Page 157 - Separation process engineering

(4-29)

From the overall mass balance around the entire column, Eq. (3-2), we know that the last term is −Fz .
F
Then, solving Eq. (4-29) for y,

(4-30)

Eq. (4-30) is one form of the feed equation. Since L, , V, , F, and z are constant, it represents a
F
straight line (the feed line) on a McCabe-Thiele diagram. Every possible intersection point of the two
operating lines must occur on the feed line.

For the special case of a feed that flashes in the column to form a vapor and a liquid phase, we can relate
Eq. (4-30) to flash distillation. In this case we have the situation shown in Figure 4-9. Part of the feed, V ,
F
vaporizes, while the remainder is liquid, L . Looking at the terms in Eq. (4-30), we note that − L is the
F
change in liquid flow rates at the feed stage. In this case,

(4-31)

Figure 4-9. Two-phase feed

The change in vapor flow rates is

(4-32)

Equation (4-30) then becomes

(4-33)

which is essentially the same as Eq. (2-11), the operating equation for flash distillation. Thus the feed line
represents the flashing of the feed into the column. Equation (4-33) can also be written in terms of the
fraction vaporized, f = V /F, as [see Eqs. (2-12) and (2-13)]
F