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tion method developed for multicomponent, homogeneous
mixtures has been generalized to include heterogeneous
mixtures [9].
3. Distillation column design
Residue curve maps (RCMs) are very useful for the
characterization of azeotropic mixtures, predicting feasible
splits, selecting entrainers, and analyzing potential column
operability problems [2–5,10,11]. They display the shape
of the separation space, including distillation boundaries,
distillation regions and azeotropes. Residue curves areequivalent to the composition profiles of infinitely long
packed column at total reflux (continuous model described
by differential equations). Composition profiles of staged
column at total reflux (discrete model described by finite
difference equations), can be approximated by simple dis-
tillation residue curves and usually the differences between
these two types of curves are small [2]. Using residue curve
maps, infeasible specifications can be immediately identi-
fied, and alternative distillation sequences can be inferred
without trial and error. The shapes of residue curves are
very useful in the design of real finite reflux separators since
they give a qualitative picture of the composition profiles
in actual staged towers.
In this paper, we use the boundary-value design method
(BVDM) [11] for the distillation column design. For a
one-feed, two-product distillation column, we define the
feed, specify completely distillate and bottoms (using com-
ponent and overall mass balances) and select the column’s
internal flows (by specifying reflux or reboil ratio and using
an energy balance). The composition profiles are then cal-
culated using a combination of flashes and mass balances
starting from both ends. If the composition profiles for
rectifying and stripping sections of the column cross in the
composition space, the column is feasible and the number
of stages in each section of the column can be counted.
The BVDM algorithm for a ternary one-feed two-product
distillation column can be summarized as follows:
1. Specify feed composition and thermodynamic state.
2. Specify column pressure.
3. Specify three of six possible products’ mole fractions.
4. Calculate the remaining products’ mole fractions using
mass balances.
5. Guess a value for the reflux ratio.
6. Calculate reboil ratio using energy balance.
7. Compute the composition profiles for the rectifying and
stripping sections of the column starting from distillate
and bottoms compositions.
8. Repeat (5)–(7) until composition profiles intersect in the
composition space.
9. Repeat (2)–(7) to optimize reflux ratio and pressure.
10. Count the number of stages in each section of the
column.
For distillation columns with top decanter, a side stream
draw or two feeds, the algorithm requires modifications.
These modifications will be explained within the following
examples. P, column pressure
r, reflux ratio
s, reboil ratio
q, feed quality
n, number of stages in the column
f, feed stage location
These variables are related by 3 summation equations for
mole fractions in each stream, c−2 co-linearity conditions
between x x xB and x x xD (derived from mass balances), and one
condition between r and s (energy balance). The BVDM
makes it possible to compute the rectifying composition pro-
file starting from the distillate composition, and the stripping
profile starting from the bottoms composition. The distilla-
tion column will be feasible only if the profiles intersect in
the composition space. The point of intersection represents
the composition of the liquid stream leaving the feed stage