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    temperature allows an appropriate amount of the feed to
    vaporize at column pressure; however it should not be so
    high as to incur excessive amounts of cracking in the
    furnace.
    The hot crude oil is fed to the lower part of a distillation
    tower, the condenser of which is at approximately atmos-
    pheric pressure. The feed is partially vaporized at the
    column pressure and is further vaporized by the injection of
    steam into the bottom of the column. The column, which
    usually has 30 to 50 stages and four to eight products, serves
    to separate the feed into products with relatively narrow
    boiling ranges. The overhead condenser condenses the
    stripping steam (as a separate phase) and any condensable
    hydrocarbons; some of this stream is returned to the column
    as re¯ ux and some is withdrawn as the top product. Liquid
    side-streams are withdrawn from the column at variouspoints and are stripped in side-strippers before being
    removed as products. Stripping steam, reboiling or, less
    commonly, vacuum, may be used to strip the liquid side-
    streams; the volatile material is returned to the main
    column. The stripping steam is at a low pressure; to prevent
    it from condensing in the stripper, it is superheated.
    The cooling requirements of the column consist of
    product cooling before storage (to reduce the risk of
    explosion), vapour condensation and intermediate cooling
    in the column. Without intermediate cooling, the vapour
    traf
    c in the column would increase up the column; this
    could lead to loading problems or would increase the cost of
    the column. These intermediate coolers also enhance
    control of the column and provide sources of heat at
    higher temperatures than the top condenser.
    It is complicated and costly to withdraw and condense an
    intermediate vapour stream, so a common method of
    providing intermediate cooling is to withdraw and cool a
    liquid stream. The liquid may be withdrawn from a stage,
    cooled and returned to just below the stage (this is known as
    a `pump-back’ ) or may be withdrawn from a stage, cooled
    and returned to a stage above in a pump-around loop. In both
    cases, vapour condensation on the three to four stages below
    the liquid return provides heat to the subcooled liquid. On
    these stages, since no liquid is vaporized, no separation
    takes place. The cooling duty of a pump-back scheme is
    limited by the nite ¯ ow of liquid in the column.
    1.2 Objectives of the New Design Procedure
    A design procedure for a crude oil distillation system
    should determine the distribution of stages in the column,
    the optimum pump-around ¯ ows and duties and the
    optimum ¯ ows of live steam for stripping and duties for
    reboiling. This work develops a systematic procedure for
    the design of crude oil distillation towers.We shall focus on
    towers with side-strippers, since these are typically found in
    the re
    ning industry. The extension of the principles to
    consider any sequence of columns is discussed brie¯ y at the
    end of the paper.
    The literature concerning the design and retro
    t of crude
    oil distillation systems is relatively scarce and mostly fairly
    old. One of the reasons for its scarcity is that much of the
    knowledge in this area is kept in-house by the big re
    ning
    and contracting companies. The literature is heuristic in
    nature and often based on case studies. These shortcomings
    arise because crude oil distillation is a highly complex
    system, which is dif
    cult to model and analyse.
    Design procedures for the crude oil distillation system
    were proposed by Nelson3
    , Packie4
    and Watkins5
    . These
    design procedures leave the design of the HEN and feed
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