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The batch distillation has the advantage that more
than three components can be separated by one
column. Therefore, this paper extends the above discus-
sion to the separation of ternary mixture. Also, in the
previous papers, the slop cut withdrawal is not permit-
ted in the operation of the total reflux column. This
restriction could be disadvantageous for the separation
performance of the total reflux column, especially in
case of the separation of high specification products. In
this paper, the slop cut withdrawal is allowed in the
operation of all columns.
2. Dynamic model and optimal operation problem of
batch distillation columns
In this study, a simple model is adopted to simulate
the optimal operation of batch distillation columns. It
is assumed that all the trays as well as the reboiler and
the reflux drum are first filled with fresh feed at a
boiling temperature. Furthermore, the following as-
sumptions are introduced:
1. Constant molar boil up rate at the reboiler
2. Constant molar liquid and vapor flows
3. Constant molar holdup on each tray
4. Negligible vapor holdup
5. Constant relative volatility
Using the above assumptions, the three types of
batch distillation columns are modeled as a differential
and algebraic equation (DAE) system.
The separation performance of a batch distillation
column is influenced by many factors such as the type
of the objective function, the holdups on trays and in
the reflux drum, the treatment of the slop cut, etc. Even
if the feed and product specifications are the same, the different conclusions may be obtained. Thus, it is im-
portant to clarify the conditions used in the problem
formulation before comparing the separation perfor-
mance of the columns. The dominant conditions intro-
duced into this research are as follows:
1. All the light, intermediate and heavy components
are regarded as products.
2. The slop cut and tray holdup are discarded and not
recycled to the next batch. The amount of slop cut
is restricted to less than 40% of pure feed for each
component.
3. The amount of holdups on the trays is fairly small
compared with the total amount of initial feed.
4. The separation performance of the column is mea-
sured by the amount of products produced by con-
suming the unit amount of energy, and given by Eq.
(1). Feeding and product withdrawing time is not
included in the total batch time.
P.I. Amount of products per batch
Total batch time
(1)
For each type of column, the reflux flow rate during
the entire operation period is optimized as a function of
time. The optimal operation procedure is derived in the
following steps: first, the DAE system is converted into
a set of algebraic equations using the backward Euler
method. Through this conversion, the problem of find-
ing the optimal reflux flow rate is formulated as a
nonlinear programming problem. The derived nonlin-
ear programming problem is solved using a successive
quadratic programming technique proposed by
Curthrell and Biegler (1987).
In this paper, each column is operated as follows:
Rectifying column (Stripping column) : first, the re-
boiler, the reflux drum and all trays are filled with
raw material at a boiling temperature. The lightest
(heaviest) product is withdrawn from the reflux drum
(reboiler) as far as the composition of the liquid in
the product tank satisfies the product specification.
Then, the slop cut is withdrawn from the reflux drum
(reboiler). The termination condition of the slop cut
withdrawal is one of the optimization variables.
Next, the intermediate product is withdrawn from