in interbipolycondensation have dependent groups then, under a nonequilibrium regime, non-Markovian copolymers are known to form. [Pg.191]

Fig. 4. Simplified rearrangement of the pulmonary clearance features of the kinetic model for retention and organ distribution of inhaled mCe. Fig. 4. Simplified rearrangement of the pulmonary clearance features of the kinetic model for retention and organ distribution of inhaled mCe.
On account of this, the difficulties associated with developing a detailed kinetic model for the FTS, able to describe at the same time the rate of formation of all the reaction products, are obvious. It is therefore not surprising that several efforts have been devoted through the years to simplify the kinetic mechanism of the FTS. [Pg.295]

FIGURE 6-3 Simplified kinetic model for opening and closing steps of Na+ and K+ channels. (Adapted from Hodgkin and Huxley [6].)... [Pg.98]

By lifting the simplifying restrictions, the kinetic observations can be examined in more detail over much wider concentration ranges of the reactants than those relevant to pseudo-first-order conditions. It should be added that sometimes a composite kinetic trace is more revealing with respect to the mechanism than the conventional concentration and pH dependencies of the pseudo-first-order rate constants. Simultaneous evaluation of the kinetic curves obtained with different experimental methods, and recorded under different conditions, is based on fitting the proposed kinetic models directly to the primary data. This method yields more accurate estimates for the rate constants than conventional procedures. Such an approach has been used sporadically in previous studies, but it is expected to be applied more widely and gain significance in the near future. [Pg.456]

The construction of the structural kinetic model proceeds as described in Section VIII.E. Note that in contrast to previous work [84], no simplifying assumptions were used the model is a full implementation of the model described in Refs. [113, 331]. The model consists of m = 18 metabolites and r = 20 reactions. The rank of the stoichiometric matrix is rank (N) = 16, owing to the conservation of ATP and total inorganic phosphate. The steady-state flux distribution is fully characterized by four parameters, chosen to be triosephosphate export reactions and starch synthesis. Following the models of Petterson and Ryde-Petterson [113] and Poolman et al. [124, 125, 331], 11 of the 20 reactions were modeled as rapid equilibrium reactions assuming bilinear mass-action kinetics (see Table VIII) and saturation parameters O1 1. [Pg.217]

D. Visser, R. van der Heijden, K. Mauch, M. Reuss, and S. Heijnen, Tendency modeling A new approach to obtain simplified kinetic models of metabolism applied to Saccharomyces cerevisiae. Metab. Eng. 2(3), 252 275 (2000). [Pg.237]

Behr and Obendorf [21] proposed a step-wise reaction model, according to which diethers are formed from monoether and isobutene and triether is formed from diethers and isobutene. In the simplified kinetic model no difference was considered between the two monoethers and the two diethers, and disproportion reactions and all side reactions were neglected (Fig. 10.6). The conversion rate was modeled without taking into account any mass transfer processes and phase... [Pg.216]

Fig. 16.2 Simplified kinetic model of the photocatalytic process. ps represents the light absorbed per unit surface area of the photocatalyst, e b and h+b are the photogenerated electrons and holes, respectively, in the semiconductor bulk, kR is the bulk recombination rate constant and /R the related flux, whatever recombination mechanism is operating A is the heat resulting from the recombination kDe and kDh are the net first-order diffusion constants for fluxes Je and Jh to the surface of e b and h+b in the semiconductor lattice, respectively e s and h+s are the species resulting from... Fig. 16.2 Simplified kinetic model of the photocatalytic process. ps represents the light absorbed per unit surface area of the photocatalyst, e b and h+b are the photogenerated electrons and holes, respectively, in the semiconductor bulk, kR is the bulk recombination rate constant and /R the related flux, whatever recombination mechanism is operating A is the heat resulting from the recombination kDe and kDh are the net first-order diffusion constants for fluxes Je and Jh to the surface of e b and h+b in the semiconductor lattice, respectively e s and h+s are the species resulting from...
To illustrate the conditions under which a system that includes chain propagating, chain branching, and chain terminating steps can generate an explosion, one chooses a simplified generalized kinetic model. The assumption is made that for the state condition just prior to explosion, the kinetic steady-state assumption with respect to the radical concentration is satisfactory. The generalized mechanism is written as follows ... [Pg.79]

In agreement with these findings, the simplified kinetic model which has been used to describe the NO adsorption in the presence of CO2 indicates that in the presence of CO2 the data are well described by invoking the occurrence of the nitrate route alone. [Pg.424]

Howell JM, Vieth WR (1982) Biophotolytic membranes simplified kinetic model of photosynthetic electron transport, JMol Catal 16 245-298... [Pg.103]

Mavelli, F. and Luisi, R L. (1996). Autopoietic self-reproducing vesicles a simplified kinetic model. J. Phys. Chem., 100, 16600-7. [Pg.287]

However, simple kinetic models, especially of the Langmuir—Hinshel-wood type, can serve with advantage for correlation of experimental data in spite of simplifying assumptions which are necessary for their derivation. Experience shows that heterogeneous acid—base catalysis is the very field where they fit best. Their most frequent general form... [Pg.272]

We have conducted experiments to improve the selectivity of the reaction for hydrogen peroxide formation, with a special attention to the influence of the reactor will. These experimental results are interpreted by a simplified kinetic model, which is fairly well explained by knowledge of the rate of the free radical reaction. [Pg.327]

Using a chemical kinetic model is one way to describe the chemistry in reacting flow modeling. The chemical kinetic model offers a comprehensive description of the chemistry, but it requires a larger computational effort than simplified chemical models. [Pg.541]


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