The feed to a distillation column can be liquid or vapor, or both, depending on the temperature, pressure, and composition of the feed. To quantify the thermal condition of the feed, the parameter q is defined as the fraction of the feed that is liquid.
It follows that 1 — q is the fraction of feed that is vapor:
If the feed is a saturated liquid at its bubble point, q = 1. If the feed is a saturated vapor at its dew point, q = 0. If the feed is a vapor—liquid mixture, q is a fraction. Values of q greater than 1 indicate subcooled liquid feed. Values of q less than 0 indicate superheated vapor feed.
Now let us look at the intersection points (x„ y,) of the stripping and rectifying operating lines. Use of equations (2.28) and (2.30) gives:
Subtracting gives:
(F* - Vs)y, = (Lr - Ls)x, + (xdD + xB B) Using equations (2.24), (2.33) and (2.34) gives:
This is the equation of a straight line with slope (~q/( 1 — q))- It is called the q line and intersects the 45° line at zF. Thus the intersection of the operating lines must lie on the q line, which can be easily drawn given zF and q. Figure 2.25 shows q lines for several values of q.
The slope of the rectifying operating line (LR/VR) can be expressed in terms of the internal reflux ratio LR/D = R. If the reflux is a saturated liquid at its bubble point,* LR = L0.
Thus the rectifying operating line can be drawn if xD and R are specified. It is a straight line with a slope of R/(R + 1), intersecting the 45° line at xD. Then the stripping operating line can be drawn if xB and q are specified. It is a straight line joining xB on the 45° line with the intersection of the rectifying operating line and the q line.
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