Equipment Design

Separator Vessel Sizing

Size gas-liquid separators, scrubbers, and knockout drums using the Souders-Brown equation with pressure-corrected K-factors per GPSA Section 7 and API 12J.

Launch Calculator Souders-Brown Equation

Gas capacity

Souders-Brown

Terminal velocity determines minimum vessel diameter for mist elimination.

Liquid capacity

Retention Time

1-10 minutes typical depending on vessel type and separation difficulty.

Design standard

GPSA / API 12J

Industry-standard K-factors with pressure correction above 100 psig.

Contents

Use this guide when you need to:

  • Size horizontal two-phase or three-phase separators
  • Design gas scrubbers and knockout drums
  • Select appropriate mist eliminator type
  • Determine vessel dimensions for gas and liquid capacity

1. Separation Fundamentals

Gas-liquid separation is fundamental to midstream operations. Separators remove liquid droplets from gas streams and disengage gas from liquid. The sizing approach differs based on vessel function and the controlling design criteria.

Cutaway diagram of horizontal two-phase separator showing inlet diverter, gas flow path, liquid settling zone, mist eliminator, and outlet nozzles
Horizontal separator internals: Inlet device for bulk separation, settling zone for degassing, mist eliminator for fine droplet removal.

Vessel Types

Two-phase separator

Gas/Liquid

Separates gas from total liquid (oil + water mixed). Most common type in gas gathering systems.

Three-phase separator

Gas/Oil/Water

Separates gas, oil, and water into three streams. Requires longer retention time for oil/water separation.

Gas scrubber

Mist Elimination

Removes entrained liquid droplets from gas. Liquid is incidental; sized primarily for gas capacity.

Knockout drum

Slug Catching

Protects downstream equipment from liquid slugs. Sized for surge volume and quick gas-liquid disengagement.

Sizing Criteria

Separator sizing requires satisfying two independent criteria:

  1. Gas capacity: Vessel diameter must allow gas velocity low enough for liquid droplets to settle out. Governed by Souders-Brown equation.
  2. Liquid capacity: Vessel must hold sufficient liquid volume for required retention time. Governed by liquid flow rate and separation needs.

The final vessel size is determined by whichever criterion requires the larger vessel. For gas-dominated streams (scrubbers), gas capacity typically controls. For liquid-heavy streams (production separators), liquid capacity often controls.

Key concept: Separator sizing is a two-step process. First, calculate minimum diameter from gas capacity using Souders-Brown. Second, calculate minimum volume from liquid retention time. Use the larger requirement, then verify both criteria are satisfied with the final dimensions.

2. Souders-Brown Equation

The Souders-Brown equation determines the maximum allowable gas velocity through a separator. At velocities above this limit, liquid droplets become entrained in the gas stream and carry over to downstream equipment.

Terminal Velocity Equation

Souders-Brown Equation: Vt = K × √[(ρL - ρG) / ρG] Where: Vt = Terminal (allowable) gas velocity, ft/s K = Souders-Brown coefficient (empirical), ft/s ρL = Liquid density, lb/ft³ ρG = Gas density at operating conditions, lb/ft³ This equation is derived from Stokes Law for droplet settling, with the K-factor incorporating droplet size, drag coefficient, and equipment geometry empirically.

Physical Basis

The Souders-Brown equation balances gravity forces (causing droplets to settle) against drag forces (causing droplets to be carried upward with gas flow):

  • Gravity force: Proportional to droplet volume and density difference (ρL - ρG)
  • Drag force: Proportional to gas velocity squared and droplet cross-sectional area
  • At terminal velocity: Forces balance and droplet neither rises nor falls
Force balance diagram showing liquid droplet in upward gas flow with drag force, gravity force, and terminal velocity relationship per Souders-Brown equation
Droplet settling: At gas velocity below terminal velocity (Vt), gravity dominates and droplets settle out.

Gas Density Calculation

Gas Density at Operating Conditions: ρG = (P × M) / (Z × R × T) Where: P = Absolute pressure, psia (psig + 14.7) M = Gas molecular weight = SG × 28.97, lb/lbmol Z = Compressibility factor (from correlations) R = Gas constant = 10.73 psia·ft³/(lbmol·°R) T = Absolute temperature, °R (°F + 460) Example: Natural gas at 500 psig, 100°F, SG = 0.65 P = 514.7 psia, T = 560°R, M = 18.83 lb/lbmol Z ≈ 0.92 (from Standing-Katz correlation) ρG = (514.7 × 18.83) / (0.92 × 10.73 × 560) ρG = 9,692 / 5,527 = 1.75 lb/ft³

Vessel Diameter from Gas Capacity

Minimum Diameter Calculation: Step 1: Calculate actual gas volumetric flow rate Qactual = Qstd × (Pstd/P) × (T/Tstd) × Z Where: Qstd = Standard flow rate (scfd or MMscfd) Pstd = 14.7 psia, Tstd = 520°R (60°F) Step 2: Calculate allowable velocity Vt = K × √[(ρL - ρG) / ρG] Step 3: Calculate required gas flow area Agas = Qactual / Vt Step 4: Calculate diameter (for horizontal vessel at 50% liquid level) Agas = 0.5 × (π/4) × D² D = √(8 × Agas / π) The gas area fraction depends on normal liquid level: - 50% liquid level: gas occupies 50% of cross-section - 75% liquid level: gas occupies 25% of cross-section
Design velocity: Always design below terminal velocity to provide margin. Use 75% of Vt for separators (allows for upsets) and 85% for scrubbers (liquid is incidental).

3. K-Factors & Mist Eliminators

The K-factor is an empirical constant that accounts for droplet size, separation efficiency, and equipment internals. GPSA Section 7 provides K-factor values for different mist eliminator types.

Base K-Factor Values (GPSA)

Mist Eliminator Type K-Factor (ft/s) Droplet Removal Application
Wire mesh pad (standard) 0.35 99%+ of 10μm droplets Most common, general service
Wire mesh (high efficiency) 0.40 99%+ of 5μm droplets Higher capacity, clean service
Multi-cyclone 0.50 99%+ of 8μm droplets Highest capacity, fouling service
Vane pack (chevron) 0.20 99%+ of 15μm droplets Fouling/waxy service
Gravity only (no internals) 0.10 90%+ of 150μm droplets Dirty service, large droplets only
Four-panel comparison of mist eliminator types: wire mesh pad (K=0.35), vane pack (K=0.20), multi-cyclone (K=0.50), and gravity-only (K=0.10) with removal efficiencies
Mist eliminator selection: Wire mesh for general service; vane pack for fouling; multi-cyclone for high capacity.

Pressure Correction Factor

K-factors decrease at higher pressures due to increased gas density reducing the density difference term. GPSA provides correction factors:

Pressure (psig) Correction Factor Pressure (psig) Correction Factor
0 - 100 1.00 700 0.82
200 0.97 800 0.79
300 0.94 900 0.77
400 0.91 1000 0.75
500 0.88 1200 0.71
600 0.85 1500 0.65
Corrected K-Factor: Kcorrected = Kbase × Cp Example: Wire mesh at 800 psig Kcorrected = 0.35 × 0.79 = 0.277 ft/s This represents a 21% reduction in allowable velocity compared to low-pressure service, requiring a larger vessel diameter.
Chart showing K-factor pressure correction factor declining from 1.0 at low pressure to 0.65 at 1500 psig per GPSA guidelines
K-factor pressure correction: High-pressure separators require larger diameters due to reduced density difference.

Mist Eliminator Selection Guidelines

  • Wire mesh: Default choice for clean gas service. Low cost, easy maintenance, reliable performance.
  • Vane pack: Preferred for waxy crude, paraffin deposition, or fouling service. Self-draining design prevents flooding.
  • Multi-cyclone: Maximum capacity for high gas rate applications. Good for sandy or particulate-laden streams.
  • No internals: Only for very dirty service or when large droplets (>150μm) dominate. Requires larger vessel.
Flooding risk: Wire mesh pads can flood (liquid accumulation blocks gas flow) if operated above design velocity or with foaming liquids. Design velocity should include 20-25% margin below calculated terminal velocity to prevent flooding during upsets.

4. Liquid Retention Time Sizing

Liquid capacity sizing ensures adequate residence time for gas to disengage from liquid (degassing) and, for three-phase separators, for oil and water to separate by gravity settling.

Retention Time Guidelines

Vessel Type Minimum (min) Typical (min) Difficult Service (min)
Two-phase separator 1 2-3 5 (foamy oil)
Three-phase separator (oil) 3 5 10-20 (emulsion)
Three-phase separator (water) 3 5 10 (tight emulsion)
Gas scrubber 0.5 1 2
Knockout drum 1 2 5 (slug catching)

Liquid Volume Calculation

Required Liquid Volume: Vliquid = Qliquid × tretention Where: Vliquid = Liquid holdup volume, ft³ Qliquid = Liquid flow rate, ft³/min tretention = Retention time, minutes For horizontal vessel with liquid fraction fL: Vliquid = fL × (π/4) × D² × L Rearranging for length: L = Vliquid / [fL × (π/4) × D²] Typical liquid fractions: - Two-phase separator: fL = 0.50 (50% full) - Three-phase separator: fL = 0.60 (60% full) - Scrubber: fL = 0.25 (25% full)

Three-Phase Oil/Water Separation

In three-phase separators, oil and water separate by gravity based on density difference. The settling velocity for water droplets in oil (or oil droplets in water) follows Stokes Law:

Stokes Law Settling Velocity: Vs = g × d² × (ρw - ρo) / (18 × μo) Where: Vs = Settling velocity, ft/s g = Gravitational acceleration = 32.2 ft/s² d = Droplet diameter, ft ρw = Water density, lb/ft³ ρo = Oil density, lb/ft³ μo = Oil viscosity, lb/(ft·s) Example: 200μm water droplet in 30 cp oil, SG = 0.85 d = 200 × 3.28×10⁻⁶ = 6.56×10⁻⁴ ft ρw = 62.4 lb/ft³, ρo = 53.0 lb/ft³ μo = 30 × 6.72×10⁻⁴ = 0.0202 lb/(ft·s) Vs = 32.2 × (6.56×10⁻⁴)² × (62.4 - 53.0) / (18 × 0.0202) Vs = 32.2 × 4.3×10⁻⁷ × 9.4 / 0.364 Vs = 3.6×10⁻⁴ ft/s = 0.022 ft/min For 2 ft settling distance, time = 2 / 0.022 = 91 minutes This illustrates why viscous oil requires long retention times or heated separators to achieve oil/water separation.
Emulsion treatment: Tight water-in-oil emulsions may require chemical demulsifier injection, heat (typically 140-180°F), or electrostatic treaters rather than simply increasing retention time. The calculator assumes reasonable separation; difficult emulsions need specialized equipment.

5. Design Examples

Example 1: Two-Phase Separator

Given: Gas flow: 10 MMscfd Liquid flow: 1000 bpd Operating pressure: 300 psig Operating temperature: 80°F Gas gravity: 0.65 (air = 1) Liquid gravity: 0.85 (water = 1) Mist eliminator: Wire mesh (K = 0.35) Retention time: 3 minutes Target L/D: 3 Step 1: Gas Properties Pabs = 300 + 14.7 = 314.7 psia Tabs = 80 + 460 = 540°R M = 0.65 × 28.97 = 18.83 lb/lbmol Z ≈ 0.94 (calculated) ρG = (314.7 × 18.83) / (0.94 × 10.73 × 540) = 1.09 lb/ft³ ρL = 0.85 × 62.4 = 53.0 lb/ft³ Step 2: K-Factor Correction Kbase = 0.35 ft/s Cp = 0.94 (at 300 psig, interpolated) Kcorrected = 0.35 × 0.94 = 0.329 ft/s Step 3: Terminal Velocity Vt = 0.329 × √[(53.0 - 1.09) / 1.09] Vt = 0.329 × √47.6 = 0.329 × 6.90 = 2.27 ft/s Design velocity (75%): Vdesign = 0.75 × 2.27 = 1.70 ft/s Step 4: Gas Volumetric Flow Qactual = 10×10⁶ × (14.7/314.7) × (540/520) × 0.94 / 86,400 Qactual = 10×10⁶ × 0.0467 × 1.038 × 0.94 / 86,400 Qactual = 5.28 ft³/s Step 5: Diameter from Gas Capacity Gas area fraction = 0.50 (at 50% liquid level) Agas = Qactual / Vdesign = 5.28 / 1.70 = 3.11 ft² Atotal = 3.11 / 0.50 = 6.21 ft² D = √(4 × 6.21 / π) = 2.81 ft → Round to 3.0 ft (36") Step 6: Liquid Volume Required Qliquid = 1000 bpd × 5.615 ft³/bbl / 1440 min/day = 3.90 ft³/min Vliquid = 3.90 × 3 min = 11.7 ft³ Step 7: Length from Liquid Capacity At D = 3 ft, liquid area = 0.50 × π × 3²/4 = 3.53 ft² Lliquid = 11.7 / 3.53 = 3.3 ft Step 8: Length from L/D Ratio LL/D = 3.0 × 3 = 9.0 ft Step 9: Final Sizing Use L = 9.0 ft (L/D controls) Final: D = 3.0 ft (36"), L = 9.0 ft seam-to-seam Verification: Actual gas velocity = 5.28 / (0.50 × 7.07) = 1.49 ft/s Velocity utilization = 1.49 / 2.27 = 66% ✓ Actual liquid volume = 0.50 × 7.07 × 9.0 = 31.8 ft³ Volume utilization = 11.7 / 31.8 = 37% ✓

Example 2: High-Pressure Scrubber

Given: Gas flow: 50 MMscfd Liquid flow: 50 bpd (incidental) Operating pressure: 1000 psig Operating temperature: 100°F Gas gravity: 0.70 Mist eliminator: Multi-cyclone (K = 0.50) Calculation Summary: Pabs = 1014.7 psia, Tabs = 560°R Z ≈ 0.86 ρG = 4.05 lb/ft³ (high pressure = high density) ρL = 53.0 lb/ft³ Kcorrected = 0.50 × 0.75 = 0.375 ft/s (at 1000 psig) Vt = 0.375 × √[(53.0 - 4.05) / 4.05] = 1.32 ft/s Note: High pressure significantly reduces terminal velocity (compare to 2.27 ft/s at 300 psig) Qactual = 50×10⁶ × (14.7/1014.7) × (560/520) × 0.86 / 86,400 Qactual = 7.25 ft³/s Gas area (75% available for scrubber): Agas = 7.25 / (0.85 × 1.32) = 6.46 ft² Atotal = 6.46 / 0.75 = 8.61 ft² D = 3.31 ft → Round to 3.5 ft (42") L = 3.5 × 3 = 10.5 ft Final: D = 3.5 ft (42"), L = 10.5 ft seam-to-seam

L/D Ratio Guidelines

L/D Ratio Assessment Notes
< 2.5 Poor Inadequate gas/liquid separation, maldistribution
2.5 - 4.0 Optimal Recommended range per GPSA
4.0 - 6.0 Acceptable May be needed for high liquid loading
> 6.0 Not Recommended Expensive, difficult to ship, consider parallel vessels
Standard sizes: Select vessel diameter from API 12J standard sizes: 12", 16", 20", 24", 30", 36", 42", 48", 54", 60", 72", 84", 96", 108", 120", 144". Using standard sizes reduces fabrication cost and delivery time.

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