General Aspects of the Modelling Approach

The application of a combined modelling and simulation approach leads to the following advantages  

A basic use of a process model is to analyse experimental data and to use this to characterise the process, by assigning numerical values to the important process variables. The model can then also be solved with appropriate numerical data values and the model predictions compared with actual practical results. This procedure is known as simulation and may be used to confirm that the model and the appropriate parameter values are correct . Simulations, however, can also be used in a predictive manner to test probable behaviour under varying conditions, leading to process optimisation and advanced control strategies. 

Models may be used predictively for design and control. Once the model has been established, it should be capable of predicting performance under differing process conditions, that may be difficult to achieve experimentally. Models can also be used for the design of relatively sophisticated control 

Models may be used in training and education. Many important aspects of reactor operation can be simulated by the use of simple models. These include process start-up and shut down, feeding strategies, measurement dynamics, heat effects and control. Such effects are easily demonstrated by computer, as shown in the accompanying simulation examples, but are often difficult and expensive to demonstrate in practice. 

Models may be used for process optimisation. Optimisation usually involves the influence of two or more variables, with one often directly related to profits and the other related to costs. 

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The second approach is addressed to elaborate methods able to derive from accurate calculations the points of interest for the interpretation The strategy, in general, consists in the adoption of a simpler model (the mathematical aspects of the model are again concerned) and the task consists in reducing the information coming from the full in-depth calculation (not the the numerical values of observables and other statutory quantities alone) to the level of the simpler model. For example accurate calculations may be reduced at the level of a simple VB theory (Robb, Hiberty) or of a simple MO perturbation scheme (Bernardi) making more transparent the interpretation. 

We now briefly apply a continuous mixture-model approach to demonstrate the general aspect of the contribution of structural changes in the solvent. For simplicity, we refer to the energy change associated with the H(f>0 process. Following Sec. 3.5, we write... 

The purpose of this section is threefold. First, it presents a prototype of an interstitial model having features in common with the models proposed for water, notably, the Samoilov (1957) and Pauling (1960) models. These have been worked out in considerable detail by Frank and Quist (1961) and Mikhailov (1967). Second, this model demonstrates some general aspects of the mixture-model approach to the theory of water, for which explicit expressions for thermodynamic quantities in terms of molecular properties may be obtained. Finally, the detailed study of this model has a didactic virtue, being an example of a simple and solvable model. 

In Chapter 5, we elaborated on the general aspects of the mixture-model (MM) approach to the theory of liquids. In this section, we present various ad hoc models for water as approximate versions of the general MM approach. We illustrate the point by a few examples. 

In this section, we formulate the general aspect of the application of the simplest mixture-model (MM) approach to water. We shall use an exact two-structure model (TSM), as introduced in Section 6.8. In the next section, we illustrate the application of a prototype of an interstitial model for water to solutions and, in Section 6.7, we discuss the application of a more general MM approach to this problem. 

We employ the general scheme presented above as a starting point in our discussion of various approaches for handling the R-T effect in triatomic molecules. We And it reasonable to classify these approaches into three categories according to the level of sophistication at which various aspects of the problem are handled. We call them (1) minimal models (2) pragmatic models (3) benchmark treatments. The criterions for such a classification are given in Table I. 

Chapter 4 describes in general terms the processing methods which can be used for plastics and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

We have reviewed above the GH approach to reaction rate constants in solution, together with simple models that give a deeper perspective on the reaction dynamics and various aspects of the generalized frictional influence on the rates. The fact that the theory has always been found to agree with Molecular Dynamics computer simulation results for realistic models of many and varied reaction types gives confidence that it may be used to analyze real experimental results. 

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