Overall Column Efficiency

Every stage calculation in distillation returns theoretical stages, and a theoretical stage is a fiction: a device in which the leaving vapour and the leaving liquid are in perfect equilibrium. Real trays do not achieve that, so real columns need more trays than the theory asked for. Overall column efficiency is the single number that bridges the calculation and the purchase order.

Trays fall short for reasons that are all mechanical rather than thermodynamic. The liquid crossing a tray has only seconds of contact with the vapour bubbling through it, which is often not long enough to approach equilibrium. Some vapour weeps through the holes without contacting properly. Some liquid is entrained upward in the spray. And liquid can short-circuit across a wide tray rather than mixing, so parts of it never see fresh vapour at all.

O'Connell gave the correlation still used for a first estimate in 1946: efficiency falls as the product of relative volatility and liquid viscosity rises. The physical reading is sensible in both terms — a viscous liquid transfers mass slowly, and a high $\alpha$ means each stage is being asked to make a bigger composition jump. Ordinary hydrocarbon and alcohol-water distillations land somewhere between 50 and 80 per cent. Absorbers and strippers are far worse, often 15 to 40 per cent, so a figure quoted without saying which duty it came from is not usable.

Three counting rules save more grief than the correlation does. The reboiler is a theoretical stage but it is not a tray, so take it out of the theoretical count before dividing. A partial condenser is a stage too; a total condenser is not. And always round the answer up — trays come whole, and a column one tray short of its duty cannot be fixed without opening it. Most designers go further and add ten to twenty per cent over the calculated count, which buys margin against the scatter in the efficiency estimate, margin against the scatter in whatever correlation produced the theoretical count, and turndown for the day the feed drifts. Trays are cheap while the shell is on the ground and very expensive afterwards. Packed columns are not measured this way at all: they use HETP, the height of packing equivalent to one theoretical plate, and an efficiency figure quoted for packing usually means somebody has converted an HETP into one.