Distillation & Fractionation Design

1. The FUG shortcut method

Before rigorous tray-by-tray simulation, columns are scoped with the Fenske-Underwood-Gilliland (FUG) shortcut: Fenske gives the minimum number of stages at total reflux, Underwood gives the minimum reflux ratio at infinite stages, and Gilliland correlates the real column operating between those two limits. It is a screening tool — fast, transparent, and good for first sizing — but it assumes constant relative volatility and constant molar overflow.

2. Fenske — minimum stages

where LK/HK are the light and heavy key components, the subscripts D/B the distillate and bottoms, and α the relative volatility between the keys (geometric-mean across the column). N_min is the stage count at total reflux — the theoretical floor.

3. Underwood — minimum reflux

Underwood solves for the root θ (lying between the key components' volatilities) of:

where z_i,F are feed compositions, x_i,D distillate compositions, and q the feed thermal condition. Caveat: for a true multicomponent separation the first equation can have multiple roots and distributing non-key components; collapsing it to a single binary key-only root (and clamping it) can under-predict R_min and therefore under-size the column. Treat the binary form as a screening approximation and confirm wide or non-sharp splits in a rigorous simulator.

4. Gilliland — actual stages

Real columns run at R = (1.1–1.5)·R_min. The Gilliland correlation ties the operating reflux to the actual stage count:

(Molokanov form). Kirkbride's equation then estimates the feed-stage location. The reflux choice is the central economic trade-off: more reflux → fewer trays (smaller vessel) but more reboiler/condenser duty and a larger diameter (higher vapour load).

5. Condensate stabilization

A condensate stabilizer is a fractionation column (often reboiled, sometimes cold-feed) that strips light ends (C₁–C₄, H₂S) from raw condensate to hit a Reid Vapor Pressure (RVP) or true-vapor-pressure spec so the liquid can be stored/transported safely without flashing. It is sized by the FUG/hydraulics methods above, with the bottoms RVP as the separation target and overhead recovery balancing product loss against vapour-handling.

6. Tray hydraulics

Stage count comes from FUG; column diameter comes from tray hydraulics. The vapour capacity uses the same Souders-Brown form as separators, with a system/flooding factor:

where C_SB (the capacity factor) depends on tray spacing and the flow-parameter F_LV = (L/V)·√(ρ_V/ρ_L) (Fair correlation). The operating window is bounded above by jet flooding and downcomer flooding/backup, and below by weeping/dumping; weir loading and downcomer residence time must also be checked. A tray that passes the stage count but fails hydraulics either floods or weeps.

7. References

• GPSA Engineering Data Book (14th Ed) — Section 19, Fractionation & Absorption (FUG method, tray hydraulics, Fair correlation).
• Fenske (1932); Underwood (1948); Gilliland (1940); Molokanov et al. — Gilliland correlation fit; Kirkbride — feed-stage location.
• Fair, J.R. — tray flooding / capacity-factor correlation.
• King, C.J., Separation Processes; Kister, H.Z., Distillation Design.