Knock-Out (KO) Drum Sizing: Gravity Separation Theory & Engineering Calculations

1. Executive Summary & Vessel Role

A Knock-Out Drum (KO Drum) is a critical gravity separation vessel engineered to safely disengage and retain bulk liquid droplets from a continuous or intermittent vapor stream. Found ubiquitously across upstream production, petroleum refining, and petrochemical facilities, KO drums serve as the primary defensive barrier upstream of flare stacks, relief headers, fuel gas networks, and reciprocating or centrifugal gas compressors.

Unlike high-efficiency gas scrubbers or filter separators, standard KO drums operate without mist eliminator pads, wire mesh coalescers, or complex internal tortuous paths. This intentional design simplicity provides two paramount operational advantages:

• Zero Plugging Risk: In relief and flare systems subject to coking, polymerizing compounds, heavy asphaltenic sludges, or particulate debris, internals can foul rapidly, causing catastrophic backpressure spikes during emergency relief events. KO drums provide reliable, unobstructed passage.
• Severe Liquid Slugging Protection: When two-phase lines experience hydrodynamic or terrain-induced liquid surges (slugs), the KO drum acts as an expansive surge accumulator, dampening volumetric shock waves before liquid can reach burners or rotating equipment.

2. Gravity Settling Physics & Droplet Mechanics

The core separation physics in a KO drum relies entirely on differential gravity settling: the upward or horizontal drag force exerted by the moving gas stream on an entrained liquid droplet must be overcome by the downward gravitational body force acting on the droplet.

2.1 Force Balance on an Entrained Droplet

Consider a spherical liquid droplet of diameter $d_p$ and density $\rho_l$ suspended in a gas stream of density $\rho_g$. Three collinear forces act on the droplet:

1. Gravitational Force ($F_g$): $$F_g = m_p g = \frac{\pi}{6} d_p^3 \rho_l g$$
2. Buoyancy Force ($F_b$): $$F_b = \frac{\pi}{6} d_p^3 \rho_g g$$
3. Hydrodynamic Drag Force ($F_d$): $$F_d = C_D A_p \left(\frac{1}{2} \rho_g v_{rel}^2\right) = C_D \left(\frac{\pi d_p^2}{4}\right) \left(\frac{1}{2} \rho_g v_{rel}^2\right)$$

where $C_D$ is the dimensionless drag coefficient, $A_p$ is the projected area of the spherical droplet, and $v_{rel}$ is the relative slip velocity between droplet and gas.

At terminal settling velocity ($v_t$), the net gravitational body force equals the drag force ($F_g - F_b = F_d$):

Solving directly for the terminal settling velocity yields the generalized terminal settling equation:

2.2 Drag Coefficient Regimes ($C_D$)

The drag coefficient $C_D$ is a function of the droplet Reynolds number, defined as:

Depending on $Re_p$, three distinct hydrodynamic regimes apply:

For industrial flare KO drums operating near atmospheric pressure, droplets in the critical cutoff range ($300\text{--}600\,\mu\text{m}$) typically settle within the Intermediate regime ($Re_p \approx 10\text{--}150$). Sizing based on pure Stokes' law severely overpredicts settling velocity, leading to undersized vessels and liquid carryover.

3. Souders-Brown Equation & Vessel Sizing Methodology

To generalize terminal velocity without requiring iterative Reynolds number convergence for every process perturbation, process engineers apply the classical Souders-Brown equation:

where $K_{SB}$ is the empirical Souders-Brown capacity factor ($m/s$ or $ft/s$).

3.1 Sizing Criteria: Open Drum vs. Demister Vessel

Unlike vertical scrubbers equipped with wire mesh demisters (which achieve $K \approx 0.107\,m/s$ or $0.35\,ft/s$), open KO drums must utilize substantially lower design $K$-values because gravity settling without coalescing media requires lower gas velocities to prevent re-entrainment:

• Flare KO Drum (API 521 Basis): Designed to disengage droplets $\ge 300\text{--}600\,\mu\text{m}$ diameter. Standard $K$-factor ranges from $0.046\text{--}0.076\,m/s$ ($0.15\text{--}0.25\,ft/s$). API 521 recommends verifying that droplets $\ge 300\,\mu\text{m}$ drop out before entering the flare stack to avoid "rain of fire" (burning droplets reaching grade).
• Compressor Suction KO Drum: Designed to drop out droplets $\ge 150\text{--}300\,\mu\text{m}$. Sized with $K$-factor from $0.035\text{--}0.055\,m/s$ ($0.12\text{--}0.18\,ft/s$).
• Fuel Gas KO Drum: Sized for $300\,\mu\text{m}$ droplet cutoff to protect burner tips from liquid impingement and smoke formation.

4. Horizontal vs. Vertical KO Drum Architecture

The choice between horizontal and vertical configurations depends primarily on the expected liquid-to-gas ratio and slug volume requirements:

4.1 Horizontal Vessel Dropout Geometry

In a horizontal KO drum, the droplet settling trajectory is two-dimensional. A droplet entering at the top of the vapor space at velocity $v_x$ must travel downward through height $H_v$ before the gas exits at distance $L$:

Therefore, the minimum required length-to-vapor height ratio is:

This allows horizontal drums to operate at gas velocities higher than the terminal settling velocity, provided the vessel is sufficiently long to achieve droplet capture.

5. Liquid Holdup, Slug Capacity & API 521 Relief Sizing

A flare KO drum must hold liquid originating from three distinct operational phenomena:

1. Sustained Emergency Relief: Liquid accumulated during a continuous major emergency flaring event (e.g., total plant power failure, cooling water loss). API 521 specifies sizing for 20 to 30 minutes of peak liquid relief without overflowing the high-liquid level trip (LAHH).
2. Slugging Allowance: Immediate slug volume from upstream header drainage or pipeline hydrodynamic slugs ($V_{slug}$).
3. Condensation / Rainout: Vapor condensation in long flare lines due to ambient cooling during standby conditions.

The total required liquid volume ($V_{liq}$) is partitioned into operational vertical zones:

• Slump Zone ($H_{LLL}$ to Bottom): Low-low level trip zone (minimum pump suction submergence to prevent cavitation and vortexing).
• Operating Volume ($H_{LLL}$ to $H_{NLL}$): Liquid inventory accumulated between automated pump-out cycles.
• Surge / Relief Volume ($H_{NLL}$ to $H_{HLL}$): Mandated 20–30 minute emergency accumulation capacity.
• Freeboard / Vapor Space ($H_{HLL}$ to Top Tangent): Vapor disengagement corridor maintained to ensure cross-sectional area $A_v$ keeps vapor velocity below $v_{max}$.

6. Nozzle Sizing & Momentum Flux Limits

Proper nozzle sizing prevents liquid shattering and re-entrainment at the inlet:

6.1 Inlet Nozzle Momentum Limit

The kinetic energy of the incoming two-phase stream must be controlled. API Standard 521 and GPSA define maximum momentum flux criteria:

where $\rho_m$ is the homogeneous mixture density $(\text{kg/m}^3)$ and $v_{in}$ is inlet nozzle velocity $(\text{m/s})$. Exceeding these limits shatters large liquid droplets into aerosol mists ($< 50\,\mu\text{m}$), defeating gravity settling.

6.2 Gas Outlet Nozzle Sizing

The vapor outlet nozzle is sized to keep pressure drop minimal during peak flaring:

Typical design velocities for flare KO drum vapor outlets range from $20\text{--}35\,\text{m/s}$ at atmospheric pressure.

7. Step-by-Step Worked Sizing Example (Flare KO Drum)

Design a horizontal flare knock-out drum to handle a catastrophic relief event with the following process parameters:

• Peak relief vapor mass flow: $W_g = 180{,}000\,\text{kg/h}$ ($50.0\,\text{kg/s}$)
• Vapor density at relief conditions: $\rho_g = 2.40\,\text{kg/m}^3$ (MW = 45 g/mol, $T = 40^\circ\text{C}$, $P = 1.35\,\text{bar a}$)
• Vapor dynamic viscosity: $\mu_g = 1.05 \times 10^{-5}\,\text{Pa}\cdot\text{s}$
• Hydrocarbon liquid density: $\rho_l = 680\,\text{kg/m}^3$
• Liquid relief accumulation rate: $Q_l = 45\,\text{m}^3\text{/h}$
• API 521 relief duration requirement: $t_{hold} = 20\,\text{minutes}$
• Target droplet cutoff diameter: $d_p = 400\,\mu\text{m} = 4.0 \times 10^{-4}\,\text{m}$

Step 1: Calculate Terminal Droplet Settling Velocity ($v_t$)

Assuming the intermediate settling regime applies, calculate $v_t$ using the intermediate regime correlation:

Now verify the droplet Reynolds number:

Since $2 \le Re_p \le 500$, the flow is confirmed in the Intermediate regime. The terminal settling velocity $v_t = 1.18\,\text{m/s}$ is valid.

Step 2: Determine Required Liquid Holdup Volume

For 20 minutes of sustained liquid relief:

Adding 15% allowance for dead inventory below low liquid level ($V_{LLL}$):

Step 3: Establish Vessel Cross-Sectional Geometry

Assume the liquid occupies 40% of the total vessel height ($h_L/D = 0.40$), leaving 60% of the height ($H_v/D = 0.60$) for vapor flow. From standard partial cylinder geometric tables:

• Liquid area fraction: $A_L / A_{total} \approx 0.374$
• Vapor area fraction: $A_v / A_{total} \approx 0.626$

The total vapor volumetric flow rate is:

Using an allowable maximum horizontal gas velocity $v_g \le 0.80 \times v_{crit}$, where:

Required vapor cross-sectional area:

Total vessel cross-sectional area required:

Corresponding internal diameter ($D$):

With split-flow geometry ($Q_g / 2 = 10.42\,\text{m}^3\text{/s}$ per side):

Step 4: Determine Vessel Length

For liquid volume of $17.25\,\text{m}^3$ with $A_L = 0.374 \times 17.52 = 6.55\,\text{m}^2$:

However, droplet settling requires:

Total tangent-to-tangent length with inlet distributor and end allowances: $L = 2 \times 2.28 + 2.5 = 7.06\,\text{m}$.

Vessel aspect ratio: $L/D = 7.06 / 4.72 = 1.50$ (well proportioned for structural saddles and seismic stability).

8. Common Operational Traps & Design Pitfalls

1. Sizing for Normal Flaring Instead of Worst-Case Emergency: Never size the KO drum on continuous purge rates. Sizing must be governed by the governing emergency scenario (e.g., total facility depressurization or utility failure) as documented in the plant relief analysis.
2. Freezing & Hydrate Blockage: High-pressure gas depressurizing across relief valves drops drastically in temperature due to the Joule-Thomson effect. Liquid hydrocarbons and water condensed in the drum can freeze or form solid clathrate hydrates. Flare KO drums require steam coils, electrical heat tracing, or glycol injection.
3. Omitting Vortex Breakers on Drain Nozzles: High pump-out flow rates can generate strong vortices in shallow liquid layers, pulling gas into the pump suction and causing air-binding or catastrophic mechanical seal failure.
4. Liquid Re-entrainment from Surface Waves: If the horizontal gas velocity exceeds critical interfacial shear velocity ($v_{crit} \approx 3\text{--}4\,\text{m/s}$), waves are stripped from the liquid surface, re-atomizing collected liquid into the flare stream.

9. ChemProCal Integration

To perform complete gravity separation modeling, use the following ChemProCal engineering calculators:

• Knock-Out Drum Sizing Tool: Compute exact terminal velocity, droplet trajectories, and vessel dimensions per API 521.
• Horizontal Separator Calculator: Complete 3-phase liquid-liquid-gas separation sizing.
• Separator Utilities: Compute partial cylinder volumes, liquid level heights, and head volumes.