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If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. [c.104]

There is justification for allowing t to increase beyond 1, and in many particular applications this may be desirable. Here a more conservative approach is used to reduce the chance of unstable iterations. [c.116]

The Newton-Raphson approach, being essentially a point-slope method, converges most rapidly for near linear objective functions. Thus it is helpful to note that tends to vary as 1/P and as exp(l/T). For bubble-point-temperature calculation, we can define an objective function [c.118]

Later in this text an approach is presented in which some early decisions (i.e., decisions regarding reactor and separator options) can be evaluated without a complete design for the outer layers. [c.8]

Building an irreducible structure. The first approach follows the onion logic, starting the design by choosing a reactor and then moving outward by adding a separation and recycle system, and so on. At each layer we must make decisions based on the information available at that stage. The ability to look ahead to the completed design might lead to different decisions. Unfortunately, this is not possible, and instead, decisions must be based on an incomplete picture. [c.8]

This approach to synthesis is one of making a series of best local decisions. Equipment is added only if it can be justified economically on the basis of the information available, albeit an incomplete picture. This keeps the structure irreducible, and features which are technically or economically redundant are not included. [c.8]

There are two drawbacks to this approach [c.9]

The main advantage of this approach is that the designer can keep control of the basic decisions and interact with the design as it develops. By sta dng in control of the basic decisions, the intangibles of the design can be included in the decision making. [c.9]

Creating and optimizing a reducible structure. In this approach, a structure known as a superstructure or hyperstructure is first created that has embedded within it all feasible process operations and all feasible interconnections that are candidates for an optimal design. Initially, redundant features are built into the structure. As an example, consider Fig. 1.7. This shows one possible structure of a process for the manufacture of benzene from the reaction between toluene and hydrogen. In Fig. 1.7, the hydrogen enters the process with a small amount of methane as an impurity. Thus in Fig. 1.7 the option is embedded of either purifying the hydrogen feed with a membrane or passing directly to the process. The hydrogen and toluene are mixed and preheated to reaction temperature. Only a furnace has been considered feasible in this case because of the high temperature required. Then two alternative reactor options, isothermal and adiabatic reactors, are embedded, and so on. Redundant features have been included in an effort to ensure that all features that could be part of an optimal solution haVe been included. [c.9]

There are a number of difficulties associated with this approach [c.11]

On the other hand, this approach has a number of advantages. Many different design options can be considered at the same time. Also, the entire design procedure can be accommodated in a computer program capable of producing designs quickly and efficiently. [c.13]

This text concentrates on developing an understanding of the concepts required at each stage of the chemical process design. Such understanding is a vital part of process design, whichever approach is followed. [c.13]

Grossmann, I. E., Mixed Integer Programming Approach for the Synthesis of Integrated Process Flowsheets, Camp. Chem. Eng., 9 463, 1985. [c.14]

In the third model (Fig. 2.1c), the plug-flow model, a steady uniform movement of the reactants is assumed, with no attempt to induce mixing along the direction of flow. Like the ideal batch reactor, the residence time in a plug-flow reactor is the same for all fluid elements. Plug-flow operation can be approached by using a number of continuous well-mixed reactors in series (Fig. 2.Id). The greater the number of well-mixed reactors in series, the closer is the approach to plug-flow operation. [c.29]

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. [c.54]

Given the choice of a batch rather than continuous process, does this need a different approach to the synthesis of the reaction and separation and recycle system In fact, a different approach is not needed. We start by assuming the process to be continuous and then, if choosing to use batch operation, replace continuous steps by batch steps. It is simpler to start with continuous process operation [c.117]

The approach is illustrated by the following example. [c.118]

However, use of total vapor rate is still only a guide and might not give the correct rank order in some cases. In fact, given some computational aids, it is a practical proposition to size and cost all the alternative sequences using a shortcut sizing calculation, such as the Fenske-Gilliland-Underwood approach, together with cost correlations. Even though practical problems might involve a large number of components, it is rare for them to have more than six products, which means 42 possible sequences from Table 5.1. In addition, process constraints often reduce this number. [c.142]

Given the possibilities for changing the sequence of simple columns with the introduction of prefractionators, side-strippers, side-rectifiers, and fully thermally coupled arrangements, it is apparent that the problem is extremely complex with many structural alternatives. The problem can be tackled using the approach based on optimization of a reducible structure. As discussed in Chap. 1, this approach starts by setting up a grand flowsheet in which all candidates for an optimal solution are embedded. A reducible structure for a four-component mixture is shown in Fig. 5.19a. This structure is then subjected to optimization, and during the optimization, some features of the design are discarded, as shown in Fig. 5.19b. Methods also have been developed which consider sequencing, thermal coupling, and heat integration. [c.155]

Network designs tend not to approach the true minimum in practice because a minimum area design is usually too complex to be practical. Putting the argument the other way around, starting with the complex design required to achieve minimum area, then a significant reduction in complexity usually only requires a small penalty in area. [c.219]

FIgura 7.7 1-1 shells approach pure countercurrent flow, whereas 1-2 shells exhibit partial countercurrent and partial cocurrent flow. [c.222]

The final temperature of the hot stream is higher than the final temperature of the cold stream, as illustrated in Fig. 7.8a. This is called a temperature approach. This situation is straightforward to design for, because it can always be accommodated in a single 1-2 shell. [c.223]

[c.225]

Before suggesting an approach for predicting the minimum number of shells for an entire network, a more convenient method for determining the number of shells in a single unit must first be found. Adopting the design criterion given by Eq. (7.13) as the basis, then any need for trial and error can be eliminated, since an explicit [c.225]

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. [c.229]

Let us now address the question of how accurate the capital cost targets are likely to be. It was discussed earlier how the basic area targeting equation [Eq. (7.6) or Eq. (7.19)] represents a true minimum network area if all heat transfer coefficients are equal but is slightly above the true minimum if there are significant differences in heat transfer coefficients. Providing heat transfer coefficients vary by less than one order of magnitude, Eqs. (7.6) and (7.19) predict an area which is usually within 10 percent of the minimum. However, this does not turn into a 10 percent error in capital cost of the final design, since practical designs are almost invariably slightly above the minimum. There are also two errors inherent in the approach to capital cost targets [c.232]

These small positive and negative errors partially cancel each other. The result is that capital cost targets predicted by the methods described in this chapter are usually within 5 percent of the final design, providing heat transfer coefficients vary by less than one order of magnitude. If heat transfer coefficients vary by more than one order of magnitude, then a more sophisticated approach can sometimes be justified. [c.232]

If the network comprises mixed exchanger specification, then an additional degree of uncertainty is introduced into the capital cost target. Applying the -factor approach to a single exchanger, where both streams require the same specification, there is no error. In practice, there can be different specifications on two streams being matched, and (pc for specifications involving shell-and-tube heat exchangers with different materials of construction and pressure rating. This does not present a problem, since the exchanger can be designed for different materials of construction or pressure rating on the shell side and the tube side of a heat exchanger. If, for example, there is a mix of streams, some requiring carbon steel and some stainless steel, then some of the matches involve a corrosive stream on one side of the exchanger and a noncorrosive stream on the other. The capital cost of such exchangers will lie somewhere between the [c.232]

Ahmad, S., LinnhoflF, B., and Smith, R., Design of Multipass Heat Exchangers An Alternative Approach, Trans. ASME, J. Heat Transfer, 110 304, 1988. [c.237]

Plots of economic potential versus reactor conversion allow the optimal reactor conversion for a given flowsheet to be identified (Fig. 8.2). Although this approach allows the location of the optimum to be found, it does not give any indication of why the optimum occurs where it does. [c.241]

In Sec. 4.4 the possibility of using batch rather than continuous operations in the flowsheet was discussed. At that time, our only interest was the recycle structure of the flowsheet. There the approach was first to synthesize a flowsheet based on continuous [c.248]

All too often safety and health (and environmental) considerations are left to the final stages of the design. Returning to the hierarchy of design illustrated by the onion diagram in Fig. 1.6, such considerations would add another layer in the diagram outside the utilities layer. This approach leaves much to be desired. [c.255]

The first major hazard in process plants is fire, which is usually regarded as having a disaster potential lower than both explosion or toxic release. However, fire is still a major hazard and can, under the worst conditions, approach explosion in its disaster potential. It may, for example, give rise to toxic fumes. Let us start by examining the important factors in assessing fire as a hazard. [c.255]

The problem with representing a reactor profile is that, unlike utility profiles, the reactor profile might involve several streams. The reactor profile involves not only streams such as those for indirect heat transfer shown in Fig. 13.1 but also the reactor feed and effluent streams, which can be an important feature of the reactor heating and cooling characteristics. The various streams associated with the reactor can be combined to form a grand composite curve for the reactor. This can then be matched against the grand composite curve for the rest of the process. The following example illustrates the approach. [c.332]

If the objective function is considered two-dimensional, consisting of Equations (7-13) and (7-14) and the vector X includes only T and a, then the only change in the iteration is that the derivatives of with respect to composition are ignored in establishing the Newton-Raphson corrections to T and a. The new compositions can then be determined from Equations (7-8) and (7-9). Such a simplified procedure sacrifices little in convergence rate for vapor-liquid systems, where the contributions of compfosition-derivatives to changes in T and a are almost always smad 1. This approach requires only two evaluations of per iteration and still avoids creeping since it is essentially second-order in the limit as convergence is approached. [c.117]

The problem with this approach is obvious. It involves a considerable amount of work to generate a measure of the quality of the sequence, the total vapor load, which is only a guideline. There are many other factors to be considered. Indeed, as we shall see later, when variables such as reactor conversion are optimized, the sequence might well need readdressing. [c.136]

Whether this approach works in practice is easily tested. We can take a problem and design all possible nonintegrated sequences and then heat integrate those sequences and compare. Freshwater and Ziogou and Stephanopoulos, Linnhoff, and Sophos have carried out extensive numerical studies on sequences of simple distillation columns both with and without heat integration. One interesting result from the study of Freshwater and Ziogou was that the configuration that achieved the greatest energy saving by integration often already had the lowest energy requirement prior to integration. When this was not so, the difference in energy consumption between the integrated configuration with the lowest energy import and the one based on the nonintegrated configuration that required the least energy was usually minimal. [c.142]

[c.161]

This basic approach can be developed into a formal algorithm known as the problem table algorithm. To jllustrate the algorithm, it can be developed using the data from Fig. 6.2 given in Table 6.2 for AT ,i = 10°C. [c.175]

Most constraints can be evaluated by scoping the problem with different boundaries, as illustrated in Example 6.2. If this approach cannot be applied, then mathematical programming must be used to obtain the energy target. [c.184]

Papoulias, S. A., and Grossmann, I. E., A Structural Optimization Approach in Process Synthesis II. Heat Recovery Networks, Computers Chem. Eng., 7 707, 1983. [c.211]

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. [c.223]

Another design option that can be considered if a column will not fit is use of an intermediate reboiler or condenser. An intermediate condenser is illustrated in Fig. 14.5. The shape of the box is now altered because the intermediate condenser changes the heat flow through the column. The particular design shown in Fig. 14.5 would require that at least part of the heat rejected from the intermediate condenser be passed to the process. An analogous approach can be used to evaluate the possibilities for use of intermediate reboilers. Flower and Jackson," Kayihan, and Dhole and Linnhofl have presented procedures for the location of intermediate reboilers and condensers. [c.346]

See pages that mention the term

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**[c.37] [c.98] [c.11] [c.37] [c.166] [c.282]**

13 Chemistry in the Marine Environment (2000) -- [ c.70 ]