x, mole fraction benzene in liquid
Figure 2.10 (Continued)
mitting the required separation to be achieved with the existing feed location. Example 2.2 illustrates this. Increasing reflux and reboil in order to overcome a pinch, however, is achieved at the penalty of greater energy consumption, higher operating costs, and greater vapor and liquid traffic through the column. When the column or its heat exchangers are close to a capacity limit, the greater vapor and liquid traffic may reduce column feed-handling capacity.
In the field, a symptom of pinching is a very small temperature difference across many trays, particularly near the feed. This symptom can also suggest flooding, dry, or otherwise inefficient trays. A distinguishing feature of pinching is that as reboil and reflux ratios are increased, the temperature difference becomes larger and operation returns to normal. Note that "dry trays" is a specific case of pinching. When L = 0, the slope of the component balance line is 0, and it will become horizontal until it meets the equilibrium curve. A field test to check whether a column is pinching is described elsewhere (12).
Example 2.2 A 10-stage column, with feed entering between stage 4 and 5, was used to separate a benzene-toluene mixture similar to that described in Example 2.1. The composition of feedstock has changed, and the new feedstock contains 40% benzene. Relocating the feed nozzle requires column shutdown, which is costly. Is it necessary? (Product composition specifications are as given in Example 2.1.)
solution A McCabe-Thiele diagram is shown in Fig. 2.10a. With 10 stages, the overhead product can be kept on-spec, but the bottoms product will contain 17% benzene, compared to the 10% specification. If this can be tolerated, a shutdown to change column feed nozzle is unnecessary.
If 17% benzene is unacceptable in the bottom product, reflux and reboil can be raised to achieve the required separation in 10 stages. The slope of the rectifying section component balance line is increased, and that of the stripping section component balance line is lowered. This is a trial-and-error calculation, which ends when 10 theoretical stages are accommodated between the component balance line and the equilibrium curve, the top and bottom products are at their desired specifications, and the feed enters between stages 4 and 5. The slopes of the component balance lines will determine the new required reflux and boilup rate. The final result is shown in Fig. 2.10c. From this diagram,
= 0.758 (slope of rectifying section component balance line) ^ - 1.54 (slope of stripping section component balance line)
To calculate the actual vapor and liquid rates, proceed as follows:
1. From Eq. (2.11), and since D = 71 lb-mole/h (Example 2.1) and L = 0.758V (above)
V = 293 lb-molelh
2. Find L' from Eq. (2.28), and since q = 0.75 and F = 200 Ib-mole/h (Example 2.1)
L' = qF + L - 0.75 x 200 + 222 = 372 lb-mole/h Find V from Eq. (2.12), and since B = 129 lb-mole/h (Example 2.1)
3. Check that L'IV is the same as that determined from the slope of the component balance line.
Comparison of Examples 2.1 and 2.2. Table 2.4 gives a measure of the effect of nonoptimum feed point on the column in this example. Table 2.4 shows that V and V, and therefore reboiler and condenser duties, increase by about 3 to 4 percent in Example 2.2. This roughly corresponds to a 3 to 4 percent increase in energy consumption and operating costs. If the column or its heat exchangers are at a maximum capacity limit, the column feed rate will need to be reduced by 3 to 4 percent. If these consequences can be tolerated, a shutdown to change the column feed nozzle will be unnecessary. Note that in this example, the effect of nonoptimum feed was quite mild. In other cases, it may be far more detrimental.
This variable gives a measure of
Example 2.1, lb-mole/h
Example 2.2, lb-mole/h
Effect of nonoptimum feed in Example 2.2
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