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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
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