Separations as unit operations - Principles of Chemical Separations with Environmental Applications - page 17

Table 2.2 is a listing of several common separation processes, their primary separation
mechanisms, and the separating agent used. The separating agent concept will be explained
in some detail in a later section of this chapter.

2.4 Equilibrium-based processes

In an equilibrium-based process, two phases (vapor, liquid, or solid) are brought into
contact with each other, mixed thoroughly, then separated with a redistribution of the
components between phases. Often multiple contacts are made in a series of cascading
steps in which the two phases flow countercurrent to each other. At each contact the phases
are allowed to approach thermodynamic equilibrium. Once equilibrium is reached, there
can be no more separation without a change in the operating parameters of the system
that affect the equilibrium relationship. The next stage in the cascade, therefore, has
at least one process change that alters the equilibrium relationship to establish a new
equilibrium relationship. The cascade should be designed such that conditions are altered
at each stage to move closer toward the desired separation. For example, distillation
(Chapter 4) is a fractionating separation in which a binary (or multiple) feed stream is
separated into two (or more) product streams based upon their differences in boiling
point. One type of distillation column has a series of cascading contact trays such that
the temperature increases from the top tray, which is just above the boiling point of
the lower-boiling-point component, to the bottom tray, which is just below the boiling
point of the higher-boiling-point component. Thus, the lower-boiling-point component is
enriched in the gas phase, while the higher-boiling-point component is enriched in the
liquid phase. Each tray from the top to the bottom of the column, then, operates at a higher
temperature such that a new equilibrium is established down the length of the column.
As the temperature increases down the column, the lower-boiling-point species tends to
vaporize more and move up the column as a gas stream, while the higher-boiling-point
component continues down the column as a liquid. The final result is a vapor stream leaving
the top of the column which is almost pure in the lower-boiling-point species and a liquid
stream exiting the bottom of the column that is almost pure in the higher-boiling-point
component.
For phase partitioning (equilibrium), the variable of interest is the solute concentration in
the first phase that would be in equilibrium with the solute concentration in a second phase.
For example, in the distillation example above, each component is partitioned between
the vapor and liquid phases. The mathematical description of the equilibrium relationship
is usually given as the concentration in one phase as a function of the concentration in the
second phase as well as other parameters. Some examples are the Henry's Law relation
for the mole fraction of a solute in a liquid as a function of the mole fraction of the solute
in the gas phase which contacts the liquid:

y = mx , (2.1)