Optimum Approach Temperature

In summary, when designing a HEN, it is important to consider the effect of Ar j . The next example illustrates this effect, while applying the techniques for stream matching described in Section 10.3. 

Example 1014 consider the design of a HEN for four streams in a problem generated initially by Nishida et al. (1977)  

Network Utilities Cost ( /yr) Cp, Purchase Cost ( ) C, Annualized Cost ( /yr) 

In this example, a superstructure is to be created that embeds all of the altemative HENs involving one cold stream, Cl, and three hot streams, HI, H2, and H3, as presented by Roudas (1995). The elements of the HENs include (1) heat exchangers, (2) stream mixers, and (3) stream splitters. 

In this example, a superstructure is created for the potential HENs that involve hot stream, HI, and cold streams. Cl and C2, as specified below  

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The results of thermodynamic analysis may be in line with those of economic analysis when the thermodynamic cost optimum, not the maximum thermodynamic efficiency, is considered with process specifications. Figure 5.3 shows pinch technology in terms of optimum hot and cold utilities by accounting for the investment costs and exergy cost. With an optimum approach temperature ATmin, the total cost may be optimized. 

There are other mles-of-thumb based on economic experience, which the reader will recognize, such as the optimum reflux ratio in distillation and the optimum liquid to gas ratio in gas absorption. You may also specify recoveries of key conq)onents or their concentrations in an exit stream for separators. When we use any of these rules, the assim tion is that the calculated separator size will be of reasonable cost, approximating the optimum-size separator. Similarly, for chemical reactors we may specify conversion of a desirable con jound, its exit composition or an approach temperature difference. For chemical reactors, the approach temperature difference is the difference between the actual temperature and the chemical-equilibrium ten5)erature. Again, we assume that a reactor that approximates the optimum-size reactor will result when using this rule. 

Finally, Table 3.2.1 contains two economic relations or rules-of-thumb. Equation 3.2.20 states that the approach temperature differences for the water, which is the difference between the exit water teir jerature and the wet-bulb temperature of the inlet air, is 5.0 "C (9 °F). The wet-bulb temperature of the surrounding air is the lowest water temperature achievable by evaporation. Usually, the approach temperature difference is between 4.0 and 8.0 C. The smaller the approach temperature difference, the larger the cooling tower, and hence the more it will cost. This increased tower cost must be balanced against the economic benefits of colder water. These are a reduction in the water flow rate for process cooling and in the size of heat exchangers for the plant because of an increase in the log-mean-temperature driving force. The other mle-of-thumb. Equation 3.2.21, states that the optimum mass ratio of the water-to-air flow rates is usually between 0.75 to 1.5 for mechanical-draft towers [14]. 

Frequently, an approximate value of the optimum exit-water ten Derature is all that is required, and a rule-of-thumb will be satisfactory. Table 4.4 hsts the approach tenperature difference, which is the difference between the two terminal temperatures of two passing streams, for several heat exchangers. Several approach temperature differences were taken from Uhich [8], For refrigerants, Ulrich s range of 10 to 50°C is on the high side. Frank [7] recommends a range of 3 to 5°C whereas Walas [3] recommends a value of 5.6 C or less. 

Wen, Y. and Shonnard, D. R (2003). Environmental and economic assessments of heat exchanger networks for optimum minimum approach temperature, Comput. Chem. Eng., 27, pp. 1577-1590. 

For a material species graded approach, several kinds of thermoelectric material of which the optimum operating temperature is different fi-om each other are laid in order. Concerning composition graded and dopant concentration graded... 

The optimum approach to kinetic stereoselection in the Reformatsky reaction would appear to be the use of two-stage procedures, which allows the zinc aldolates to be formed at the lowest possible temperature. Gaudemar-Bardone and Gaudemar prepared a variety of zinc ester enolates in dimethoxymethane at 40 C which were then reacted at lower temperatures with benzaldehyde or with acetophenone (equation 38). Selected data from their study are shown in Table 5. If these data are the result of total kinetic control, as concluded by the authors, it is clear that the reactions exhibit only a modest kinetic stereoselectivity. 

The optimum substrate temperature, at which a maximum diamond growth rate and a highest level of crystal perfection can be achieved for a given system, is generally in the range of 800-1000°C, with a typical low bound approaching 600°C, basically independent of deposition techniques. 

The ramp rate governs the tradeoff between analysis time and resolution. The compromise between resolution and time of analysis is contrasted in Figure 3.64 for parallel capillary column separations of lemon oil generated at three different programming rates. Relying on experience and intuition in establishing optimum column temperature conditions can be time-consuming and inefficient. An alternative route is the use of computer simulation for method development this approach is discussed in much further detail in the next chapter (98-102). 

If the streams in Problem 18 have the following film heat transfer coefficients, estimate the optimum minimum approach temperature for this problem. 

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