Feed Section Operating Line (q-line)
See the Figure below for a feed tray and consider F moles/hr of feed, with fraction q of liquid; thus
liquid
flow = q F moles/hr
vapour flow = (1-q) F moles/hr
Overall material balance:
L' = L + q F
V = V' + (1-q) F
Component balance for the more volatile component - see the Figure below:
Rectifying section : V y = L x + D xD
Stripping section : V' y = L' x - B xB
At the feed point where the two lines operating lines intersect:
( V - V' ) y = ( L - L' ) x + D xD + B xB
we have:
V - V' = ( 1 - q ) F
L - L' = - q F
In addition, from component
balance around the entire column:
F xF = D xD + B xB
Thus, ( 1 - q ) F y = - q F x + F xF
Re-arranging in the form y = f(x), we have:
For a given feed condition, xF and q are fixed, therefore the q-line is a straight line with slope -q / (1-q) and intercept xF / (1-q).
If x = xF
, then y = xF.
i.e. the q-line passes through
the point (xF, xF)
on the 45o diagonal.
Different values of q will result in different slope of the q-line. See the Figure below.
Note that the q-line passes through the point (xF, xF) on the 45o diagonal for all values of q.
