Distillation limits – behavior at minimum reflux ratio For a specified separation, what happens to the required number of plates (theoretical stages) as the reflux ratio approaches the minimum value?

Introduction / Context:
Reflux ratio strongly influences the internal compositions in a distillation column and, consequently, the number of stages needed. Understanding the asymptotic limits (total reflux and minimum reflux) is essential for selecting an economical design point and for interpreting McCabe–Thiele constructions.

Given Data / Assumptions:

• Binary or multicomponent distillation under constant molar overflow.
• Specified distillate and bottoms purities.
• Reflux ratio varied while separation target is fixed.

Concept / Approach:
At total reflux (infinite reflux ratio), the minimum number of theoretical stages is required. At the opposite extreme, the minimum reflux ratio R_min is the lowest reflux that will still achieve the desired split; however, the operating lines become tangent to the equilibrium curve, so the required number of stages grows without bound. Hence, near R_min, the column must be impractically tall, motivating operation at a higher, finite reflux where a reasonable stage count is obtained.

Step-by-Step Solution:

Verification / Alternative check:
Gilliland correlations show N increases steeply as R approaches R_min from above, consistent with the asymptotic infinity at R_min.

Why Other Options Are Wrong:

• Zero plates or “minimum plates” at minimum reflux misstates the limit; it is the opposite of total reflux.
• “Most efficient” is incorrect; efficiency collapses as stages required blow up.

Common Pitfalls:
Confusing minimum reflux with minimum stages; they occur at opposite ends of the design spectrum.

Final Answer:
number of plates tends to infinity