Lumped schemes

Many fine chemistry proces.ses can be lumped into a system of two parallel or two con.secutive reactions. Selectivity can roughly be assessed using the gross kinetics for such lumped schemes, and this can be used to derive approximate criteria for reactor selection. 

The mechanisms for the NMHCs (except DMS) required to fully characterise OH chemistry were extracted from a recently updated version of the Master Chemical Mechanism (MCM 3.0, available at http //mcm.leeds.ac.uk/MCM/). The MCM treats the degradation of 125 volatile organic compounds (VOCs) and considers oxidation by OH, NO3, and O3, as well as the chemistry of the subsequent oxidation products. These steps continue until CO2 and H2O are formed as final products of the oxidation. The MCM has been constructed using chemical kinetics data (rate coefficients, branching ratios, reaction products, absorption cross sections and quantum yields) taken from several recent evaluations and reviews or estimated according to the MCM protocol (Jenkin et al., 1997, 2003 Saunders et al., 2003). The MCM is an explicit mechanism and, as such, does not suffer from the limitations of a lumped scheme or one containing surrogate species to represent the chemistry of many species. 

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 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. 

In this chapter the following topics will be reviewed KINPTR s start-of-cycle and deactivation kinetics, the overall program structure of KINPTR, the rationale for the kinetic lumping schemes, the model s accuracy, and examples of KINPTR use within Mobil. As an example, the detailed kinetics for the C6 hydrocarbons are provided. 

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

Li, G., and Rabitz, H., Determination of constrained lumping schemes for non-isothermal first order reaction systems. Chem. Eng. Sci. 46,583 (1991a). 

Fig. 4.15. A comparison of the zeroth- and first-order lumped schemes for an initial mixture H2 02 = 2 1, pressure = 20 Torr, = 800, 1000 K (a) Temperature profiles (b) Concentration of H2 and (c) Concentration of H.

The approach discussed by Verhaar et al. (1997) suggests that development of PBPK/PD models to use in assessing health risks from TPH will require similar focusing on relevant lumping schemes, exposure pathways and durations, and toxicological effects and mechanisms of action. Thus, it is likely that a PBPK/PD model developed to aid in the assessment of potential cancer risk from chronic exposure to TPH may substantially differ from a PBPK/PD model for assessing risk for potential neurological effects from acute exposure to TPH. 

It is possible that the actual chemistry of the reaction may be significantly more complex than what is shown in Equation 6.1, involving many species and steps. However, through appropriate lumping schemes, the kinetics may be simplified to individual gas- and liquid-phase reactants and products, with all steps eventually describable in a form presented in Equation 6.1. Thus, without any loss of generality. Equation 6.1 is completely descriptive of any general gas-liquid reaction scheme in a three-phase slurry reactor. 

Selection of an appropriate lumping scheme was one of the most important issues in this modelling exercise. Ten lump kinetic scheme developed by Jacob et al. (1976) and five lump kinetic model proposed by Ancheyta et al. (1999) were examined closely. The virtue of more detailed lumping scheme over other less detailed models is that rate constants is that rate constants are independent of feed composition. But utilisation of these models are limited by two problems i.e. detailed characterisation of streams is not available on a regular basis and elaborate kinetic information is scarcely available. Thus, a balance between kinetic description required and cost of laboratory analysis often decides selection of lumping strategy. 

Klein s group developed a mechanism-based lumping scheme for hydrocarbon pyrolysis involving free radicals. The model has two submodels. One is a five-component training set mixture (5CM) that calculates radical concentrations in terms of 42 representative free radical intermediates. The other is a module in which a feed mixture of many components reacts with the 5CM kemal to provide detailed rates and selectivities. The model retains the essence of pyrolysis chemistry with reasonable CPU demand. 

A deactivation function is needed to account for the catalyst activity decay due to coke deposition on the catalyst. The various forms of this function were discussed in Chapter 2 where can be a function of catalyst time-on-stream or more appropriately as a function of coke content on the catalyst. The kinetic constant, k, is the overall gas oil cracking rate constant which is the sum of ki and kj from the 3-lump scheme. Substituting this value for rA in equation (3.1) results in ... 

Kinetic Modeling of Catalytic Hydrocracking 3.1. LUMPED SCHEMES... 

Complex Feedstocks. Rate Coefficients for Lumped Schemes. Feedstocks for hydrocrackers are complex mixtures of hydrocarbons with a wide range of molecular weights and carbon numbers extending, e.g., from 15 to 33. A combination of high pressure liquid chromatography, HPLC, and GC-MS permits an individual identification and quantification of all the normal paraffins, but for the iso-paraffms an identification beyond the carbon number is not or only partly possible. Mono-, di-, tri-naphthenes and -aromatics can be separated per C-number. 

The autocatalytic nature of the early steps of the MTG reaction was first recognized by Chen and Reagan [27], who proposed the following simple lumping scheme ... 

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