Introducing the Case Study

In this section, the phenol-formaldehyde reaction is introduced as a case study. This reaction has been chosen because of its kinetic complexity and its high exothermic-ity, which poses a strong challenge for modeling and control practice. The kinetic model presented here is adopted to simulate a realistic batch chemical process the identification, control, and diagnosis approaches developed in the next chapters are validated by resorting to this model. 

In the alkaline solution, phenol is essentially present as phenate ion, so that the first steps of the reaction may be depicted as electrophilic additions of formaldehyde to the aromatic ring. Those attacks are essentially favored in the -ortho (0) and -para (p) positions, as sketched in Fig. 2.8, because relatively stable low activation energy intermediates can be formed on the contrary, the attacks in the -meta positions are much slower and are not considered here. 

The condensation reactions become important in a later stage when the concentration of the substituted phenols has increased. These reactions can occur in two different modes, as in the two examples sketched in Fig. 2.10 namely, the substituted methylol groups can react either with a nonsubstituted (free) position of a different aromatic ring (a) or with a second methylol group (b). 

In the first case, the reaction produces a methylene-diphenol (MDPh), i.e molecules in which two phenolic rings are linked by a methylene group. In the second case, the reaction produces an aromatic ether, i.e., a molecule in which two aromatic rings are linked by a dimethyl-ether group. However, these compounds are relatively unstable and rapidly decay (producing a formaldehyde molecule) to the corresponding methylene-diphenols (MDPh). Thus, the first reaction step is the rate limiting step, whereas the second one determines the final product and the total stoichiometry of the reaction. 

In these reactions, a large number of two-ring isomers are formed, depending on the position of attack. In a later stage of reaction, these diphenols can undergo both addition reactions of one more methylol group on a free position of the aromatic 

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The paper is organized as follows. Section 2 presents the state of the art and highlights the current limitations of existing approaches for sequences assessment. Section 3 introduces the theoretical framework of the probabilistic languages (Garg et al. 1999) and the used notations. In section 4 is introduced the case study which is used like a support for the rest of the paper. Section 5 develops a theoretical framework based on probabilistic languages for quantitative assessment of events sequences. This proposed approach is illustrated using the case study in the section 6. Finally, section 7 presents the conclusions of this work and identifies some future research directions. 

This section introduces the case study used in this paper and recalls the basics of the BDMP... 

The first part of the chapter introduces the case study. We focus on the design of a parallel processing computer targeted for the rapid execution of neural networks. We have chosen this design for a number of reasons. 

The press had been designed with a capacity to deliver 280 kN press force and to work at a production rate of 40 lids per minute. Calculations to determine the distribution of forming loads required indicated that the press capacity was adequate to form the family of steel lids to be produced on the machine. One of the major areas of interest in the design was the con-rod and pin (see Figure 4.66). The first option considered was based on a previous design where the con-rod was manufactured from cast iron with phosphor bronze bearings at the big and small ends. However, weaknesses in this approach necessitated the consideration of other options. The case study presents the analysis of the pin and con-rod using simple probabilistic techniques in an attempt to provide in-service reliable press operation. The way a weak link was introduced to ensure ease of maintenance and repair in the event... 

The case study described here concerns a human factors audit of a computer controlled process system which was being introduced in a distillation imit of a chemical plant. The unit was in transition from replacing its pneumatic panel instrumentation with the new system. However, control had not yet been transferred and the staff were still using the panel instrumentation. The role of the project was to evaluate a preliminary design of the computer-based display system and provide recommendations for future development. 

Our science building at Brigham Young University is not complete. We are still adding equipment and modifying laboratories to accommodate the latest of experiments. In the same way, these two volumes do not represent a completed study of chemical thermodynamics. This is especially true in Chapters 15 and 16 where we have chosen to use the "case study approach in which we introduce selected examples where we apply thermodynamics to the study of processes of an industrial, geological, and biological nature. It is impossible to cover these broad fields in one book. The examples that we have... 

The case studies on supported rhodium, sulfide, and chromium catalysts nicely illustrate the principles of the ideal strategy for research on catalysts that we introduced in Chapter 1 ... 

Section 13.5 introduces a set of process patterns that are elaborated on throughout the case study. These patterns describe some of the broad contexts for development and a reasonable strategy for each one. Pattern 13.1, Object Development from Scratch, outlines an approach for developing a system from scratch. Pattern 13.2, Reengineering, addresses the case when an existing design is being reworked. Pattern 13.3, Short-Cycle Development, motivates development in short incremental cycles as a useful basis for many projects. 

Much of the notation is useful throughout different stages of the process. For example, we use the same tools to describe the interactions between people and a machine we propose to build, to describe the interactions between objects collaborating inside the machine once designed, and to describe business tasks and processes. For this reason, many of the notational tools are introduced early in the case study and are then reapplied in each phase. 

Finally, it is worth introducing the case of the derivatives containing alkylisocya-nides (Figure 7.23) [21]. These derivatives have been studied by DSC and POM, which... 

In the case study, the adaptive model-based approach is designed on the basis of a reduced model of the phenol-formaldehyde reaction introduced in the Chap. 2. Noticeably, the results show that the model-based control scheme achieves very good performance even when a strongly simplified mathematical model of the reactive system is adopted for the design. 

Our case study is introduced in Section 1.4. The assumptions behind, and the steps involved in, sequential bifurcation are described in Sections 2.2 and 2.3 and the steps are illustrated using a first-order polynomial model with random noise. In Section 2.4, a more realistic model involving interactions is used for screening the important factors in the case study. Issues of programming are addressed in Section 3. 

In order to illustrate the main concepts of PCA, we will introduce two case studies, both from chromatography (although there are many other applications in the problems at the end of the chapter). It is not necessary to understand the detailed chemical motivations behind the chromatographic technique. The first case studies represents information sequentially related in time, and the second information where there is no such relationship but variables are on very different scales. 

In this section, we will show the process of the construction of a mathematical model, step by step, in accordance with the procedure shown in Fig. 3.4. The case studied has already been introduced in Figs. 1.1 and 1.2 of Chapter 1. These figures are concerned with a device for filtration with membranes, where the gradient is given by the transmembrane pressure between the tangential flow of the suspension and the downstream flow. The interest here is to obtain data about the critical situations that impose stopping of the filtration. At the same time, it is important to, a priori, know the unit behaviour when some of the components of the unit, such as, for example, the type of pump or the membrane surface, are changed. 

An inefficiency in the original configuration of the case study is shown where the product of the AGO side stripper is spht into two streams one of is cooled and introduced again in the main column. This sub-cooled returned liquid performs the function of a pump around. This separation and remixing is clearly inefficient because of the higher amount of stripping steam required. 

The remainder of this paper is organized as follows Section 2 relates our model to well known approaches based on multi-period investment models proposed in the literature. In Section 3, our investment planning model is introduced while in Section 4 the investment planning strategy of a generic process is presented as a case-study. Section 5 gives a discussion on the results of the case study. Finally, in Section 6 our findings are summarized. 

In the case study on integrator modeling (see Sect. 6.3, column (c) in Fig. 6.1) we find general specifications, either as a basic layer of the conceptual realization model in the form of graph transformation rules, or in a coded form as a part of the integrator framework. Specific models are introduced to represent link types, link templates, and rules of TGGs. Thereby, different forms of determinations for specific are introduced in one step. 

Models in the case study of Sect. 6.4 (column (d) in Fig. 6.1), on the conceptual realization layer, have an explicit basic specification, which is independent of the application domain. The characteristics of an application domain are specified interactively by the so-called parameterization environment (types of tasks, documents etc.). A graph transformation specification is generated from these interactive specifications, which extends the basic and domain-independent specification. Again, using this parameterization environment, different kinds of determinations for specific could have been introduced. 

The ideas introduced in this section provide a skeletal description of some of the ways in which the geometric deformations in solids are considered. To provide a more concrete realization of these ideas, we now introduce several case studies... 

Our goal in this section is to examine diffusion in Si from several of the perspectives introduced in previous sections. For the purposes of illuminating the connection between transition state theory and microscopic analysis as presented in earlier chapters, we consider the diffusion of a self-interstitial in Si. As with many of the case studies to be presented in this book, the particulars of the implementation described here may well not stand the test of time. On the other hand, these implementations will more than suffice to illustrate how to apply these ideas in the context of a concrete problem. 

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