How do you determine the number of stages and feed location for a multicomponent distillation column?

For multicomponent systems, shortcut methods include Fenske equation (minimum stages at total reflux), Underwood equations (minimum reflux), and Gilliland correlation (actual stages from R/Rmin). The Kirkbride equation estimates feed stage: log(NR/NS) = 0.206*log[(B/D)(xHK,F/xLK,F)^2(xLK,B/xHK,D)]. Rigorous methods use stage-by-stage calculations with equilibrium and material balances, typically via process simulators (Aspen, HYSYS) with MESH equations.