Steps coupled parallel

Most of the step combinations examined in this chapter are covered in advanced texts on kinetics and reaction engineering [G1-G10], with the exception of coupled parallel steps and reactions with fast pre-dissociation (Sections 5.3 and 5.6, respectively) and the equations for continuous stirred-tank reactors. The material is reviewed here for the user s convenience and for ease of reference. 

The second example is that of a network with coupled parallel steps ... 

Coupled parallel steps are an important combination not covered in any standard texts, and are therefore examined in more detail. Typical examples are isomerization in concert with conversion of the isomers to different products. If isomerization is very fast compared with conversion, the isomers are at quasi-equilibrium and act as "homogeneous source," producing a kinetic behavior like that of a single reactant. If isomerization is very slow compared with conversion, the reactions of the different isomers are essentially uncoupled. If the rates of isomerization and conversion are comparable, a more complex behavior ensues. Most interesting is the case with isomerization being somewhat faster than conversion. The isomer distribution then approaches a steady state (not necessarily close to equilibrium), and from then on the isomers act as homogeneous source. 

H2 and CO reactants not shown arrows represent multistep pathways for mechanistic details, see Example 6.2 in Section 6.3). This basic network structure of coupled parallel steps has been verified as described in Section 5.3, in refutation of the earlier postulate of a common intermediate. 

The aldehydes arise from the olefin isomers by addition of CO to a carbon atom on either side of the double bond in coupled parallel steps (see Example 5.3 in Section 5.3) and are hydrogenated to the respective alcohol isomers. Fortunately, only the straight-chain aldehyde condenses to a significant extent. In comparison, the detailed network consist of 111 steps. 

Where applicable, the shortsightedness principle can significantly simplify quantitative modeling, especially in networks with coupled parallel steps. Examples are olefin reactions that involve double-bond migration in parallel to conversion to products, as in homogeneous catalytic hydrogenation, hydroformylation, hydro-cyanation, and hydrohalogenation [16]. 

The first of the two situation above is occasionally encountered in petroleum processing, where multicomponent mixtures of reactants are common. The second may arise in reactions with coupled parallel steps [14] (see Section 5.3). 

Example 12.1. Hydroformylation of long-chain 1-olefins with phosphine-substituted cobalt hydrocarbonyl catalysts. Hydroformylation of long-chain 1-olefins with phosphine-substituted cobalt hydrocarbonyl catalysts provides a striking example of coupled parallel steps and the potential of an uncommon heat-transfer problem. The network is of the type 12.5 below, with the A, as the olefin isomers and the P, as the isomeric alcohol products (arrows represent multistep pathways see also Example 5.3, Figure 5.9, and network 5.43 in Section 5.3 and network 7.40 in Section 7.4). 

In other fields of kinetics, the principle is particularly useful in two situations for pathways with repetitive, consecutive addition reactions such as multiple ethoxylation or paraffin oxidation (see examples in Section 5.5) and for networks with coupled parallel steps, as in olefin reactions such as hydrogenation, hydroformylation, and hydrocyanation that involve double-bond migration in concert with conversion to products [17]. Consider as a prototype the network 12.13 of n-heptene hydroformylation, keeping in mind that the arrows represent multistep pathways and that the reactions of higher straight-chain olefins involve still more... 

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