Total reflux in distillation — What requirement reaches its minimum under total-reflux operation (no product withdrawal, maximum internal reflux)?

Introduction:
Total reflux is a limiting operating condition where all condensed distillate is returned as reflux and no products are withdrawn. It is a valuable conceptual point for understanding column behavior and for establishing minimum stage count independent of feed and product rates.

Given Data / Assumptions:

• No material is withdrawn as products; all condensed vapor returns as reflux.
• Internal liquid and vapor rates are at their maximum for a given column.
• Separation specified by compositions at the top and bottom.

Concept / Approach:
At total reflux, the operating lines in the McCabe–Thiele diagram coincide with the 45-degree diagonal, yielding the minimum theoretical number of stages needed for the specified separation. However, because internal flows are the largest, both reboiler and condenser duties are maximized, not minimized.

Step-by-Step Solution:
Set reflux to total (R → ∞), product rates → 0.Operating lines approach the diagonal → best separation per stage.Count stages: minimum theoretical count achieved.Recognize heat duties are high due to large internal circulation.

Verification / Alternative check:
Textbook derivations and simulations consistently show fewer stages are needed at higher reflux, with the minimum at total reflux. Energy balances show higher condenser and reboiler loads under total reflux since all vapor generated must be condensed and returned.

Why Other Options Are Wrong:

• (a) and (c) Heat loads are not minimal; they are maximal.
• (d) Cannot be true given (a) and (c) are false.
• (e) Cooling-water use generally increases at total reflux due to higher condenser duty.

Common Pitfalls:
Confusing the “minimum stages” limit with “minimum energy” limit (which is attained at minimum reflux, not total reflux).

Final Answer:
Number of plates (theoretical stages) needed