Binary distillation methods: Smoker’s equation for estimating the number of equilibrium stages is specifically applied under which condition?

Introduction / Context:
Several shortcut correlations estimate the number of ideal stages for binary distillation: Fenske’s method at total reflux, Underwood’s method for minimum reflux, Gilliland-type correlations for operating conditions, and specialized equations such as Smoker’s. These tools simplify early design when detailed stage-to-stage calculations are not yet warranted.

Given Data / Assumptions:

• Binary system with relative volatility α not much larger than 1.
• Goal: obtain a realistic stage count without full rigorous simulation.
• Ordinary tray or packed columns with equilibrium stages as the modeling basis.

Concept / Approach:
When α approaches unity, the separation becomes difficult; traditional shortcuts can lose accuracy or require many stages. Smoker’s equation is tailored to such near-ideal, close-boiling systems and offers a way to approximate stage numbers accounting for the small driving force inherent to α ≈ 1.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check against rigorous simulation or McCabe–Thiele methods shows Smoker’s predictions are most useful when α is near 1; deviations grow as α increases.

Why Other Options Are Wrong:

• Feed thermal condition (bubble/dew) affects operating lines but is not the defining trigger for Smoker’s equation.
• Limiting to stripping section only is unrelated.
• “Very small” stage counts do not describe close-boiling separations, which usually need more stages.

Common Pitfalls:
Applying the correlation outside its intended α range; ignoring non-idealities or azeotropy; skipping verification with rigorous methods before final design.

Final Answer:
Relative volatility is close to one (e.g., separation of close-boiling isomers).