Lumped mechanism

Lumped mechanisms are based on the grouping of chemical compounds into classes of similar stmcture and reactivity. For example, all alkanes might be lumped into a single class, the reaction rates and products of which are based on a weighted average of the properties of all the alkanes present. For example, as shown in Table 1, the various alkanes, CH2 2 > react with OH in a similar manner to form alkyl radicals,. When expressed... 

The carbon bond mechanism (64—66), a variation of a lumped mechanism, spHts each organic molecule into functional groups using the assumption that the reactivity of the molecule is dominated by the chemistry of each functional group. 

A good understanding of the detailed chemistry of oxidant formation makes it possible to construct more compact chemical models. These generalized or lumped mechanism models reduce the number of individual chemical reactions by combining similar or sequential reactions and ig-... 

The most difficult term to close in Eq. (5.11) is the reaction rate term. Reaction rates are seldom formulated by considering all the elementary reactions. More often than not, the reactive system is represented by a lumped mechanism, considering only a few species. The case of m components participating in n independent chemical reactions is usually represented by two two-dimensional matrices (m x n) of stoichiometric coefficients and order of reactions and two one-dimensional vectors (n) of frequency factors and activation energy, n chemical reactions are written ... 

For sticky solids with a tendency to cake or form lumps, mechanically stirred or vibrated fluid beds can be used for low- or medium-scale applications. 

As well as the propagation reactions mentioned in Table 4, the following reactions must be taken into account in order to obtain a lumped mechanism which is complete ... 

The lumped mechanism deduced from the detailed mechanism (1-6) can be written as follows ... 

The rates of production of the products of propagation must be the same for the lumped mechanism and for the detailed mechanism ... 

SPYRO is a computer program for calculating a steamcracking reactor with hydrocarbon loads ranging from ethane to the naphthas. The computer program contains a detailed reaction mechanism for the pyrolysis of molecules containing from 1 to 4 carbon atoms and lumped mechanisms for larger species. The approach developed by the authors has been validated industrially. 

Lumped mechanical models have been used to analyze impact dynamics. Generally, muscle is represented by a combination of a spring and a dashpot, whereas a ligament is modeled by a spring. Human body vibrations can be analyzed by similar models (Fritton et al., 1997). 

An early application of this idea was used by Dunker (1986), who applied it to the modelling of tropospheric ozone formation. He started from a lumped mechanism containing 47 species and identified 10 parameterising variables (species concentrations or functions of species concentrations). All in aU, 20,736 grid points... 

The generation of reduced and lumped mechanisms described in the preceding sections relies on chemical intuition and understanding e.g., in the selection of surrogate species. It is also possible to use more objective methods, based, for example, on sensitivity analysis. The methods available have been discussed by Tomlin et al. (1997). 

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