Tray efficiency: 20 real trays are not 20 stages

Every equilibrium column model quietly assumes each tray reaches equilibrium. Real trays do not, and the gap is not small enough to ignore when you are buying a shell. The same depropaniser is solved twice at 20 trays, a 2.5 reflux ratio and a 50/50 split. As 20 equilibrium stages it puts 99.61% propane overhead. As 20 actual trays on the rate-based model it manages 96.63% — the tower is the same height and the separation is measurably worse, because the model applies an efficiency instead of assuming one. Left to itself it derives that efficiency from the feed's relative volatility and liquid viscosity through the O'Connell correlation; give it a stage_efficiency and it uses yours, and at a punishing Murphree 0.5 the overhead drops further to 95.33%. The practical reading: an equilibrium model sized this column at 20 trays and the tray efficiency spent roughly three points of product purity. Size on equilibrium stages and you will under-build the tower — that is what the efficiency is for. Bounded: this applies a single overall efficiency to every tray, which is a screening treatment. It is not a rigorous rate-based column — for genuine two-film Maxwell-Stefan transfer with per-stage interface composition and energy coupling, use nonequilibrium_distillation instead. O'Connell itself is a correlation fitted to commercial tray data, so it carries that scatter.