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FRACTIONATING TOWERS

CHORD HEIGHTS, LENGTHS, AND AREAS

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November, 2003 Changes shown by ➧

CONTENTS Section

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SCOPE ...................................................................................................................................................................2 DEFINITIONS .........................................................................................................................................................2 APPLICATION........................................................................................................................................................2 CHORDAL DOWNCOMERS..........................................................................................................................2 MODIFIED ARC DOWNCOMERS .................................................................................................................2 HORIZONTAL CYLINDRICAL DRUMS..........................................................................................................2 DESIGN CONSIDERATIONS .................................................................................................................................2 CHORDAL DOWNCOMERS..........................................................................................................................2 MODIFIED ARC DOWNCOMERS .................................................................................................................2 COMPUTER PROGRAMS......................................................................................................................................3 Tables Table 1

Chord Lengths And Chord Areas Vs. Chord Heights ..............................................................................4

Table 2

Chord Height Vs. Chord Length..............................................................................................................9

Figures Figure 1 Chord Height Vs. Chord Area..................................................................................................................5 Figure 2 Chord Height Vs. Chord Length ..............................................................................................................8 Figure 3 Geometrical Relationships For Modified Arc Downcomers ...................................................................11

Revision Memo 11/03

New criteria for inlet and outlet chord lengths of downcomers is that they be at least 62.5% or the tower diameter for good liquid distribution.

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FRACTIONATING TOWERS

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CHORD HEIGHTS, LENGTHS, AND AREAS

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SCOPE This Subsection contains a table and six figures giving data on the geometrical relationship of chords, segments and circles and of modified arc downcomers. These charts simplify calculations concerning tray downcomers, tower shed sections and horizontal cylindrical drums.

DEFINITIONS The terms “chord height" and “chord length" are used in their conventional mathematical sense. The area of a segment is called “chord area", in keeping with standard tray design nomenclature. These terms are also defined graphically on the table and figures themselves.

APPLICATION CHORDAL DOWNCOMERS For most tray designs, chordal type downcomers are normally specified. Table 1 and Figures 1A, 1B, 1C and 2A and 2B apply.

MODIFIED ARC DOWNCOMERS Where the use of a chordal downcomer would result in excessive downcomer area, a modified arc downcomer can be used and Figure 3 applies (for one and two-pass trays). This type of downcomer provides maximum tray contacting area. Modified arc downcomers can be used to reduce the tower diameter in new designs, or to debottleneck existing towers which are limited by vapor handling capacity.

HORIZONTAL CYLINDRICAL DRUMS Table 1 and Figures 1A, 1B and 1C can be used for calculating the holdup of the cylindrical portion of a horizontal cylindrical drum. Figures 2A and 2B will find application in calculating the liquid surface area in such drums.

DESIGN CONSIDERATIONS Only downcomers are discussed below. For drum design considerations, see Section V, Drums.

CHORDAL DOWNCOMERS ➧

To ensure good liquid distribution to the tray, the inlet and outlet chord length of the downcomer of one and two-pass trays should be at least 62.5% of the tower diameter. For three and four-pass trays, downcomer chordal dimensions can be as low as 60% and 10% of the tower’s diameter for chord length and chord height respectively, and 5.2% of the tower’s cross-sectional area for the chord area.

MODIFIED ARC DOWNCOMERS The “rise" for a modified arc downcomer is the minimum distance between the tower wall and the downcomer. It must be at least 6 inches (150 mm), regardless of tower diameter. This requirement limits the use of modified arc downcomers to towers with diameters greater than about 6 feet (1800 mm). At this diameter, a modified arc downcomer is not much different from a chordal downcomer, and gives only about 1% more tray contacting area. The higher cost of the modified arc downcomer is therefore not justified. The advantage of a modified arc downcomer over a chordal downcomer increases with increasing tower diameter. Figure 3 shows how a modified arc downcomer is designed. The ends adjoining the shell are two equal chord sections. These are joined by three other equal sections, as shown in Figure 3. For three and four-pass trays, see COMPUTER PROGRAMS.

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FRACTIONATING TOWERS

CHORD HEIGHTS, LENGTHS, AND AREAS

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COMPUTER PROGRAMS For three and four-pass trays, computer program 1143 “Multipass Sieve Tray Design Program” can be used to calculate modified arc downcomer areas when their chordal length is 60% of the tower cross-sectional area. Interconversion calculations for chord length, chord height, chord area and vessel diameter can be done using the PEGASYS computer program by selecting “Geometry” on the main menu, followed by “Segments of Circle”.

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CHORD HEIGHTS, LENGTHS, AND AREAS

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Table 1 Chord Lengths And Chord Areas Vs. Chord Heights

l θ Chord Length = = sin = sin cos -1 (1- 2R*) Diameter D 2

R* =

Chord Height = Diameter

A* =

r 2 (θ - sin θ) é A chord 2h ö ù θ - sin θ æ = = ; θ = 2 êcos-1 ç 1 ÷ ú , θ in radians 2 è A circle 2π D øû 2π r ë

h D

L* =

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Figure 1 Chord Height Vs. Chord Area

(Customary Units)

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Figure 1b Chord Height Vs. Chord Area (Metric Units)

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Figure 1c Chord Height Vs. Chord Area (Metric Units)

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Figure 2 Chord Height Vs. Chord Length

(Customary Units)

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Table 2 Chord Height Vs. Chord Length

(Customary Units)

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Figure 2b Chord Height Vs. Chord Length (Metric Units)

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Figure 3 Geometrical Relationships For Modified Arc Downcomers

(Same For Customary And Metric Units)

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