Tray hydraulics: what is the recommended maximum liquid height gradient across a tray to avoid maldistribution and weeping?

Introduction / Context:
Liquid flows across distillation trays from the inlet downcomer to the outlet weir. Excessive liquid height gradient (difference between inlet and outlet liquid levels) can cause non-uniform froth, premature weeping near the outlet, and reduced mass-transfer efficiency. Designers therefore limit the permissible gradient.

Given Data / Assumptions:

• Conventional sieve/valve trays with typical weir heights and tray spacings.
• Moderate vapour and liquid rates; no extreme foaming assumed.
• Gradient expressed in inches of liquid height across the tray.

Concept / Approach:
A modest gradient ensures adequate residence time and even contacting. Industry practice uses limits roughly around an inch, recognizing that higher gradients promote maldistribution and increased entrainment or weeping. The exact limit is tuned during detailed design but remains in this narrow band.

Step-by-Step Solution:
Identify typical design target: keep gradient below about 1–1.25 inches.Relate to hydraulics: higher vapour rates raise froth density variations and increase gradient; weir cresting adds to outlet head.Select the answer band that captures accepted practice: 0.5"–1.25".

Verification / Alternative check:
Tray rating programs and vendor guidelines often flag gradients above ≈1–1.5 inches as risk points depending on tray spacing and L/V ratios.

Why Other Options Are Wrong:
2"–3.5" and 5" are excessive for most services and would indicate maldistribution; “half the tray spacing” is unrelated; “no limit” is unsafe.

Common Pitfalls:
Confusing gradient with weir height; overlooking that increased vapour rates raise froth height and can aggravate gradients.

Final Answer:
0.5" – 1.25"