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    Abstract Geometricmethods are valuable tools for process synthesis and design since they provide designerswith intuition and quantitative results.
    The calculation and graphical representation of azeotropes, residue curves and distillation boundaries provide a wealth of knowledge about
    the entire composition space. This paper shows how these tools can be used for optimal design of complex azeotropic distillation columns.
    Two examples of the design of distillation systems of industrial importance are shown. In the first example, the second feed location of a
    two-feed distillation column with a top decanter is optimized. In the second example, the side stream draw-stage location of a distillation
    column with a top decanter and a side stream draw is optimized. In both cases, a feasible and near optimal structure has been designed
    based on information obtained by examining the whole composition space. © 2000 Elsevier Science S.A. All rights reserved.5637
    Keywords: Distillation column; Azeotropic distillation; Optimization 1. Introduction
    The separation of mixtures with several azeotropes and
    one or more two-liquid phase regions is a task commonly
    encountered in chemical processes. These mixtures usually
    have more than one distillation region that complicates the
    design of the distillation systems used to separate them.
    Design by simulation is still the dominant method for
    distillation system design. For complex azeotropic distilla-
    tion systems, however, this is a tedious and time-consuming
    trial-and-error method that often requires many years of
    experience. In this technique, all the input variables (feed
    flow rate, its thermodynamic state and composition) and pro-
    cess parameters (pressure, reflux ratio, number of stages,
    feed stage location) are specified, and the composition and
    flows of the products are calculated. This is a robust tech-
    nique for establishing the performance of existing columns.
    For design purposes, however, it requires the estimation of
    the above parameters by guessing, extrapolation of exist-
    ing separation systems or by applying short-cut methods
    (e.g. the Fenske–Underwood–Gilliland–Eduljee–Kirkbride
    method) [1]. Since these methods have been developed for
    ideal mixtures under several simplifying assumptions, they
    are not accurate for non-ideal mixtures and can give initial
     Corresponding author. Tel.: C1-403-520-6000; fax: C1-403-520-6060.
    E-mail address: stan.wasylkiewicz@software.aeat.com
    (S.K. Wasylkiewicz).estimates that are either far from the final solution or are not
    feasible.
    Establishing feasibility as quickly as possible is very im-
    portant in the design of complex azeotropic distillation sys-
    tems [2] since neither all separation schemes nor all desired
    specifications are feasible. Using the design by simulation
    approach, these facts are often discovered only after exten-
    sive simulation studies. Geometric methods allow designers
    to find feasible separation schemes far more quickly, even
    for highly non-ideal azeotropic systems, by examining the
    overall separation space, its stationary points (azeotropes),
    distillation boundaries, residue curves, and rectifying and
    stripping profiles. Difficult separation problems that can po-
    tentially take several months of trial and error simulations
    to complete can be solved in a few hours instead.
    There is often an extra degree of freedom in the design
    of some complex distillation columns. There are multiple
    solutions for the same design problem. All of them sat-
    isfy product specifications, but require different number
    of stages in the column. To obtain the best solution, we
    perform the appropriate parametric study and display the
    results of this study in a diagram, which shows the effect
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