Packed towers: liquid distribution difficulties are accentuated when the ratio (tower diameter / packing size) is especially small. Which range indicates greatest difficulty?

Introduction / Context:
Uniform liquid distribution at the top of a packed tower is crucial to achieve design mass-transfer performance. A key geometric parameter is the ratio of tower diameter (Dt) to packing characteristic size (dp). When Dt/dp is too small, edge effects and insufficient drip points create severe maldistribution.

Given Data / Assumptions:

• Random or structured packings used in countercurrent gas–liquid contact.
• Conventional top liquid distributor.
• We assess qualitative difficulty as Dt/dp decreases.

Concept / Approach:
Rules of thumb suggest that to minimize wall effects and ensure multiple liquid drip points across the cross-section, Dt should be many times larger than packing size. If Dt/dp falls below roughly 8–10 for random packings, uniform distribution becomes difficult; fewer drip points and proximity to the wall lead to channeling and reduced efficiency.

Step-by-Step Solution:
Relate difficulty to Dt/dp: smaller ratios mean fewer packing elements across the diameter.Identify the “worst” among choices: values below ~7 are most prone to maldistribution.Select the range indicating greatest difficulty: < 7.

Verification / Alternative check:
Design guides specify minimum tower diameters for a given packing to keep Dt/dp above a threshold, and recommend special distributors or re-distributors if the ratio is small.

Why Other Options Are Wrong:
< 30 or ranges > 7: these provide many packing elements across the diameter, easing distribution compared with < 7.

Common Pitfalls:
Using standard trough distributors in small columns; not accounting for wall flow; ignoring need for re-distribution on tall beds.

Final Answer:
< 7