Lumps lumped chemical species

The model includes fundamental hydrocarbon conversion kinetics developed on fresh catalysts (referred to as start-of-cycle kinetics) and also the fundamental relationships that modify the fresh-catalyst kinetics to account for the complex effects of catalyst aging (deactivation kinetics). The successful development of this model was accomplished by reducing the problem complexity. The key was to properly define lumped chemical species and a minimum number of chemical reaction pathways between these lumps. A thorough understanding of the chemistry, thermodynamics, and catalyst... 

An important part of the model development was first defining a set of lumped chemical species from the 300 identified species and then defining... 

Two different reduced kinetic models have been considered, both involving four lumped chemical species and three and four lumped reactions, respectively. These models describe the time evolution of the following components ... 

In a model for catalytic reforming of gasoline, cited in problem P2.03.26, some 300 chemical species are identified, broken up in one case into 13 lumps characterized by carbon number and hydrocarbon class. The kinetic characteristics of such lumps are proprietary information. 

Although the chemistry of alkylation is very complex, we will use the following reactions to capture the essential features of the process, where 1-butene (A), isooctane (B) 2,2,4 tri-methyl pentane (P) and dodecane (R) are used to lump the chemical species involved in the process ... 

Sample dimension and mass should be small. For most TA techniques, samples in the form of a powder with sample mass less than 10 mg are preferred. Heat transfer between the sample and atmosphere will be faster in such a sample than in a lump thus, thermal equilibrium is more likely to be achieved between sample and atmosphere during analysis. Samples to be analyzed should have the same thermal and mechanical history. Thermal events are affected by such history and different results for the same chemical species are likely to be generated if the samples have different histories. The main reason for this is that thermal measurement is affected by the internal energy of samples, and the internal energy can be changed by thermal and mechanical processes. 

According to Horne et al. (1969), pressures up to several thousand atmospheres seem to have no significant effect on Dj. A confusing variety of data are found in the literature, probably because of a misinterpretation of results or lumping of "net ion flux" and "pure diffusion processes". A critical review of the subject is presented in a paper by Manheim (1970). Table 8-4 provides a list of values found in the literature for the most common dissolved chemical species in sediment. Values for Ds are sometimes not available or are difficult to estimate but can be obtained indirectly by means of electrical conductivity measurements (Klinkenberg, 1951). 

The case to be considered here is that of a continuum mixture of chemical species in which chemical reactions occur. (A lumped-parameter model is given in (2).) The model for each different chemical compound is called a constituent. Were the constituents inert, then the amount of each would be an external constraint. However, since compounds can be produced or destroyed by chemical reactions in the mixtures being considered, the amount of each constituent is a non-conserved property. Then, if a mixture contains N constituents, and if R independent reactions are allowed to take place, N - R of the constituents can be selected as components and the amount of each component is a conserved property, i.e. its value can change only by being transported — it cannot be produced. Thus, every component is a constituent, but not every constituent is a component. However, the component amount, and the constituent amount of the same species are different. The amount of a constituent in a mixture at any instant represents the... 

What goes by cellular metabolism is an immense class of chemical and physical rate processes within and without the cell marked most strikingly by their diversity and specificity. It forms the basis of the response of microorganisms to their environment, the modelling of which must of necessity suffer some oversimplification if it is to be of any value. In this context, kinetic models of microbial growth within the framework of interaction between lumped biochemical species and the environment have had considerable appeal in the past. However, the subtle facilities which derive from the elaborate Internal machinery of the cells pose a challenge that no meager expansion of the kinetic framework will ever meet. 

Coal is a nonhomogeneous material and its liquefaction produces a very large number of products. A completely detailed kinetic analysis involving all chemical species is therefore impossible. All the studies reported in the literature evaluate kinetic models using different types of lumped reacting species. 

Compartmental models are lumped models. The concept of a compartmental model assumes that the system can be divided into a number of homogeneous well-mixed components called compartments. Various characteristics of the system are determined by the movement of material from one compartment to the other. Compartmental models have been u to describe blood flow distribution to various organs, populatirMi dynamics, cellular dynamics, distribution of chemical species (hormones and metabolites) in various organs, temperature distribution, etc. 

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 ... 

In practice, some constraints are usually imposed on the lumped model. For example, certain chemical species (e.g., coke precursors) need to be kept unlumped. In this and similar situations, the lumping matrix needs to reflect the constraint a priori. Li and Rabitz also extended their analysis to include nonisothrmal effect and intraparticle diffusion. ... 

All isomeric trees with the same counts of groups are lumped into the same chemical species leading to vector count distributions with Nza = Nz + Na independent variables. 

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