Engineering & Science
Souders-Brown Equation: Knockout-Drum Max Vapor Velocity & Diameter
Size vertical vapor-liquid flash drums, demister pads, and distillation columns against droplet entrainment using V_max = K_SB * SQRT((rho_L - rho_V) / rho_V) (m/s) and minimum vessel inside diameter D_min.
Prevent liquid droplet carryover into compressors with Souders & Brown’s settling balance!
Entraining liquid hydrocarbon or water droplets out the top of a suction knockout drum shatters reciprocating and centrifugal compressor impellers! Mott Souders Jr. and George Granger Brown (Industrial & Engineering Chemistry 1934) balanced upward gas drag against downward Stokes/Newtonian gravity settling of liquid droplets to establish the maximum allowable superficial vapor velocity: V_max = K_SB * SQRT((rho_L - rho_V) / rho_V), where rho_L and rho_V are operating liquid and vapor densities (kg/m^3) and K_SB (m/s) is the Souders-Brown sizing factor (~0.06 m/s for bare gravity drums, ~0.107 m/s with knitted wire-mesh demister pads per GPSA)!
Once V_max is known, volumetric gas flow Q_V (m^3/s at actual T, P) sets minimum vessel inside diameter D_min = SQRT((4 * Q_V) / (PI() * V_max))! For a wire-mesh flash separator (K_SB = 0.107 m/s) separating condensate (rho_L = 780 kg/m^3) from natural gas at moderate pressure (rho_V = 18.5 kg/m^3, Q_V = 4.20 m^3/s), V_max = 0.686 m/s and D_min = 2.791 m; compressing to higher gas density rho_V = 45.0 kg/m^3 increases vapor buoyancy/drag, dropping V_max to 0.432 m/s!
| Separator Operating Pressure (rhoL = 780 kg/m^3, K_SB = 0.107 m/s) | Density Ratio (rhoL - rhoV) / rhoV | Max Vapor Velocity V_max (m/s) | Min Vessel ID D_min (Q_V = 4.2 m^3/s) |
|---|---|---|---|
| Moderate Pressure Gas (rhoV = 18.5 kg/m^3) | 41.16 | 0.686 m/s | 2.791 m |
| High-Pressure Dense Gas (rhoV = 45.0 kg/m^3) | 16.33 | 0.432 m/s | 3.517 m |
| Supercritical Singularity (rhoL <= rhoV) | Phase-Density Guard | "Invalid Phase Densities" | Requires rho_L > rho_V > 0 |
Maximum Allowable Superficial Vapor Velocity V_max (m/s)
Evaluates K_SB * SQRT((rho_L - rho_V) / rho_V) while guarding rho_L <= rho_V.
=IF(OR(B2 <= 0, B4 <= 0, B3 <= B4, B5 <= 0), "Invalid Phase Densities", ROUND(B2 * SQRT((B3 - B4) / B4), 3))Minimum Vertical Knockout-Drum Inside Diameter D_min (m)
Sizes vessel cross-sectional diameter SQRT((4 * Q_V) / (PI() * V_max)) from actual volumetric gas flow B5 (m^3/s).
=IF(OR(B2 <= 0, B4 <= 0, B3 <= B4, B5 <= 0), "Invalid Phase Densities", ROUND(SQRT((4 * B5) / (PI() * (B2 * SQRT((B3 - B4) / B4)))), 3))Try the example
Use the original values or change them to test your understanding.