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Key components are the two components in the feed mixture whose separation is specified. The more volatile of these components is the light key, and the less volatile is the heavy key. In Example 2.4, propane is the light key and «-butane the heavy key. Other components are termed nonkeys. The nonkeys which are more volatile than the keys are termed light nonkeys (methane and ethane in Example 2.4), and those less volatile are heavy nonkeys (pentane and hexane in Example 2.4).

The key components appear to a significant extent in both overhead and bottom products. Light nonkeys end up almost exclusively in the overhead product, and heavy nonkeys end up almost exclusively in the bottom product.

In many separations, components are present whose relative volatilities are intermediate between the light key and the heavy key. These components are termed intermediate keys or distributed keys. Intermediate keys are split between the top and bottom products.

2.3.2 Column composition and temperature profiles

King (7) discusses highlights from Edmister's (22) rigorous solution to Example 2.4. The separation requires 17 theoretical stages (including reboiler and condenser), with feed entering on stage 9 (reboiler being stage 0, condenser stage 16). Figure 2.16 shows the liquid and vapor composition profiles in the column. The following observations are made:

■ There is a significant concentration of all components at the feed stage. The heavy nonkeys, C6 and C6, die out rapidly in both the liquid and vapor above the feed because of their low volatilities. Pentane persists longer than hexane because it is more volatile. A similar behavior is exhibited by the light nonkeys (methane and ethane) below the feed.

■ The heavy nonkeys, C5 and C6, have relatively constant mole fractions in the liquid and vapor below the feed until about three or four stages above the bottom. These heavy nonkeys are merely trans ported from the feed to the bottom. In this region, the nonkeys are diluted with keys, and the main separation taking place is that of the light key from the heavy key. A similar behavior is apparent for the light nonkeys in the rectifying section.

■ About three or four stages above the bottom, the concentration of heavy nonkeys starts to rapidly climb, with C6 rising faster than C6. The climb begins roughly where most of the light key is depleted from the mixture. Below that point, the mixture consists mainly of heavy key and heavy nonkeys. The heavy nonkeys regard the heavy key as a "light," and fractionate it up. In this bottom region, both keys are fractionated up against the nonkeys, resulting in a rapid growth of the concentration of the heavy nonkeys at the expense of the keys (particularly the heavy key, which is the more plentiful of the keys in this region). A similar behavior is apparent for the light nonkeys in the rectifying section.

■ The heavy key mole fraction increases down the column, until about three to four stages from the bottom. This behavior is similar (except near the bottom) to the behavior of a binary system. About three to four stages from the bottom, the column begins fractionating the heavy key from the heavy nonkeys (see above); therefore, the mole fraction of the heavy key diminishes down the column. This is the reason for the maximum in the C4 concentration near the bottom. Again, a similar behavior is apparent for the light key in the rectifying section.

Physically, between the composition peaks of Fig. 2.16, the main terms on the left-hand side of the bubble-point equation, Eq. (1.15), belong to the keys. Since the light key jf-value is greater than unity, it concentrates upward (Sec. 1.2.1), while the heavy key, whose K-value is below unity, concentrates downward. Moving down the tower, a point is reached where the light key concentration is depleted to the extent where it makes little contribution to Eq. (1.15). Mixture temperature rises to generate K-values high enough to satisfy Eq. (1.15). Since the K-values of the heavy nonkeys are low and the lights are gone, Eq. (1.15) can only be satisfied when the K~value of the heavy key rises above unity. Once it does, the heavy key begins concentrating upward like a light. The heavy key concentration will therefore peak when its .K-value passes through unity. Again, an analogous behavior is apparent for the light key in the top section.

Figure 2.17 is a temperature profile for the column. The temperature changes most rapidly at the very top, the very bottom, and near the feed points. These are the regions where nonkey concentrations are changing fastest. At the top, and just below the feed, the light non-keys concentrations in the liquid change rapidly, and the bubble-point

Stage number (a)

Figure 2.16 Composition profiles in multicomponent distillation, Example 2.4. (a) Liquid; (6) vapor. (From C. J. King, Separation Processes, 2d ed., Copyright © by McGraw-Hill, Inc. Reprinted by permission.)

Stage number (a)

Figure 2.16 Composition profiles in multicomponent distillation, Example 2.4. (a) Liquid; (6) vapor. (From C. J. King, Separation Processes, 2d ed., Copyright © by McGraw-Hill, Inc. Reprinted by permission.)

temperatures are highly sensitive to the amount of lights present. At the bottom, and just above the feed, the heavy nonkeys concentrations in the liquid change rapidly, and the bubble-point temperature is sensitive to the amount of heavies present.

2.3.3 Hengstebeck diagrams: principles

Hengstebeck's (15) procedure extends the x-y diagram to multicomponent distillation. A multicomponent separation is treated as a binary separation between the keys. Flows and compositions are based on the two keys alone, that is,

0 R I 2 4 5 6 7 S 9 10 ! I 12 M 14 15 C Stage number (b>

Figure 2.16 (Continued)

0 R I 2 4 5 6 7 S 9 10 ! I 12 M 14 15 C Stage number (b>

Figure 2.16 (Continued)

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