Classification of models

Before discussing in more detail what reaction models (Sect. 2) and reactor models (Sect. 3) are, some general considerations about the classification of models appear convenient. 

Himmelblau [32] and Himmelblau and Bischoff [33] have considered three types of model which are useful in process analysis, i.e. empirical models, population balance models and transport phenomena models. Empirical models involve mathematical relationships between dependent and independent variables, which are postulated either entirely a priori, or by considering the nature of the experimental data, or by analogies, etc. On the other hand, transport phenomena models are based on the laws of 

These authors [32, 33] have considered an alternative classification based on the nature of the variables involved in the model. They classify models by grouping them into opposite pairs deterministic vs. probabilistic, linear vs. non-linear, steady vs. non-steady state, lumped vs. distributed parameters models. In a lumped parameters model, variations of some variable (usually a spatial one) are ignored and its value is assumed to be uniform throughout the entire system. On the other hand, distributed parameters models take into account detailed variations of variables throughout the system. In the kinetic description of a chemical system, lumping concerns chemical constituents and has been widely used (see Sects. 2.4 and 2.5). 

Himmelblau and Bischoff [33] consider yet another classification more oriented towards the solution of equations and based on their mathematical structure algebraic equations, ordinary differential equations, partial differential equations, etc. 

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Table 2 Classification of Model-Independent Indices According to the Power Used in Summation and the Relating Factor...

Another classification of model is related to the time and space scales of interest. Ambient air quality standards are stated for measurement averaging periods varying from an hour to a year. However, for computational purposes, it is often necessary to use periods of less than an hour for a typical resolution-cell size in a model. Spatial scales of interest vary from a few tenths of a meter (e.g., for the area immediately adjacent to a roadway) up to hundreds of kilometers (e.g., in simulations that will elucidate urban-rural interactions). Large spatial scales are also warranted when multiday simulations are necessary for even a moderate-sized urban area. Under some climatologic conditions, recirculations can cause interaction of today s pollution with tomorrow s. Typical resolution specifications couple spatial scales with temporal sc es. Therefore, the full matrix of time scales and space scales is not needed, because of the dependence of time scales on space scales. Some typical categories by scale are as follows ... 

The reviews by Johnson and by Seinfeld give helpful guidelines in the classification of models by space and time scale. 

Models are either dynamic or steady-state. Steady-state models are most often used to study continuous processes, particularly at the design stage. Dynamic models, which capture time-dependent behavior, are used for batch process design and for control system design. Another classification of models is in terms of lumped parameter or distributed parameter systems. A lumped parameter system... 

The classification of models for convective diffusion to a rotating disk electrode may be imderstood in the context of the solution to the steady-state equation (11.3). 

Models of every type are used in environmental toxicology. There are three broad classifications of models in ecology (Nisbet and Gurney 1982) ... 

Classification of Models for Nonisothermal Nonadiabatic Fixed-Bed Reactors (NINA-FBR) (Doraiswamy, 2001)... 

Another basis for classification of models of population dynamics is provided by the observation that cells may be assumed to be either structured or unstructured. In a segregated model, we assume a cell to be structured if we specify some means of distinguishing it from its fellows. This means may be visual, by comparison of morphology and size under the microscope, or it may be indirect, by comparison of the mass and chemical composition of cells. When we deal with a distributed model, the population will be structured if the composition of the population varies with the conditions of propagation. In other words, specification of the state of the population requires more than specification of a single quantity. 

Table 12.1 Classification of models for nonisothermal nonadiabatic reactors... 

Figure 13.1. Classification of models of multi-echelon distribution systems...

A final important classification of models is into the categories deterministic or probabilistic. Deterministic models calculate a specific result from a given input dataset. Because there are always uncertainties in data due to measurement accuracies or to natural variations, it will normally be necessary to run the deterministic models for a variety of different datasets. Probabilistic models refine and automate this process in that data can be input as ranges or as probability density functions. 

In the classification of models for metal-molecule electrodynamic coupling that we have done in Sec. 5.1, the model that we have described so far (a classical punctiform dipole close to a metal nanoparticle described as a continuous medium) is the simplest. While it has proven to be extremely useful, not only as a mean to grasp the basic physics of molecular plasmonics phenomena, but also to provide semi-quantitative and, sometimes, even quantitative results, it still remains a model empirical in nature. In this section we shall briefly describe models that goes beyond such an approach. 

Table 4 Classification of models into Effective (E) and Transferable (T), depending on the choice of the intra- and inter-molecular functional form and the simulation protocol used...

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