Engineering task and calculation objective
The L2.7 module calculates the wet pressure drop and the weeping limit (rain-through) of column trays according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for thermal separation and fluid flow. In tray columns for distillation and absorption, the gas flows upward through the holes of the tray and through the liquid layer; the total pressure drop is composed of the dry share (flow through the holes) and the wet share (penetrating the two-phase layer on the tray). Weeping denotes the lower load limit below which liquid rains through the holes and the tray loses its separation performance.
The column designer needs this calculation for every hydraulic tray design: the tray-by-tray pressure drop determines the total pressure drop of the column (and thus, in vacuum distillation, the bottoms temperature), while the load limits — weeping or rain-through at the bottom, flooding and droplet entrainment at the top — define the permissible operating range of the tray. The operating-range check is also mandatory for rating calculations at changed operating conditions (turndown, load changes).
The method starts from the hole geometry of the sieve tray — plate thickness, hole diameter, hole count and relative free area — and calculates the dry pressure drop via hole velocity, Reynolds number and loss coefficients. The wet share follows from the height and density of the two-phase layer, which is determined from weir height, weir length and liquid volume flow; via the critical Weber number and droplet diameter, the maximum gas load is additionally assessed.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Record the tray geometry: Plate thickness, hole diameter and hole count are entered, from which the total hole area and the relative free area of the tray follow. These quantities define how strongly the gas is accelerated as it passes through.
- Calculate the dry pressure drop: From the gas volume flow and the hole area, the velocity in the hole follows; with the gas density and viscosity, the hole Reynolds number results. The loss coefficient of the hole is determined from the correlations of the VDI Heat Atlas — depending on the ratio of plate thickness to hole diameter and the Reynolds number, with correction and weighting factors between the equation ranges. This yields the dry pressure drop of the unirrigated tray.
- Determine the two-phase layer on the tray: From the height and length of the outlet weir and the liquid volume flow, the height of the two-phase layer on the tray is calculated; its liquid volume fraction, together with the liquid density, determines the wet pressure-drop share that the gas must overcome while bubbling through.
- Form the total pressure drop: The dry and wet shares are added to give the total pressure drop of the tray. Multiplied by the number of trays, the total hydraulic pressure drop of the column results — a hard design criterion for vacuum columns.
- Check the load limits: Via the drag coefficient of droplets in the gas stream, the critical Weber number and the droplet diameter, the maximum gas load is determined, above which droplet entrainment and flooding threaten. At the lower end, the weeping limit is checked: if the gas load falls below the minimum value, the gas stream can no longer hold the liquid on the tray and it rains through the holes.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Plate thickness | s | mm |
| Hole diameter | dh | mm |
| Ratio s/dh | s/dh | - |
| Number of holes | NLoch | - |
| (Sum) hole cross section | Ah | m² |
| Relative free cross section | φ | - |
| Corresponding plate surface | A | m² |
| Superficial velocity | wG | m/s |
| Hole velocity | wh | m/s |
| Density gas | ρG | kg/m³ |
| Dyn. viscosity gas | ηG | mPa·s |
| Reynolds number (hole) | Reh | - |
| Correction factor for ζ0 | Zeta0 | - |
| Drop factor | (φ→0) ζ0 | - |
| Drop factor (Eq. 16, | s/dh→0) ζ1 | - |
| Drop factor (Eq. 17, | s/dh>>0) ζ2 | - |
| Weighting factor | exp(-s/dh) gew | - |
| Drop factor hole | ζ | - |
| Drop factor related to | Aak | - |
| Dry pressure drop | ΔPtr | Pa |
| Fricton factor sphere | ζK | - |
| Density liquid | ρL | kg/m³ |
| Dyn. viscosity liquid | ηL | mPa·s |
| Surface tension | σ | N/m |
Frequently asked questions
What exactly does 'weeping' of a column tray mean?
On sieve trays, only the dynamic pressure of the gas flowing through holds the liquid on the tray. If the gas load drops below a limit, liquid drips or rains through the holes (weeping); in the extreme case, the tray empties. The liquid then bypasses the intended path over the outlet weir, the cross-flow contact collapses and the tray efficiency falls drastically.
Why is the wet pressure drop greater than the static height of the clear liquid?
On the contrary, it is generally smaller: what stands on the tray is not clear liquid but a gas-laden froth layer whose mean density lies well below the liquid density. The governing quantity is the product of the height of the two-phase layer, the liquid volume fraction and the liquid density. Anyone who calculates with the clear weir height and full density systematically overestimates the wet share.
What role does the ratio of plate thickness to hole diameter play?
The ratio s/dh determines the jet contraction and reattachment in the hole and thus the loss coefficient of the dry tray: thin plates with sharp-edged holes have higher loss coefficients than thick plates in which the flow reattaches. The correlations of the VDI Heat Atlas interpolate with a weighting factor between the equations for the two limiting cases.
How are operating range and turndown flexibility of a sieve tray related?
The permissible operating range lies between the weeping/rain-through limit at the bottom and the entrainment/flooding limit at the top. Sieve trays inherently have a narrower turndown range than valve trays because the free area is fixed. With strongly fluctuating loads, the tray must be designed so that even the turndown point lies above the weeping limit — or a different tray type must be chosen.