Page 77 - Separation process engineering

or

Figure 2-10. Illustration of lever-arm rule

which gives the same result as Eq. (2-26). The seesaw is a convenient way to remember the form of the
lever-arm rule.

The lever-arm rule can also be applied on ternary diagrams for extraction, where it has several other uses
(see Chapter 13).

2.5 Multicomponent VLE

If there are more than two components, an analytical procedure is needed. The basic equipment
configuration is the same as Figure 2-1.

The equations used are equilibrium, mass and energy balances, and stoichiometric relations. The mass
and energy balances are very similar to those used in the binary case, but the equilibrium equations are
usually written in terms of K values. The equilibrium form is

(2-27)
where in general

(2-28)

Equations (2-27) and (2-28) are written once for each component. In general, the K values depend on
temperature, pressure, and composition. These nonideal K values are discussed in detail by Smith (1963)
and Walas (1985), in thermodynamics textbooks, and in the references in Table 2-2.

Fortunately, for many systems the K values are approximately independent of composition. Thus,

(2-29)

For light hydrocarbons, the approximate K values can be determined from the nomographs prepared by
DePriester. These are shown in Figures 2-11 and 2-12, which cover different temperature ranges. If
temperature and/or pressure of the equilibrium mixture are unknown, a trial-and-error procedure is
required. DePriester charts in other temperature and pressure units are given by Green and Perry (2008),
Perry and Green (1997), and Smith and Van Ness (1975). The DePriester charts have been fit to the
following equation (McWilliams, 1973):

(2-30)

Figure 2-11. Modified DePriester chart (in S.I. units) at low temperatures