Liquid–liquid shell-and-tube exchangers: what is the typical range of the ratio of tube length to shell diameter (L/Ds) used for design?

Introduction / Context:
The length-to-diameter ratio (tube length L versus shell inside diameter Ds) influences heat-transfer area packing, pressure drop, vibration control, and fabrication practicality in shell-and-tube exchangers. Liquid–liquid services typically allow moderate pressure drops and benefit from longer tubes for compact designs.

Given Data / Assumptions:

• Conventional TEMA construction with segmental baffles.
• Single-phase on both sides; non-fouling to moderately fouling liquids.
• Economically acceptable pressure-drop constraints.

Concept / Approach:
Short tubes increase shell diameter or number of shells for a given area, raising capital cost. Very long tubes raise vibration concerns and fabrication complexity. A balanced design for liquid–liquid duties often uses L/Ds ≈ 4–8, enabling practical layouts, good area density, and manageable pressure drops.

Step-by-Step Solution:
Consider trade-offs: longer tubes → fewer shells and heads but higher risk of vibration if unsupported; shorter tubes → larger shell diameter for same area.Industry heuristics place liquid–liquid duties in the mid-range of length ratios.Select 4 to 8 as the representative range.

Verification / Alternative check:
Design guides and vendor ratings frequently show liquid–liquid exchangers in L/Ds ranges of 4–8, with gas–gas duties often below 4 to limit pressure drop.

Why Other Options Are Wrong:
(a)–(b) are on the short side, leading to bulky shells; (d)–(e) are longer than commonly economical and can complicate supports and vibration control.

Common Pitfalls:
Ignoring allowable nozzle loads and support spans; overlooking cleaning access for longer tubes; not checking acoustic/vortex-induced vibration criteria.

Final Answer:
4 to 8