Appropriability

The virial equation is appropriate for describing deviations from ideality in those systems where moderate attractive forces yield fugacity coefficients not far removed from unity. The systems shown in Figures 2, 3, and 4 are of this type. However, in systems containing carboxylic acids, there prevails an entirely different physical situation since two acid molecules tend to form a pair of stable hydrogen bonds, large negative... 

The estimated true values must satisfy the appropriate equilibrium constraints. For points 1 through L, there are two constraints given by Equation (2-4) one each for components 1 and 2. For points L+1 through M the same equilibrium relations apply however, now they apply to components 2 and 3. The constraints for the tie-line points, M+1 through N, are given by Equation (2-6), applied to each of the three components. 

The partial molar enthalpy for every component i is found from an appropriate form of the Gibbs-Helmholtz equation... 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

For each experiment, the true values of the measured variables are related by one or more constraints. Because the number of data points exceeds the number of parameters to be estimated, all constraint equations are not exactly satisfied for all experimental measurements. Exact agreement between theory and experiment is not achieved due to random and systematic errors in the data and to "lack of fit" of the model to the data. Optimum parameters and true values corresponding to the experimental measurements must be found by satisfaction of an appropriate statistical criterion. 

King, 1971 Naphtali and Sandholm, 1971 Newman, 1963 and Tomich, 1970). Moreover the choice of appropriate computation procedures for distillation, absorption, and extraction is highly dependent on the system being separated, the conditions of separation, and the specifications to be satisfied (Friday and Smith, 1964 Seppala and Luus, 1972). The thermodynamic methods presented in Chapters 3, 4, and 5, particularly when combined to... 

For bubble-point and dew-point pressure calculations, the appropriate forms are, respectively ... 

The subsequent representations are probably reliable within the range of data used (always less broad than 200° to 600°K), but they are only approximations outside that range. The functions are, however, always monotonic in temperature, to provide appropriate corrections when iterative programs choose temperature excursions outside the range of data. 

PRCG cols 21-30 the maximum allowable change in any of the parameters when LMP = 1, default value is 1000. Limiting the change in the parameters prevents totally unreasonable values from being attained in the first several iterations when poor initial estimates are used. A value of PRCG equal to the magnitude of that anticipated for the parameters is usually appropriate. 

In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

Intermediate separation followed by further reaction is clearly most appropriate when the intermediate separation is straightforward, as in the case of sulfuric acid production. 

Another way to keep the concentration of PRODUCT low is to remove the product as the reaction progresses, e.g., by intermediate separation followed by further reaction. For example, in a reaction system such as Eq. (2.18), intermediate separation of the PRODUCT followed by further reaction maintains a low concentration of PRODUCT as the reaction progresses. Such intermediate separation is most appropriate when separation of the product from the reactants is straightforward. 

However, the laboratory data seem to indicate that a constant concentration in the reactor to maintain 63 percent sulfuric acid would be beneficial. Careful temperature control is also important. These two factors would suggest that a continuous well-mixed reactor is appropriate. There is a conflict. How can a well-defined residence time be maintained and simultaneously a constant concentration of sulfuric acid be maintained ... 

For multiple reactions in which the byproduct is formed in series, the selectivity decreases as conversion increases. In this case, lower conversion than that for single reactions is expected to be appropriate. Again, the best guess at this stage is to set the conversion to 50 percent for irreversible reactions or to 50 percent of the equilibrium conversion for reversible reactions. 

Analogous effects are caused by the inappropriate use of utilities. Utilities are appropriate if they are necessary to satisfy the enthalpy imbalance in that part of the process. Above the pinch in Fig. 6.7a, steam is needed to satisfy the enthalpy imbalance. Figure 6.86 illustrates what happens if inappropriate use of utilities is made and some cooling water is used to cool hot streams above the pinch, say, XP. To satisfy the enthalpy imbalance above the pinch, an import of (Q mjj,+XP) is needed from steam. Overall, (Qcmin+AP) of cooling water is used. ... 

Although the composite curves can be used to set energy targets, they are not a suitable tool for the selection of utilities. The grand composite curve is a more appropriate tool for understanding the interface between the process and the utility system. It is also, as is shown in later chapters, a useful tool for study of the interaction between heat-integrated reactors and separators and the rest of the process. 

Thus the appropriate placement of heat pumps is that they should be placed across the pinch. Note that the principle needs careful interpretation if there are utility pinches. In such circumstances, heat pump replacement above the process pinch or below it can be economic, providing that the heat pump is placed across a utility pinch. Such considerations are outside the scope of the present text. 

A refrigeration system is a heat pump in which heat is absorbed below ambient temperature. Thus the appropriate placement principle for heat pumps applies in exactly the same way as for refrigeration cycles. The appropriate placement for refrigeration cycles is that they also should be across the pinch. As with heat pumps, refrigeration cycles also can be appropriately placed across utility pinches. It is common for refrigeration cycles to be placed across a utility pinch caused by maximizing cooling water duty. 

As with heat pumping, the grand composite curve is used to assess how much heat from the process needs to be extracted into the refrigeration system and where, if appropriate, the process can... 

Linnhoff, B., and de Leur, J., Appropriate Placement of Furnaces in the Integrated Process, IChemE Symp. ries No 109, 1988. 

Rgura 7.2 To target the number of units for pinched problems, the streams above and below the pinch must be counted separately, with the appropriate utilities included. 

If the problem is dominated by equipment with a single specification (i.e., a single material of construction, equipment type, and pressure rating), then the capital cost target can be calculated from Eq. (7.21) with the appropriate cost coefficients. However, if there is a mix of specifications, such as different streams requiring different materials of construction, then the approach must be modified. 

Calculate factors for those streams which require a specification different from that of the reference using Eq. (7.23) or Eq. (7.24). If Eq. (7.23) is to be used, then the actual network area Anetwork must first be calculated using either Eq. (7.6) or Eq. (7.19) and (VuNiTs or - SHELLS, whichever is appropriate. 

Also, if there are two separators, the order of separation can change. The tradeoffs for these two alternative flowsheets will be different. The choice between different separation sequences can be made using the methods described in Chap. 5. However, we should be on guard to the fact that as the reactor conversion changes, the most appropriate sequence also can change. In other words, different separation system structures become appropriate for different reactor conversions. 

We should be on guard for the fact that as the reactor conversion changes, the most appropriate separation sequence also can change. In other words, different separation system structures become appropriate for different reactor conversions. 

Each of these measures can, in the appropriate circumstances, minimize waste (see Fig. 2.10). 

If the composition of the waste stream is known, then the theoretical oxygen demand can be calculated from the appropriate stoichiometric equations. As a first level of approximation, we can assume that this theoretical oxygen demand would be equal to the COD. Then, experience with domestic sewage indicates that the average ratio of COD to BOD will be on the order 1.5 to 2. The following example will help to clarify these relationships. 

There is no obvious benefit from integrating an exothermic reactor below the pinch. The appropriate placement for exothermic reactors is above the pinch. ... 

The preceding appropriate placement arguments assume that the process has the capacity to accept or give up the reactor heat duties at the given reactor temperature. A quantitative tool is needed to assess the capacity of the background process. For this purpose, the grand composite curve can be used and the reactor profile treated as if it was a utility, as explained in Chap. 6. 

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