First Illustrative Example

In order to illustrate these cases an example taken from the publications of Ierapetritou and Floudas (1998) and Majozi and Zhu (2001) will be used. The flowsheet for the example is given in Fig. 3.5 with the SSN representation shown in Fig. 3.6. The data for the example is shown in Table 3.2, the time horizon of interest for this example has been altered from 12 h presented in Ierapetritou and Floudas (1998) and Majozi and Zhu (2001) to 24 h for illustrative purposes. 

State Storage capacity Initial amount Price 

The way this improvement is achieved is clearly seen in Fig. 3.8. A portion of a batch is stored in a unit while the remaining batch is sent to processing. In this case half of the batch processed in the mixer is taken for storage in the purificator while the remaining mass is processed in the reactor. Once the reaction has proceeded to completion the mass that was stored in the purificator is moved to the reactor for processing. Further latent storage is required at 13.5 and 18 h, in this case the mass is stored in the reactor after processing and then moved to the purificator for 

The model was solved using GAMS and the CPLEX solver version 9.1.2. The computational results for case 1 are shown in are shown in Table 3.3. From these results it is clear to see the potential benefits for using the PIS operational philosophy, with a 50% increase in throughput. 

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The first illustrative example deals with an operation involving three water using units. There are three contaminants present within the system, with each unit producing wastewater containing each of the three contaminants. The relevant concentration data is given for each unit in Table 6.1. Important to note that each unit produces a unique product, and each product requiring no intermediate material from the other units. 

Table 6.1 Concentration data for the first illustrative example...

Fig. 6.3 Gantt chart for the first illustrative example with no storage (Majozi and Gouws, 2009)...

The first illustrative example was solved with the addition of a central storage vessel. The maximum capacity of the storage vessel was 200 t and any of the three units could send or receive water from the central storage vessel. 

The first illustrative example deals with the minimisation of wastewater in an operation that involves three processing units, with each unit producing a distinct product. Wastewater produced from units 1 and 2 each contain single, but different, contaminants. Wastewater from unit 1 contains contaminant Cl and wastewater from unit 2 contains contaminant C2. Unit 3 produces wastewater that contains three contaminants, namely, contaminants Cl, C2 and C3. Unit 1 can only receive water contaminated with contaminant Cl. Similarly, unit 2 can only receive water contaminated with contaminant C2. 

Fig. 8.2 Process diagram for first illustrative example operating in zero effluent mode...

Table 9.1 Data for first illustrative example using inherent storage...

The resulting number of binary variables for both the MILP and MINLP was 360 with 6 time points. The optimal value of the objective function for both the MILP and MINLP was 3620.52 kg of water, which means that the solution obtained is globally optimal (Gouws et al., 2008). This is a lower objective function value than that achieved in the previous case. In this case an improved savings of 15.3% is achieved. The final solution was attained in 896.37 CPU seconds using the same processor as in the first illustrative example. 

The first illustrative example is the dissociation of LiF. It is well known that alkali halides are compounds with strong ionic character and that they dissociate as neutral atoms in vacuo but as a pair of ions in aqueous solution. By means of the model shown in the previous Section, this effect can be observed quantitatively. In the example the LiF has been studied... 

The dissociation of the molecular ions of the isomeric hydroxymethylanilines is used as the first illustrative example (Figure 12). Loss of water from the ionized ortho isomer to form the [M — H20]+ fragment ion of m/z 105 is greatly favored owing to the ortho position of the hydroxyl substituent that allows for intramolecular [1,5-H] shift. This ion subsequently loses either a hydrogen atom or a HNC molecule to yield two equally prominent fragment ions of m/z 104 and 78, respectively. Scheme 18 displays rationalizations for such losses. 

As a first illustrative example, two animals are to be compared. Each time things are compared, some selected properties of the test objects must be examined. Animals may be classified by properties such as species, number of extremities, or number of eyes. Table 2 shows the results of the diversity examination of an elephant and a mouse 100% similarity or 0% diversity are found. Just looking for other typical characteristics such as weight, shape of nose or the ratio (length of tail/size of animal) will give quite different results 0% similarity or 100% diversity for this example. 

Although the chemical sinicture of liquid crystalline polymers is rather complex, one of them is selected as a first illustrative example for dielectric studies because its structure is very well defined. 

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