Shortcut column sizing (Fenske-Underwood-Gilliland)

Before anyone builds a rigorous column they size it in about a second, and this is that step — Aspen's DSTWU, the calculation every distillation design starts from. State the two keys and how well you want them separated, and the shortcut answers the four questions that set the capital cost. For a depropaniser feed (30% propane, 40% n-butane, 30% n-pentane) at 10 bar recovering 98% of the propane overhead and 98% of the n-butane in the bottoms: Fenske gives 8.34 minimum stages — the count at total reflux, where you spend infinite energy to buy the fewest trays. Underwood gives a minimum reflux of 1.54 — the reflux at infinite stages, the opposite corner. Neither is buildable; the real column lives between them, and Gilliland interpolates: at 1.3x the minimum reflux you need 17.7 theoretical stages, with Kirkbride putting the feed on stage 7.85. That is a little over twice the minimum stage count for 1.3 times the minimum reflux, which is the trade every column is designed on. The energy follows: 1.67 MW reboiler against a 1.35 MW condenser. Bounded, and this is the important part. These are screening numbers, not a design. The shortcut assumes constant relative volatility and constant molal overflow — it cannot see a pinch, a tangent, an azeotrope, or a temperature profile. Its job is to give a rigorous MESH column a starting point that converges, not to replace it. Run the distillation unit op on 18 stages with a feed at 8 to check it.