# W 0 V r

(See nomenclature at the end of this chapter.)

These equations should not be applied to mixtures having minimum reflux ratios determined by a tangent contact in one section of the tower only. It is customary to use relative volatility values corresponding to approximately the feed-plate temperature. Actually some of the values correspond to the pinched-in region above the feed and the others to the lower section, but usually this refinement is not made although it can be done if necessary.

In addition to Eq. (9-17), it is possible to develop a large number of alternate relations. The most helpful of those are obtained by equating the ratio of the key components at the pinched-in region to the optimum feed-plate ratio.

Matching the optimum feed-plate ratio, <t>, with the pinched-in region, a = SOU (= [ (0/D)zik + xpik 1 othh (9-18)

* <xik VJhk) L 00/D)xhk + xDhk\ aik and solving for O/D,

0 __ (cthk%Dik/<l>) — aikXphk D (aik — athk)%hk

Equation (9-18) is applicable to either binary or multicomponent nixtures, and the problem is one of evaluating xhh. Tor Case I:

For Case II:

or, in general, where = 1 for a binary

= 1 — 2xi for Case II = 1 — Xxi - 2xh for Case I The terms Xxt and Xxh can be evaluated by Eqs. (9-13) and (9-15) to give

OihkXDlk

The first term is the minimum reflux ratio for a binary mixture with the same ratio of key components in the distillate and <f>. Equation (9-20) can be written

Equation (9-20) involves no trial and error if On = Om, but it does for other cases. By equating the liquid-phase ratios instead of the vapor-phase ratios of Eq. (9-18), one obtains