Packed Column Height from HTU and NTU

A tray column has a natural unit of height — the tray — and a packed column has none. Packing is continuous, so the stage concept has nothing to attach to. Chilton and Colburn's transfer-unit idea solves this elegantly by splitting the height into two factors that answer genuinely different questions: $Z = H_{OG} N_{OG}$, where the NTU says how hard the separation is and the HTU says how good this packing is at it.

The division of labour is the reason the method has lasted. The number of transfer units is thermodynamic — it depends on the equilibrium relationship, the flow ratio and the purity demanded, and no supplier can change it. The height of a transfer unit is equipment — it depends on the packing type and size, the wetting, the flow rates and the distribution, and it is precisely what a supplier sells. Ask for a purer product and NTU rises. Buy better packing and HTU falls. Keeping them separate means a change in one does not require recalculating the other, and it lets a packing be quoted as a single number in metres that means something across applications.

Typical HTU values run from about 0.3 to 1 metre for random packings such as Pall rings, and lower for structured packing, which is much of what you are paying for when you buy it. But an HTU is not a property of the packing alone: it depends on the flow rates, and it degrades sharply if the liquid distribution is poor, if the packing is not properly wetted, or if the column is operating far from its design loading. A supplier's quoted HTU assumes good distribution, and poor distribution is the most common reason a real column underperforms its design.

Two practical points about the height that comes out. Beyond roughly 5 to 10 metres — or about ten column diameters for random packing — liquid drifts to the wall as it descends and the centre of the bed stops being wetted, so tall columns are built as several beds with redistributors between them. And the calculated $Z$ is packing only: distributors, supports, the sump, the disengagement space and the nozzles all add height that is column but not packing, and a vessel quoted from this number alone will be short.