Page 227 - Separation process engineering

stage in column = 2, and so forth. Now we calculate y values from equilibrium and x values from the
operating equations.

Stepping off stages up the column, the equilibrium calculation on every stage is a bubble-point
calculation. In this case, the K value for the reference component is

(5-29)

and the vapor compositions are determined from the equilibrium equation,

(5-30)

Derivation of Eqs. (5-29) and (5-30) is left as an exercise. The liquid mole fractions are found from the
operating equations, which are inverted to find x .
i,j

(5-31)

(5-32)

Convergence requires checking the assumed and calculated values of the fractional recovery of the HNK
in the bottoms.

For problems where both light and heavy non-keys are present, Lewis and Matheson (1932) and Thiele
and Geddes (1933) calculated from both ends of the column and matched compositions at the feed stage
(see Smith, 1963, Chapter 20, for details). Unfortunately, closure can be very difficult. When there are
both light and heavy non-keys, and when there is a sandwich component, other calculation methods such
as the matrix method discussed in Chapter 6 are preferable.

5.3 Profiles for Multicomponent Distillation

What do the flow, temperature, and composition profiles look like? Our intuition would tell us that these
profiles will be similar to the ones for binary distillation. As we will see, this is true for the total flow
rates and temperature, but not for the composition profiles.

If CMO is valid, the total vapor and liquid flow rates will be constant in each section of the column. The
total flow rates can change at each feed stage or sidestream withdrawal stage. This behavior is illustrated
for a computer simulation for a saturated liquid feed in Figure 5-2 and is the same behavior we would
expect for a binary system. For nonconstant molal overflow, the total flow rates will vary from section to
section. This is also shown in Figure 5-2. Although both liquid and vapor flow rates may vary
significantly, the ratio L/V will be much more constant.

Figure 5-2. Total liquid and vapor flow rates. Simulation for distillation of benzene-toluene-cumene.
Desire 99% recovery of benzene. Feed is 0.233 mole frac benzene, 0.333 mole frac toluene, and