1. Souders-Brown Terminal Settling Velocity
The maximum gas velocity through a vertical separator before bulk liquid entrainment occurs is governed by the Souders-Brown equation, derived from a balance between upward aerodynamic drag and downward gravitational settling:
\[ v_{max} = K \cdot \sqrt{\frac{\rho_L - \rho_g}{\rho_g}} \]
where \(K\) is the design empirical separation factor (m/s or ft/s), \(\rho_L\) is liquid density, and \(\rho_g\) is gas density. Actual superficial gas velocity in the vessel is:
\[ v_g = \frac{Q_{actual}}{A_{vessel}} = \frac{4 \cdot Q_{actual}}{\pi \cdot D_i^2} \]
2. Gas Kinetic Energy & \(F\)-Factor
Gas momentum and mist re-entrainment potential are characterized by the Gas \(F\)-factor:
\[ F = v_g \cdot \sqrt{\rho_g} \quad \left[\text{Pa}^{0.5} \text{ or } \frac{\text{m}}{\text{s}} \cdot \sqrt{\frac{\text{kg}}{\text{m}^3}}\right] \]
For standard knitted mesh pads, exceeding \(F > 2.5\text{ Pa}^{0.5}\) causes shear stripping and catastrophic liquid re-entrainment.
3. Debottlenecking Capacity Multiplier
The brownfield capacity gain achievable by upgrading internal mist elimination technologies at constant vessel diameter is:
\[ \text{Capacity Multiplier} = \frac{K_{new}}{K_{current}} \qquad \Delta Q_{\%} = \left( \frac{K_{new}}{K_{current}} - 1 \right) \times 100\% \]