Tray efficiency — real trays vs ideal stages

The same ethanol–water column solved with a Murphree vapor tray efficiency of 0.7 instead of ideal equilibrium stages. A real sieve/valve tray never reaches full vapor-liquid equilibrium — the vapor leaving it only partly approaches the equilibrium composition with the tray liquid, mixing in un-equilibrated vapor from the tray below: y = E·K·x + (1−E)·y_below (Murphree 1925). At E = 0.7 each of these 12 trays does 70% of an ideal stage's work, so the overhead ethanol is lower than an equilibrium column of the same tray count would predict — which is exactly why a real column needs more trays than a shortcut (ideal-stage) calculation says. Both HYSYS and Aspen RadFrac expose this per-tray efficiency; set murphree_efficiency back to 1.0 to recover the ideal-stage column. The efficiency auto-selects the component-flow Naphtali-Sandholm solver (the reduced-form solvers carry no explicit per-tray VLE row to apply an efficiency to).