Lumping primary reactions

Table 4 Lumped primary mechanism for the oxidation of an alkane propagation reactions. Units mol, cm, s, kJ.

Table 5 gives the propagation reactions (not including metatheses) of the lumped primary mechanism of the oxidation of n-pentane. It must be noted that this scheme only includes 4 free radicals instead of 24 for the detailed mechanism 3 pentyl radicals, 3 peroxy radicals, 9 hydroperoxypentyl radicals and 9 hydroperoxypentyl-peroxy radicals the dihydroperoxypentyl radicals have not been considered. 

To describe the kinetics of the OCM reaction quantitatively, rate equations for the primary reaction steps i.e., the formation of CO and of ethane plus ethylene were determined (these two hydrocarbons were lumped since ethylene is formed from ethane only). To derive rate equations a micro-catalytic-fixed-bed reactor was operated differentially in such a way that only small conversions of the key reactants were obtained, allowing to determine reaction rates which could then be correlated with the prevailing reaction conditions (for further details see [24]). 

General interventions, such as increasing the fluids in the diet, allowing for adequate rest, and keeping the atmosphere quiet and nonstimulating, may be beneficial. The primary health care provider may prescribe acetaminophen, every 4 hours, to control these reactions. Local irritation at the injection site may be treated with warm or cool compresses, depending on the patient s preference. A lump may be palpated at the injection site after a diphtheria, pertussis, tetanus (DPT) injection or other immunization. This is not abnormal and will resolve itself within several days to several months. 

E. Ranzi, T. Faravelli, P. Gaffuri and A. Sogaro, Low Temperature Combustion Automatic Generation of Primary Oxidation Reactions and Lumping Procedures, Comb, and Flame 102 (1995) 179-192. 

Appendix 1. MAMA Program Automatic Generation of Primary Lumped Reactions 152... 

In principle, heavy radicals could undergo also H-abstraction, addition on unsaturated bonds and recombination reactions. It is quite easy to demonstrate how little relevance these reactions have compared with the isomerization and decomposition ones. This helps drastically reduce the total number of radicals and reactions to be considered. All of the intermediate alkyl radicals, higher than C4, are supposed to be instantaneously transformed into their final products. With reference to the primary products of Table III, the heavy radicals from pentyl up to octyl undergo direct isomerization and decomposition reactions to form smaller radicals and alkenes. Therefore, large sections of the kinetic scheme can be reduced to a few equivalent or lumped reactions whilst still maintaining a high level of accuracy. The complete kinetic scheme shown in Fig. 2 can be then simply reduced to this single, equivalent or lumped reaction ... 

The clear advantage of this lumping approach is that the analysis of new components only requires the definition of the primary pyrolysis reactions. For large alkanes, only the initiation and H-abstraction reactions need to be defined. 

Figure 5 demonstrates the sensitivity of the primary products of this lumped H-abstraction reaction by varying the probability of methyl substitution, i.e. by varying the relative amount of the different classes of isomers (mono-, di-, tri-, tetra-methyl and so on). While ethylene and 1-butene selectivities decrease with the increase in degree of methyl substitution, methyl radical, 2-butene and isobutene formation is enhanced. 

Due to the regular branched structure of this isomer, linear 1-alkenes heavier than 1-heptene are not present and the relative amount of propyl and butyl radicals is significantly different too. In other words, the lumped H-abstraction reaction of a single model component loses the variety of primary products obtained from the previous lumped A0C15. It seems relevant to observe that to improve ethylene selectivity prediction, alkene components heavier than hexenes can be conveniently described with two different species, respectively corresponding to the true component 1-C H2 and to a lumped mixture of the remaining normal and branched isomers. 

Figure A2 shows the number of components involved in the primary propagation reactions of normal alkenes. These data clearly indicate that this number rapidly becomes very large, increasing the carbon number of the initial alkene. This fact justifies the need to turn to the component lumping when dealing with detailed and mechanistic models describing the hydrocarbons pyrolysis of such heavy species.

If just a single radical is considered (see Fig. A3), propagation reactions produce a smaller and/or stabilized radical and an olefin and/or UC. Each new radical is then processed according to its primary propagation reactions (isomerization and decomposition) which results in the production of new olefin or UC and a smaller radical. The olefins produced define the whole set of components involved in this chain so that the lumping technique conveniently applies only to them. 

These authors31 also reported that the desulphonylation reaction of the mixture of 19 and 32 was endothermic by 3.6kcalmol-1 and resulted in a mixture of primary and secondary chlorododecanes (33 and 34) they could also form by direct chlorination of the hydrocarbon. The heat of formation of 1-chlorododecane (33) is well established as —93.8 + 0.6 kcal mol l. Let us assume that the difference between heats of formation of isomeric primary and secondary chlorides is a constant, and so <5A/Jf(lq, 33, 34) = <5AHf(lq, n-PrCl, i-PrCl) = 2.7 + 0.5 kcal mol-1. [Interestingly, there are no reliable data for any isomeric pair of alkyl chlorides save these propyl chlorides—for 1- and 2-chlorobutane 35a and 35b, <5AHf(lq, 35a, 35b) = 1.1 + 2.0 kcal mol - The heats of formation of any of the various liquid secondary chlorododecanes lumped together here as 34 are all ca... 

This mechanism contains the main generic reactions that can be found also in the detailed primary mechanisms for the oxidation of the alkanes at low temperatures (T < 750 K) in Chapter IX. It is also very similar to the reduced mechanisms obtained by the "lumping" of the detailed mechanisms. Its analysis therefore gives information about the structure of oxidation mechanisms, but also demonstrates the limits of this approach. 

The lumping of the propagation reactions of the detailed primary mechanism described in Figure 4 can be carried out by considering effectively only four lumped free radicals, parents of the initial alkane molecule RH, i.e. ... 

RANZI E., FARAVELLI T., GAFFURI P., SOGARO A., Low-temperature combustion automatic generation of primary oxidation reactions and lumping procedures. Combustion and Flame, 102. 179 (1995) ... 

This computer program generates detailed primary mechanisms of oxidation and combustion reactions of alkanes and lumped secondary mechanisms of the primary products formed. It is interfaced with the KERGAS reaction database and the THERGAS, KINBEN and KINCOR computer programs. It produces reaction models (mechanisms, thermodynamic and kinetic data) which can be used directly in the CHEMKIN computer programs. 

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