Simple Design Equations

Minimum Number of Stages - Infinite Energy

The minimum number of stages for a given separation (or equivalently, the maximum separation for a given number of stages) is obtained with infinite internal flows (infinite energy) per unit feed. (This always holds for single-feed columns and ideal

Figure 6 McCabe-Thiele diagram with an optimally located feed.

mixtures, but may not hold, for example, for extractive distillation with two feed streams.)

With infinite internal flows (total reflux) LJF = go and Vn/F =00, a material balance across any part of the column gives Vn = Ln + 1, and similarly a material balance for any component gives Vnyn = Ln+ 1xn +1. Thus, yn = xn +1, and with constant relative volatility we have:

For a column or column section with N stages, repeated use of this relation gives directly Fenske's

Figure 8 McCabe-Thiele diagram for the same example as shown in Figure 7. Observe that the feed stage location is not optimal.

molfraction I

Figure 8 McCabe-Thiele diagram for the same example as shown in Figure 7. Observe that the feed stage location is not optimal.

formula for the overall separation factor:

For a column with a given separation, this yields Fenske's formula for the minimum number of stages:

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