Bubble-cap tray hydraulics: in common practice, how are the riser annulus area and the slot area sized relative to each other to balance vapor traffic and pressure drop?

Introduction / Context:
Bubble-cap trays use risers and caps with slots to distribute vapor into the liquid layer. Relative sizing of the riser annulus and cap slot areas determines the local pressure drop and the uniformity of vapor distribution across the tray.

Given Data / Assumptions:

• Aa denotes the annular cross-sectional area between riser and cap skirt.
• Sa denotes the total slot flow area on the cap.
• Normal turndown ratios and hydrostatic submergence are assumed.

Concept / Approach:
For steady operation, designers seek comparable flow restrictions in the annulus and through the slots so neither feature chokes the vapor. Making these areas approximately equal helps keep the pressure drop contributions balanced and reduces sensitivity to fouling or minor fabrication tolerances.

Step-by-Step Solution:

Verification / Alternative check:
Tray design guides commonly present relations where Aa and Sa are of similar magnitude, followed by final tuning with vendor correlations.

Why Other Options Are Wrong:

• Large mismatches (1.5× either way) unnecessarily shift pressure drop to one element, increasing sensitivity and risking maldistribution.
• Scaling statement “1.2 Aa = 1.2 Sa” adds no information beyond equality and is not a standard guideline.

Common Pitfalls:
Oversizing slots leading to weeping at low vapor rates; too small annulus causing excessive ΔP and entrainment.

Final Answer:
Aa = Sa (annular passage area approximately equals slot area)