Approach temperature difference

As the feed-to-steam ratio is increased in the flow sheet of Fig. 11-125 7, a point is reached where all the vapor is needed to preheat the feed and none is available for the evaporator tubes. This limiting case is the multistage flash evaporator, shown in its simplest form in Fig. 11-125 7. Seawater is treated as before and then pumped through a number of feed heaters in series. It is given a final boost in temperature with prime steam in a brine heater before it is flashed down in series to provide the vapor needed by the feed heaters. The amount of steam required depends on the approach-temperature difference in the feed heaters and the flash range per stage. Condensate from the feed heaters is flashed down in the same manner as the brine. 

For cooling tow ers, one specifies the required cold water temperature and heat duty. Usually, the 95% summer hours maximum w et bulb temperature for the area is the starting point. To this, an allowance is added for recirculation by raising the wet bulb temperature (say, 1-3°F). After the design air wet bulb inlet temperature is set, the cold w ater approach temperature difference to this W et bulb temperature is specified (often, 10°F). 

Approach temperature differences between the oudet process fluid temperature and the ambient air temperamre are generally in the range of 10 to 15 K. Normally, water cooled heat exchangers can be designed for closer approaches of 3 to 5 °K. Of course, closer approaches for air cooled heat exchangers can be designed, but generally these are not justified on an economic basis. 

Figure lc reveals that this is not the case. Even if exchanger 1 had infinite area (ie., infinite overdesign factor), for a heat capacity flow rate of 1.359 kW/K the outlet temperature of stream Sh] cannot be decreased below 344 K. With a reasonable approach temperature difference of 10 K (Fig. Id), the minimum attainable outlet temperature for stream Shl is 375.4 K, corresponding to a target temperature violation of 52 K. If Sh] were the feed stream to a reactor, this design error could have serious consequences. 

It is difficult to make an exhaustive list of the applications of quantitative imaging, because a large number of parameters are quantifiable proton density, relaxation time T, T2, T2 or T 2, T p), data qualifying interaction of pools by magnetization transfer, apparent diffusion coefficients, indices characterizing diffusion phenomena from tensor estimation or a (/-space approach, temperature difference, static magnetic field, B1 field amplitude, current density or values related to dynamic MRI contrast agent uptake. 

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. 

Table 4.4 Summary of Heat-Exchanger Approach Temperature Differences and Pressure Drops... 

Heat-Exchanger Heat- Transfer Fluid Approach Temperature Difference, °C Pressure Drop , bar ... 

Calculate the exit temperature, t2, from Equation 4.5.8 for the approach temperature difference. 

For a cooler, select from Table 4.4 an approach temperature difference of 5.0 °C, which is an economic rule-of-thumb. This approach is selected rather than the upper limit of 50.0 C to conserve heat, but the surface area will be larger for the 5.0 C approach. From Equation 4.5.8, the exit raw-water temperature, tz, equals 29 °C, Because the raw water has a tendency to scale, it is located on the tube side. At a water temperature of about 50 °C and above, scale formation increases so that the exit water temperature should never exceed 50 °C (122 F). From Equation 4.5.5, the logarithmic-mean temperature difference is... 

To calculate the logarithmic-mean temperature difference, the terminal temperatures of the condenser must be fixed. Because the condensation is essentially isobaric, the inlet and outlet temperatures of the ammonia stream are 41.4°C (106.5 °F). From Table 4.1, the inlet cooling-water temperature is 30°C (86.0 °F) if cooling-tower water is used. Also, for thermodynamic considerations the exit water temperature must be less than 41.4°C, and it is calculated from Equation 4.7.6. If the lower value of the approach temperature difference of 5 °C (9.0 °F) is selected from Table 4.4, a low cooling-water flow rate will be needed. Thus, exit water temperature is 36.4°C. Therefore, from Equation 4.7.5, the logarithmic-mean temperature difference,... 

Understand the importance of the specified minimum approach temperature difference on the design of a heat exchanger network (HEN). 

Q, to the cold stream that has a heat-capacity flow rate of Q, entering at F<, and exiting at F. On the cold end of the heat exchanger, where the temperatures of the hot and cold streams are the lowest, the approach temperature difference is AFj. On the hot end, where the temperatures are the highest, the approach temperature difference is AF2. Carrying out energy balances for the hot and cold streams ... 

In many cases, the selected AJ in is such that no pinch exist, and MER design calls for either hot or cold utility to be used, but not both. The critical Ar in below which no pinch exists is referred to as the threshold approach temperature difference, ATt res. The following two examples illustrate how this arises and demonstrate how the guidelines presented previously are adapted for HEN design. 

Be able to design a HEN when the minimum approach temperature difference is below Arthres, at which no pinch occurs. 

When minimizing the utilities in heat integration, the approach temperature difference is the key specification. As decreases, the utilities decrease, but the heat exchange area... 

For the condenser. Aspen IPE uses the cooling water utility. However, its default inlet and outlet temperatures were changed from 75 and 95 F to 90 and 120°F. Also, Aspen IPE has three built-in utilities for steam at 100, 165, and 400 psia. Because 100 psia steam condenses at 377.8°F and the bubble point temperature of the bottoms product at 252 psia is 260.8 F, when 100 psia steam is used in the reboiler, AT = 117°F, which often results in undesirable film boiling as discussed in Section 13.1 of the book. To reduce the approach temperature difference, and assure nucleate boiling, a low pressure steam utility, at 50 psia, is defined. 

If the condenser uses the flow rate of a cooling medium (typically cooling water) or if the reboiler uses the flow rate of a heating medium (hot oil), a model, using a log-mean temperature differential driving force (temperature differentials at outlet and inlet ends), can be used. The inlet medium temperature and the minimum approach temperature difference between the process and the medium are specified. Then Aspen calculates the required UA product (overall heat-transfer coefficient U and heat-transfer area A) and the required flow rate of the medium from the known heat-transfer rate. 

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