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 No feed is introduced and no products are withdrawn, but heat is added in the reboiler and all the overhead vapor is condensed and returned to the column as liquid reflux.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.
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.
FIGURE 2.29
Minimum number of trays required at total reflux
FIGURE 2.29
Minimum number of trays required at total reflux
2.5 EFFECTS OF VARIABLES
Now that the McCabe-Thiele method has been introduced, we can visualize the effects of various operating and design parameters.
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