Page 52 - Separation process engineering

In phase equilibrium, the rate at which each species is vaporizing is just equal to the rate at which it is
condensing. Thus there is no change in composition (mole fraction in Figure 1-2). However, in general,
the compositions of liquid and vapor are not equal. If the compositions were equal, no separation could
be achieved in any equilibrium process. If temperature and pressure are constant, equal rates of
vaporization and condensation require a minimum in the free energy of the system. The resulting condition
for phase equilibrium is

(1-3)

The development of Eq. (1-3), including the necessary definitions and concepts, is the subject of a large
portion of many books on thermodynamics (e.g., Balzhiser et al., 1972; Denbigh, 1981; Elliott and Lira,
1999; Sandler, 2006; Smith et al., 2005; Walas, 1985) but is beyond the scope of this book. However, Eq.

(1-3) does require that there be some relationship between liquid and vapor compositions. In real systems
this relationship may be very complex and experimental data may be required. We will assume that the
equilibrium data or appropriate correlations are known (see Chapter 2), and we will confine our
discussion to the use of the equilibrium data in the design of separation equipment.

1.3 Mass Transfer

In the vapor-liquid contacting system shown in Figure 1-2 the vapor and liquid will not be initially at
equilibrium. By transferring mass from one phase to the other we can approach equilibrium. The basic
mass transfer equation in words is

(1-4)

In this equation the mass transfer rate will typically have units such as kmol/h or lbmol/h. The area is the
2
2
area across which mass transfer occurs in m or ft . The driving force is the concentration difference that
drives the mass transfer. This driving force can be represented as a difference in mole fractions, a
difference in partial pressures, a difference in concentrations in kmol/L, and so forth. The value and units
of the mass transfer coefficient depend upon which driving forces are selected. The details are discussed

in Chapter 15.
For equilibrium staged separations we would ideally calculate the mass transfer rate based on the transfer
within each phase (vapor and liquid in Figure 1-2) using a driving force that is the concentration
difference between the bulk fluid and the concentration at the interface. Since this is difficult, we often
make a number of simplifying assumptions (see Section 15.4 for details) and use a driving force that is the
difference between the actual concentration and the concentration we would have if equilibrium were
achieved. For example, for the system shown in Figure 1-2 with concentrations measured in mole
fractions, we could use the following rate expressions.

(1-5a)

(1-5b)

In these equations K and K are overall gas and liquid mass transfer coefficients, y * is the mole fraction
A
x
y
in the gas in equilibrium with the actual bulk liquid of mole fraction x , x * is the mole fraction in the
A
A