Page 232 - Separation process engineering

Understanding the differences between binary and multicomponent distillation will be helpful when you
are doing calculations for multicomponent distillation.

5.4 Bubble-Point and Dew-Point Equilibrium Calculations

Although convenient mathematically, few systems have constant or almost constant relative volatilities. In
this case we need to do a complete equilibrium calculation on each stage. If the distillation has HNKs,

HK, and LK, we should step off stages from the bottom up and do a bubble-point calculation on each
stage. The bubble-point temperature is the temperature of stage j at which the liquid mixture on the stage
begins to boil. The pressure, p , and the mole fractions of the liquid, x , will be known. We wish to find
j
i,j
the temperature, T, at which Σ y = 1.0, where the y are calculated as y = K (T)x Stepping off stages
i,j
i,j
i,j
i,j
j
j i,j.
down the column (HK, LK, and LNKs present), we use dew-point calculations with known y to
i,j
determine T and x .
j
i,j
Consider the distillation column shown in Figure 5-7, where all the non-keys are HNKs. Note that the
column is now numbered from the bottom up, since that is the direction in which we will step off stages.
With no LNK, a good first guess of concentrations can be made at the bottom of the column, and we can
start the stage-by-stage calculations by calculating the reboiler temperature and the values of y from a
i,R
bubble-point calculation. For the bubblepoint calculation, we want to find the temperature that satisfies
the stoichiometric equation.

(5-33)

If a simple expression for K as a function of temperature is available, we may be able to solve the
i
resulting equation for temperature. Otherwise, a root-finding technique or a trial-and-error procedure will
be required. When graphs or charts are used, a trial-and-error procedure is always needed. When we are
finished with the calculation, the y calculated are the mole fractions of the vapor leaving stage j.
i,j
Figure 5-7. Distillation column for stepping off stages from the bottom up