Chemical lumping

The approach used in chemical lumping is based on the fact that for complex hydrocarbons with several isomers, the main propagation reactions can be split into relatively few reaction classes (see discussion in Sect. 3.1). For example, for n-heptane, the classes of propagation routes are defined in Ranzi et al. (1995) as  

For example, within the -heptane scheme described in Battin-Leclerc et al. (2000) and Foumet et al. (2000), there are 4 alkyl radicals noted by R i, R 2 R 3 R 4 giving rise to 4 reactions involving the addition of O2  

The rate coefficient is calculated using the weighted mean of the elementary rate coefficients for the individual isomers  

Other examples of reduced hydrocarbon mechanisms developed via chemical lumping include a primary oxidation mechanism for iso-octane containing only five intermediate lumped radicals (Ranzi et al. 1997), lumped schemes for higher 

In non-lumped form, the reaction system is described by the following set of rate equations  

We now discuss an example from Frenklach s review to illustrate how chemical lumping is applied. The mechanism Frenklach describes is the production of polycyclic aromatic hydrocarbons (PAH) in flame environments. Here, the PAH growth proceeds by a replication process, and so the lumping can be guided by the similarity in structure of the hydrocarbon 

This is a one-dimensional lumped system which describes the evolution of the total PAH concentration Mp. However, it does not describe the detailed dynamic behaviour of the system of equations, and to do this we need to move to a higher-dimensional lumped system. 

If we multiply each of equations (4.41) by an integer roughly corresponding to the molecular mass, i.e., the first equation by mp, where mp is the number of carbon atoms present in A,, the second equation by mp and the third equation by (nip + 2) etc., and again sum the equations, we get 

We can see now that there are lumped concentrations of the reaction system and can define a new set of variables c where 

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The quantitative estimation of species by SEC-GC-MS technique requires a mathematical solution. Two types of approaches for the quantitative estimation can be envisioned. One for the estimation of one or more selected species of interest. The second approach is based on grouping of various species in coal liquids into a few chemical lumps and estimating the quantity of these lumps by using the data derived from the analysis is technique. 

Phenols are a major chemical lump present in coal liquids. Phenols have basically one or more aromatic ring structures with alkyl substituents. Methyl, ethyl and propyl are the most common alkyl substituents. The smallest specie is the one with a hydroxyl group attached to a benzene ring. Addition of a methyl group produces three isomers - o-, m-, and p-cresols. It appears that all three are present in more or less same proportion. The number of possible isomers increases as the possible number and size of alkyl substituents increases. It is expected that higher... 

The chemical lumping pattern shown in Figure 4 is very similar to the plotting of distillation temperatures vs. composition, a technique commonly used in petroleum refining to simulate the composition of distillate as a function of temperature. Since SEC includes nonvolatiles, information on their size distribution is also shown. In each chemical lump the molecular weight decreases as SEC retention volume increases. The individual chemical lump has a SEC separation pattern similar to a distillation temperature vs. molecular weight plot, a technique used in petroleum refining to illustrate the composition of various distillation cuts. 

The species which are unknown and have not been identified as one of the major chemical lump such as alkanes, phenols and aromatics are lumped together as unidentified. However, the species in this lump include saturated and unsaturated cycloalkanes with or without side chains, which resembles the naphthenes, a petroleum refinery product group. A number of well known species in coal liquid are not mentioned in this lumping scheme. Such as heterocyclic compounds with sulfur, nitrogen or oxygen as the heteroatom, and other heteroatora containing species. Some of these compounds appear with aromatics (e.g. thiophenes, quinolines) and with phenols (e.g. aromatic amines), and most of them are lumped with the unidentified species lump. 

Dennison JE, Andersen ME, Clewell HJ, Yang RSH. 2004a. Development of a physiologically based pharmacokinetic model for volatile fractions of gasoline using chemical lumping analyses. Environ Sci Technol 38 5674—5681. 

Dennison JE, Andersen ME, Yang RSH. 2003. Characterization of the pharmacokinetics of gasoline using PBPK modeling with a complex mixture chemical lumping approach. Inhalation Toxicol 15 961-968. 

Frenklach, M., Computer modeling of infinite reaction sequences. A chemical lumping. Chem. Eng. Sci. 40, 1843 (1985). 

The novelty in the work of Ranzi et al. is the automatic simplification of the large detailed reaction mechanism obtained by lumping both the species and the reactions. Isomers with similar kinetic behaviour were considered as single-lumped species (see Section 4.7.3 for a discussion of chemical lumping). Parallel reaction routes were lumped together based on kinetic assumptions. Finally, the model parameters were fitted to the predictions of the complete scheme. 

This example illustrates that chemical lumping is nothing other than a special case of linear lumping, and that this system is a good example of the application of exact linear lumping. In fact, we can express the relationship between the original and lumped species in the same formal way as we described in the previous section ... 

R. Fournet, V. Warth, P.A. Glaude, F. Battin-Leclerc, G.M. Come and G. Scacchi, Chemical Lumping of Detailed Mechanisms Obtained by Computer Aided Design Application to the Modelling of Alkanes Oxidation, 26th Symp. (Int.) Comb., Poster WIP-078 (1996). 

The first approach to be checked industrially for the development of detailed mechanisms and the technique of chemical lumping has been worked out at the Polytechnic Institute in Milan for steamcracking The modelled hydrocarbon loads include ethane, propane, the naphthas and even vacuum-distilled diesel fuel, i.e. complex mixtures of hydrocarbons possessing from two to forty carbon atoms. 

FOURNET R., WARTH V., GLAUDE P.A., BATTIN-LECLERC F., SCACCHI G., COME G.M., Automatic Reduction of Detailed Mechanisms of Combustion of Alkanes by Chemical Lumping, Int. J. Chem. Kin., 32, 36 (2000). 

It is also possible to split the chemical lump i into reactive and refractory compounds to account for the difference in reactivity when the feed includes a broad distribution of chemical species. The resulting expression comprises a set of two competing first-order reactions ... 

The mathematical model was constracted on the basis of a three-phase plug-flow reactor model developed by Korsten and Hoffmaim [63]. The model incorporates mass transport at the gas-liquid and liquid-solid interfaces and uses correlations to estimate mass-transfer coefficients and fluid properties at process conditions. The feedstock and products are represented by six chemical lumps (S, N, Ni, V, asphaltenes (Asph), and 538°C-r VR), defined by the overall elemental and physical analyses. Thus, the model accounts for the corresponding reactions HDS, HDN, HDM (nickel (HDNi) and vanadium (HDV) removals), HD As, and HCR of VR. The gas phase is considered to be constituted of hydrogen, hydrogen sulfide, and the cracking product (CH4). The reaction term in the mass balance equations is described by apparent kinetic expressions. The reactor model equations were built under the following assumptions ... 

The formulation of the model equations is based on the transport of reactants between the gas-liquid-solid phases that takes place in TBRs [51]. Hydrogen, being the main gaseous reactant, is first transferred from the gas phase to the liquid bulk. The reactants in the liquid phase (chemical lumps and dissolved H2) travel to the catalyst particle in order to react Products such as H2S and CH4 are released to the gas phase passing through the liquid phase, whereas hydrocarbon products return to the liquid. 

The chemical lumps are transferred from the liquid bulk to... 

In general, the model predictions are in good agreement with the experimental observations. The model is capable of predicting the evolution of the various chemical lumps along the reactor at various temperatures as well as the gas yields and H2 consumption. 

Figure 13.34 presents one possible reactor configuration and the simulation of reactor temperature, H2/oil ratio, and conversion of the chemical lumps. In order to limit the sharp temperature rise caused by the hydroprocessing reactions, the total catalyst volume was divided into six catalyst beds. Ri required four beds as a result of the large heat release in this section ( 72°C), whereas R2 required only two beds. Bed inlet temperatures and delta-Ts for each reactor were adjusted to be more or less equal in order to match the average temperature... 

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