L 620

Warning: Minimum reflux ratios calculated by this method are somewhat lower than true values. This is because the method neglects the presence of light nonkeys just below the feed and heavy nonkeys just above it (see Sec. 2.3.6).

2.3.6 Key ratio piots and retrograde distillation

Key ratio is the mole fraction ratio of the light key to the heavy key.

Key ratio plots (Figs. 2.19, 2.20) plot key ratio in the liquid ULK/i:HK) against stage number on a semilog scale. The slope of each curve gives a measure of the relative fractionation accomplished per stage in various locations along the fractionator. Fenske's equation (Sec. 3.2.1) implies that at total reflux and constant relative volatility, the logarithm of the key ratio is a linear function of the stage number. This is approached in the key ratio plot for the high reflux ratio (Fig. 2.19a). At lower reflux, this proportionality usually applies near the two ends of the column (24), but the curve flattens as the pinch zone near the feed is approached (Fig. 2.196-d).  Figure 2.19 Key ratio plots, depropanizer example. Feed and products compositions identical to Example 2.4. (a) 15 theoretical stages, RiRmi„ = 2.66; (6) 20 theoretical stages, RIR^ = 1.40; (c) 25 theoretical stages, RIR^ = 1.19; 'rfl 33 theoretical stages, R/Rmin = 1.094.

As reflux ratio is reduced, the key ratio profile develops an inflection point. As minimum reflux is approached, the profile develops a maximum below the feed point and a minimum above the feed point. Between the maximum and the minimum, there is a region in which the key ratio actually decreases as one moves up the column. This be- Theoretical stage number (c)

Figure 2.19 (Continued)

Theoretical stage number (c)

Figure 2.19 (Continued)

havior is unique to multicomponent distillation near minimum reflux or when the keys make up a small part of the feed, and is termed retrograde distillation or reverse distillation. Figure 2.20 shows a similar behavior when the feed points are nonoptimum.

This behavior results from the presence of light nonkeys below the feed and heavy nonkeys above it. The pinch zones in multicomponent to