Page 156 - Separation process engineering

is calculated from Eq. (4-17), which is repeated below:

(4-17)

Then is given by Eq. (4-19), = L + qF, and = − B. We can calculate L as (L/D)D, where D and B
are found from mass balances around the entire column. Alternatively, for a simple column Eqs. (3-3) and
(3-4) can be substituted into the equations for and . When this is done, we obtain

(4-25)

With / and x known, the bottom operating equation is fully specified, and the bottom operating line
B
can be plotted. Eq. (4-25) is convenient for computer calculations but is specific for the simple column
shown in Figure 3-8. For graphical calculations the alternative procedure shown in the next section is
usually employed.

4.4 Feed Line

In any section of the column between feeds and/or product streams the mass balances are represented by
the operating line. In general, the operating line can be derived by drawing a mass balance envelope
through an arbitrary stage in the section and around the top or bottom of the column. When material is
added or withdrawn from the column the mass balances will change and the operating lines will have
different slopes and intercepts. In the previous section the effect of a feed on the operating lines was
determined from the feed quality and mass balances around the entire column or from Eq. (4-25). Here we
will develop a graphical method for determining the effect of a feed on the operating lines.

Consider the simple single-feed column with a total condenser and a partial reboiler shown in Figure 3-8.
The mass balance in the rectifying section for the more volatile component is

(4-26)

while the balance in the stripping section is

(4-27)

where we have assumed that CMO is valid. At the feed plate we switch from one mass balance to the
other. We wish to find the point at which the top operating line—representing Eq. (4-26)—intersects the
bottom operating line—representing Eq. (4-27).
The intersection of these two lines means that

(4-28)

Equations (4-28) are valid only at the point of intersection. Since the y’s and x’s are equal at the point of
intersection, we can subtract Eq. (4-26) from Eq. (4-27) and obtain