Lumping reaction network

Fig. 9. Reforming lump reaction network. N, cyclopentane and cyclohexane naphthenes P, C6. paraffins A, aromatics C5-, pentane and lighter.

The reaction network is shown in the paper. The kinetic characteristics of the lumps are proprietary. Originally, the model required 30 person-years of effort on paper and in the laboratory, and it is kept up to date. 

The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

There are four species containing Rh in the reaction scheme in Figure 3.2B Xo, Xi, Xi and X2. Since quasi-equilibrium between Xj and Xj is assumed, these two can be lumped into one pseudo-component X, thereby reducing the total number of intermediates containing Rh from 4 to 3. This results in a simplified reaction network as shown in Figure 3.2C. However, the mathematical expressions for [XJ, Kqs, and s2need to be established the detailed derivation is described below. 

If the number of components is very large, a mixture can be regarded as continuous and sharp distinctions between individual components are not made. Methods for dealing with stoichiometry, thermodynamics and kinetics for continuous mixtures are discussed by Aris and Gavalas [33]. An indication is given that rules for grouping in such mixtures depend on the nature of the reaction scheme. Wei and Kuo [34] considered ways in which species in a multicomponent reaction mixture could be lumped when the reaction network was composed of first-... 

A number of mechanistic modeling studies to explain the fluid catalytic cracking process and to predict the yields of valuable products of the FCC unit have been performed in the past. Weekman and Nace (1970) presented a reaction network model based on the assumption that the catalytic cracking kinetics are second order with respect to the feed concentration and on a three-lump scheme. The first lump corresponds to the entire charge stock above the gasoline boiling range, the second... 

The hydrocarbon lumps and reaction network for both the start-of-cycle and the deactivation kinetics were defined. 

Start-of-cycle kinetic lumps in KINPTR are summarized in Table V. A C5-light gas lump is required for mass balance. Thirteen hydrocarbon lumps are defined. The reforming kinetic behavior can be modeled without splitting the lumps into their individual isomers (e.g., isohexane and n-hexane). Also, the component distribution within the C5- lump can be described by simple correlations, as discussed later. The start-of-cycle reaction network that defines the interconversions between the 13 kinetic lumps is shown in Fig. 9. This reaction network results from kinetic studies on pure components and narrow boiling fractions of naphthas. It includes the basic reforming reactions... 

In general, the lumping scheme and reaction network of our model are considerably less complicated than that of Kmak (9). 

Many working groups have modeled the performance of diesel particulate traps during the past few decades. Concentrated parameter models (CSTR assumption) have been applied for the evaluation of formal kinetic models and model parameters. The formal kinetic parameters lump the heat and mass transfer effects with the reaction kinetics of the complicated reaction network of diesel soot combustion. Those models and model parameters were used for the characterization of the performance of different filter geometries and filter materials, as well as of the performance of a variety of catalytically active coatings and fuel additives [58],... 

Approximate reaction networks have become customary for modeling reactions in which the species are too numerous for a full accounting or chemical analysis. Lumped components or continuous distributions commonly take the place of single components in process models for refinery streams (Wei and Kuo 1969 Weekman 1969 Krambeck 1984 Astarita 1989 Chou and Ho 1989 Froment and Bischoff 1990). Polymerization processes are described in terms of moments of the distributions of molecular weight or other properties (Zeman and Amundson 1965 Ray 1972, 1983 Ray and Laurence 1977). Lumped components, or even hypothetical ones, are also prevalent in models of catalyst deactivation (Szepe and Levenspiel 1968 Butt 1984 Pacheco and Petersen 1984 Schipper et al. 1984 Froment and Bischoff 1990). 

Lumping and Mechanism Reduction It is often useful to reduce complex reaction networks to a smaller reaction set which still maintains the key features of the detailed reaction network but with a much smaller number of representative species, reactions, and kinetic parameters. Simple examples were already given above for reducing simple networks into global reactions through assumptions such as pseudo-steady state, rate-limiting step, and equilibrium reactions. 

It should be added here that these huge reaction networks have to be generated by computer [Baltanas Froment, 1985]. Booleans relation matrices were used to describe the molecules and carbenium ions. Since a component analysis of a vacuum gas oil is not entirely feasible some lumping is inevitable but the rate coefficients for the reactions between the lumps can be constructed from those of the single events entering in the reactions of the components of the lump [Vynckier Froment, 1991]. 

To conclude, we will give the example of a lumped network, built as part of the thesis of (Cochegrue, 2001) and including cyclic and acyclic molecules up to Cl 1, to represent a complex reaction network of catalytic reforming, Fig. 27. 

For the hydrocracking process, we must therefore find a way of directly calculating the lumping coefficients between chemical families (see Section V ), without having to generate the reaction network (no storage of molecules and reactions), Fig. 32. 

The equation of lumping coefficients is the product of a sum of inverse symmetry numbers and an entire series of thermodynamic terms (see Section V.E). This complex sum is generally calculated by adding its component terms after generating a reaction network. If we examine the problem which led to this complex sum from a different angle, we can determine another equation which is as rigorous but formally simpler. 

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