Page 158 - Separation process engineering

(4-34)

In terms of the fraction remaining liquid, q = L /F [see Eqs. (2-14) and (2-15)], Eq. (4-33) is
F

(4-35)

Equations (4-33) to (4-35) were all derived for the special case where the feed is a two-phase mixture,
but they can be used for any type of feed. For example, if we want to derive Eq. (4-35) for the general
case, we can start with Eq. (4-30). An overall mass balance around the feed stage (balance envelope
shown in Figure 4-9) is

which can be rearranged to

Substituting this result into Eq. (4-30) gives

and dividing numerator and denominator of each term by the feed rate F, we get

which becomes Eq. (4-35), since q is defined to be ( − L)/F. Equation (4-34) can be derived in a similar
fashion.

Previously, we solved the mass and energy balances and found that

(4-17)

From Eq. (4-17) we can determine the value of q and hence the slope, q/(q − 1), of the feed line. For
example, if the feed enters as a saturated liquid (that is, at the liquid boiling temperature at the column
pressure), then h = h and the numerator of Eq. (4-17) equals the denominator. Thus q = 1.0 and the slope
F
of the feed line, q/(q − 1) = ∞. The feed line is vertical.
The various types of feeds and the slopes of the feed line are illustrated in Table 4-1 and Figure 4-10.

Note that all the feed lines intersect at one point, which is at y = x. If we set y = x in Eq. (4-35), we obtain

(4-36)

Table 4-1. Feed conditions