Distillation - Principles of Chemical Separations with Environmental Applications - page 92

column via these perforations. Unless the vapor flow is significantly below the operating
range, the vapor velocity is adequate to prevent leakage, called weeping, of the liquid
through the holes. The perforations also serve the purpose of dividing the vapor into many
small bubbles, which pass through the pool of liquid on the trays, thus enhancing the
contact of vapor with liquid. The vapor bubbles create a boiling mass of liquid on each
tray. Just above this mass and just below the next higher tray is a fog of collapsing bubbles.
Some of this fog settles back into the liquid, but some becomes entrained in the vapor and
is carried to the plate above. Because of the difference in column operating temperature
at each sieve plate, the vapor becomes purer in the more volatile species as it rises, while
the liquid becomes more pure in the less volatile species.

4.4.1 McCabe-Thiele analysis

From Chapter 3 we saw that a McCabe-Thiele method of “stepping off ” stages could
be applied to determine the number of equilibrium stages required to perform a desired
separation using only the vapor-liquid equilibrium relationship and a mass balance of
the system. Let us begin to apply this technique to distillation by examining the simplest
possible scenario. Some simplifying assumptions, therefore, must be made. First, we
assume that our feed stream is binary such that only two components, a more volatile and
a less volatile, exist throughout the column. Second, the system is operating at steady-state
so that all flow rates, compositions, stage temperatures and pressures are constant with
respect to time. Third, pressure in the column is assumed to be constant, allowing us to
neglect pressure drop through the column. Fourth, it is assumed that there is no chemical
reaction between the two components in the system. As a first approximation, the stages
are assumed to be ideal; i.e., equilibrium between the liquid and vapor phases is reached
at each sieve tray. Methods to account for stage efficiencies will be discussed later in the
chapter. Fifth, it is assumed that the column operates adiabatically. This means that heat
exchange between the column and the external environment is neglected. This assumption
becomes useful in calculating the optimal location of the feed plate.
Figure 4.3 shows a schematic of a binary system distillation column. The x concentra-
tions all refer to the more volatile species in the feed. For analysis the column is divided
into two distinct sections: the rectifying section which includes the feed tray and all oth-
ers above it; and the stripping section which includes all trays below the feed tray. The
rectifying section operates to provide an almost pure vapor stream, D ,ofthe more volatile
component and the stripping section provides an almost pure liquid stream, B ,ofthe less
volatile component. It is important to note that a portion of the vapor stream, or distillate,
is condensed and fed back to the top of the column and a portion of the liquid stream, or
bottoms, is vaporized and returned to the bottom of the column. The condensed vapor, L ,
that is returned to the top of the column provides a liquid stream in the rectifying portion
of the column. The vaporized liquid from the bottoms that is fed back into the stripping
section provides a vapor stream in the stripping section. Without these two recycle streams,