The GATE Grind

GATE 2022 CH – Question 25

Plant Design and Economics · Optimization in process design and equipment sizing · 1 mark · Multiple choice

A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. If $RR_{min}$ is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost (TAC) of the column with reflux ratio (RR).

  1. TAC has a minimum with respect to RR
  2. The sharpest rise in TAC occurs as RR approaches $RR_{min}$ from above
  3. The sharpest decrease in TAC occurs as RR approaches $RR_{min}$ from above
  4. TAC increases with RR for RR >> $RR_{min}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) The sharpest decrease in TAC occurs as RR approaches $RR_{min}$ from above

Explanation

Near $RR_{min}$ the number of stages (and so the capital cost) rises without limit, so the TAC rises very steeply as RR approaches $RR_{min}$ from above (B is correct) and the cost does not fall there (C is not correct). The TAC has a minimum at an intermediate RR (A) and rises again at large RR because of the energy cost (D).