Gas-Liquid Separation — Fundamentals

1. The Souders-Brown velocity

A gas-liquid separator works by letting gravity pull entrained droplets down faster than the rising gas can carry them up. Setting the droplet's terminal settling velocity equal to the gas velocity gives the classic Souders-Brown equation for the maximum allowable vapour velocity:

V_max = K · √( (ρ_L − ρ_V) / ρ_V )

This comes directly from the droplet drag/gravity force balance — the √((ρ_L−ρ_V)/ρ_V) term is the terminal-velocity group, and K bundles the droplet size and drag coefficient into a single empirical capacity factor. The required cross-sectional area (and hence vessel diameter) is then A = Q_actual,V / V_max.

2. The K-factor

The GPSA Engineering Data Book gives K values by vessel type and service:

Configuration	Typical K (ft/s)
Vertical, no mist eliminator	~0.10 – 0.20
Vertical, wire-mesh pad	~0.35 (derate at high P)
Horizontal (with mesh)	~1.25 × vertical value
Vane-pack mist eliminator	~0.40 – 0.65 (vendor)

K is derated at elevated pressure and for high liquid load or viscous/foaming systems. The GPSA de-rating is a percentage schedule applied to the base mesh/vane K — roughly 100% at atmospheric, 90% at 150 psig, 85% at 300 psig, 80% at 600 psig and 75% at ~1,150 psig. (The linear "−0.01 per 100 psi" rule sometimes quoted is Manning's approximation, which under-derates at high pressure — use the percentage schedule.) Using the sea-level mesh-pad K at 1,000 psig over-sizes the velocity and under-sizes the vessel.

3. Demisters

A bare gravity vessel only removes large droplets (≳ 150 µm). A wire-mesh pad captures droplets down to ~3–10 µm by inertial impaction and is good for clean service; a vane pack handles higher velocity and dirtier/waxy service; an axial cyclone bundle gives the highest capacity and turndown. The demister sets the K-factor used above — i.e. the separation device and the vessel sizing are coupled, not independent choices.

4. Liquid handling & retention

Beyond removing droplets from gas, the vessel must give the liquid enough residence time to degas and to provide control/surge volume between level alarms. Two-phase separators are sized for a liquid hold-up time (typically 1–5 min depending on service and downstream control); three-phase separators add oil-water settling time governed by Stokes-law droplet rise/fall between the phases. The vessel length-to-diameter ratio (often L/D ≈ 2.5–5) balances the gas-capacity and liquid-residence requirements.

Distillation tray hydraulics & flooding

The same vapour-capacity logic governs a distillation tray, but the limit there is entrainment flooding rather than droplet carry-over. The Fair flooding correlation gives a capacity factor C_F as a function of the tray spacing and the dimensionless flow parameter F_LV = (L/V) · √(ρ_V/ρ_L), where L and V are the liquid and vapour mass flows. The flooding velocity (referenced to the net area) is

u_flood = C_F · (σ / 20)^0.2 · √( (ρ_L − ρ_V) / ρ_V )

with σ the surface tension in dyne/cm (normalised to a 20 dyne/cm reference). The percentage of flood is then % flood = U_s / u_flood, where U_s is the operating vapour velocity on the same area basis; designers typically hold trays to ~80–85% of flood. Note the structural similarity to Souders-Brown — C_F·(σ/20)^0.2 plays the role of the separator K-factor.

5. Vortex breakers

As liquid drains from the bottom outlet, a vortex can form and pull gas down into the liquid line (gas blow-by / pump cavitation). The minimum liquid submergence above the outlet to prevent air-core vortexing follows the Hecker correlation adopted by ANSI/HI 9.8 (pump intake design):

S / d = 1 + 2.3 · Fr, Fr = V / √( g · d )

where S is the submergence, d the outlet diameter, V the outlet velocity and Fr the outlet Froude number. A flat-plate or cruciform vortex breaker over the nozzle then provides margin. (This Hecker/ANSI-HI 9.8 basis — not a vessel-internals standard such as API 660 — is the correct reference for the submergence relation.)

6. References

GPSA Engineering Data Book (14th Ed) — Section 7, Separators & Filters (Souders-Brown, K-factors, pressure derating, retention times).
API SPEC 12J — Specification for Oil and Gas Separators.
ANSI/HI 9.8 — Rotodynamic Pumps for Pump Intake Design (Hecker, 1987 — submergence vs Froude number).
Souders, M. & Brown, G.G. (1934) — entrainment / allowable vapor velocity.

Frequently Asked Questions

What is the Souders-Brown equation used for in separator design?

The Souders-Brown equation gives the maximum allowable vapor velocity, V_max = K·√((ρ_L−ρ_V)/ρ_V), from a droplet drag/gravity force balance. The required vessel cross-sectional area is the actual vapor flow divided by V_max.

How is the K-factor derated at elevated pressure?

The GPSA Engineering Data Book applies a percentage schedule to the base mesh or vane K: roughly 100% at atmospheric, 90% at 150 psig, 85% at 300 psig, 80% at 600 psig, and 75% at about 1,150 psig. The linear −0.01 per 100 psi rule is Manning's approximation and under-derates at high pressure.

What sets the flooding limit on a distillation tray?

Tray flooding is governed by the Fair flooding correlation, which gives a capacity factor C_F as a function of tray spacing and the flow parameter F_LV = (L/V)·√(ρ_V/ρ_L). Designers typically hold trays to about 80–85% of flood.

How much liquid submergence prevents vortexing at the outlet?

The minimum submergence to prevent an air-core vortex follows the Hecker correlation adopted by ANSI/HI 9.8: S/d = 1 + 2.3·Fr, where Fr = V/√(g·d). This pump-intake basis, not a vessel-internals standard such as API 660, is the correct reference.