Figure 227

Column operation at minimum reflux ratio

In some unusual VLE systems, the pinch between the VLE curve and an operating line can occur at some point other than the feed point.

B. Minimum Number of Trays

The minimum number of trays to make a specified separation is found when an infinitely large reflux ratio is used. The L/V ratios in both sections of the column become unity and lie on the 45° line (Figure 2.29).

This situation actually takes place in a column when it is operated under "total reflux" conditions. No feed is introduced and no products are withdrawn, but heat is added in the reboiler and all the overhead vapor is condensed and returned to the column as liquid reflux. Since D = 0, R/D = Also:

Thus a column with fewer than the minimum number of trays cannot achieve the desired separation, even at very high reflux ratios.

Number Trays Versus Reflux Ratio

reflux ratio (r)

FIGURE 2.28 Costs vs. reflux ratio reflux ratio (r)

FIGURE 2.28 Costs vs. reflux ratio

For a system with constant relative volatility aLH, the Fenske equation can be used to solve analytically for the minimum number of trays (NT)min.

Xdl/xDH

log aLH

A partial reboiler is assumed in the above equation. The L and H subscripts refer to light and heavy components.

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