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GATE 2024 CH – Question 14

Process Calculations · Gibbs phase rule and degree of freedom analysis · 1 mark · Multiple choice

A homogeneous azeotropic distillation process separates an azeotropic AB binary feed using a heavy entrainer, E, as shown in the figure. The loss of E in the two product streams is negligible so that E circulates around the process in a closed-circuit. For a distillation column with fully specified feed(s), given operating pressure, a single distillate stream and a single bottoms stream, the steady-state degrees of freedom equals 2. For the process in the figure with a fully specified AB feed stream and given column operating pressures, the steady-state degrees of freedom equals

an azeotropic column that takes the AB feed and the entrainer E and gives product A at the top. Its bottoms (A-free, mostly E and B) go to an entrainer recovery column, which gives product B at the top and nearly pure E at the bottom. The E returns to the first column.
  1. 3
  2. 4
  3. 5
  4. 6

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Correct answer: (C) 5

Explanation

The recovery column has a feed fixed by the first column and so has 2 degrees of freedom. The first column has the fully specified AB feed, but also the entrainer stream, whose flow rate is free (its composition and temperature follow from the recovery column), so it has $2 + 1 = 3$ degrees of freedom. The total is $3 + 2 = 5$.