Distillation - Principles of Chemical Separations with Environmental Applications - page 94

the rectifying section; and L and V in the stripping section. Third, there is a q -line which
describes the vapor-liquid quality of the feed and is derived with an energy balance. The
q -line, to be discussed later in this chapter, occurs at the intersection of two operating lines.
The q -line is often called the feed line when it is drawn for a feed stream. The location of
the q -line depends on the concentration of the feed and its slope depends on the quality
of the feed (the fraction which is liquid). The q -line is used to determine the optimal feed
tray in a column.
The McCabe-Thiele analysis begins with deriving the mass balances for the rectifying
and stripping sections of the column. Before we begin, an additional assumption of constant
molar overflow, CMO, is made. A CMO occurs when the molar flowrates in the liquid and
vapor phases remain constant in each section of the column. This assumption corresponds
physically to the fact that the molar heats of vaporization for each component in the
feed are approximately equal. This means if you condense one mole of vapor, you will
create one mole of vapor by evaporation from the liquid phase. This assumption applies
to total molar flowrates. The one mole of vapor which condenses will normally have a
different composition from the one mole of liquid evaporated. In addition, if the total molar
flowrates in each of the stripping and rectification sections of the column are constant, a
mass balance of the section when plotted as vapor mole fraction vs liquid mole fraction,
results in a straight line.

Mass balances

Both component and total mass balances can be performed using the entire column as the
control volume. The total and component for the more volatile species are:

Overall: F = D + B (4.2)

Component A : x F F = x D D + x B B , (4.3)

where x refers to the more volatile component and the subscripts F , D and B refer to its
respective concentrations in the feed, distillate and bottoms streams.

Upper (rectifying) section - enrichment of more volatile component

First, remember the assumption that liquid and vapor flowrates in the rectifying section
of the column are constant. An overall mass balance can then be written around the top
of the column:

V = D + L ⇒ D = V − L . (4.13)

In addition, a component mass balance can be performed which describes the net flowrate
of component A in the upper section for any tray. For clarification, trays in distillation
columns are typically numbered from the top to the bottom, such that the top tray is stage
1 and the bottom is stage m . Thus, liquid flows down the column from tray n to tray n

+ 1