Rotary dryers: for typical length-to-diameter (L/D) ratios between 4 and 10, what is the usual economic range of the number of transfer units (NTU) targeted in design and operation?

Introduction / Context:
Rotary dryers are widely used in chemical, fertilizer, mineral, and food industries to remove moisture from granular or lumpy solids. A convenient way to describe gas–solid contact performance is by the number of transfer units (NTU), which relates the driving force for mass transfer to the overall drying achieved. Designers aim for an NTU range that balances capital cost (drum length, lifters, gas heater size) and operating cost (fuel, fan power) while safeguarding product quality.

Given Data / Assumptions:

• Cylindrical, flighted rotary dryer operating in steady state.
• Length-to-diameter ratio, L/D, between 4 and 10.
• Free-flowing, non-sticky solids; conventional gas temperatures; no special internals beyond standard lifters.

Concept / Approach:
NTU for drying expresses the extent of approach to equilibrium between bulk gas humidity and the solid moisture. Too small NTU underdries the product and makes operation sensitive to feed variability; too large NTU implies excessive residence time, larger shell length, and higher energy use without proportionate performance gains. Empirical practice for rotary dryers with L/D in the 4–10 range typically targets a modest NTU window to ensure efficient yet economical operation.

Step-by-Step Solution:

Verification / Alternative check:
Back-calculations from pilot tests and commercial units that meet product moisture specs commonly yield overall NTU in the 1.5–2.5 range when lifter design and inlet humidity/temperature are appropriately selected.

Why Other Options Are Wrong:

• 3.5–5.5 and 7.5–10.0: Implies unusually long drums or excessive residence time and heat duty for most commodities.
• 10–15: Far above typical practice; would be uneconomic for standard duties.

Common Pitfalls:
Confusing NTU with height of a transfer unit (HTU); assuming sticky materials behave like free-flowing solids; ignoring the impact of gas recirculation or high inlet humidity that can distort apparent NTU.

Final Answer:
1.5–2.5