อัปเดต 2026-09-07

Gas–Liquid Separator (KO Drum)

Souders–Brown / GPSA §7 / API 12J

Vertical or horizontal knock-out drum sizing so entrained liquid droplets settle out of the rising gas instead of carrying over, using the Souders–Brown terminal-velocity criterion with GPSA K-value pressure/mist-pad derating, plus a Stokes/intermediate/Newton droplet-settling cross-check.

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Vertical: closed-form area A=Q/Vmax and diameter D=√(4A/π). Horizontal: liquid hold-up volume (Q_L·t) sets the diameter via a closed-form cube root against the target L/D and the circular-segment liquid area (reusing the frozen vessel-volume geometry for the exact reported hold-up volume); vapour-space velocity is then checked against Vmax. No iterative solve in either path.

สมการ

Souders–Brown maximum vapour velocity

V_{ma x} = K \frac{ρ _{L} - ρ _{V}}{ρ _{V}}

K = GPSA §7 K-value: base 0.107 m/s (vertical, with wire-mesh mist pad, ~7 barg reference), derated ~0.003 m/s per 7 bar of operating pressure above the reference, and halved when no mist pad is fitted. Souders, M. & Brown, G.G. (1934), Ind. Eng. Chem. 26(1):98 — original force-balance derivation.

Vertical KO drum minimum diameter

A_{min} = \frac{Q _{V}}{V _{ma x}}, D_{min} = \frac{4 A _{min}}{π}

GPSA §7 / API 12J area/diameter sizing at the terminal-velocity limit; an optional design margin rounds D up. Validation anchor (self-derived): K=0.107 m/s, ρL=600 kg/m³, ρV=30 kg/m³, QV=0.50 m³/s → Vmax=0.4664 m/s, Dmin=1.168 m (exact closed-form match).

Droplet terminal settling velocity (Stokes regime, Re<1)

v = \frac{g d ^{2} ( ρ _{L} - ρ _{V} )}{18 μ _{V}}

Independent force-balance cross-check on K (the K factor is an empirical lump of this same balance for the design cut size). Intermediate/Allen law (1≤Re<1000) and Newton's law (Re≥1000) are used at higher droplet Reynolds numbers Re=ρV·v·d/μV.

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