Distillation operation: the working reflux ratio can vary between which practical limits when compared with the minimum reflux ratio?

Introduction / Context:
The reflux ratio R is a key design and operating parameter in distillation. It trades off energy (reboiler and condenser duties) with capital (number of stages). Theoretical extremes define bounds for feasibility and optimization during column design and operation.

Given Data / Assumptions:

• Binary or multicomponent distillation with total condenser.
• Minimum reflux ratio R_min is the smallest value at which separation is just possible with infinite stages.
• Infinite reflux corresponds to total reflux operation with zero product withdrawal.

Concept / Approach:
In practice, the operating (working) reflux must be at least the minimum (R ≥ R_min). As R approaches infinity, the number of theoretical stages needed approaches the minimum possible. Economic optimum typically lies between 1.1–1.5 times R_min for binaries, but the theoretical upper limit is unbounded (infinite) while the lower limit is R_min.

Step-by-Step Solution:

Verification / Alternative check:
McCabe–Thiele and Ponchon–Savarit analyses show stage and reflux tradeoffs and confirm these bounds.

Why Other Options Are Wrong:

• “Zero and infinity” ignores the minimum reflux constraint.
• “Zero and one” is unrelated to column feasibility.

Common Pitfalls:
Confusing minimum reflux with minimum stages; forgetting composition/spec constraints when choosing operating R.

Final Answer:
Minimum and infinity