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GATE 2020 CH – Question 16

Chemical Reaction Engineering · Non-ideal reactors and residence time distribution · 1 mark · Multiple choice

A unit tracer pulse enters a steady ideal plug-flow reactor with recycle ratio R = 1, defined as recycled volume divided by volume leaving the system. No reaction or dead recycle-loop volume is present. The first four outlet pulses occur at t₁,…,t₄ as shown. If space time based on fresh feed is τ, which is correct?

Diagram for GATE 2020 CH question 16
  1. $t_1=\tau,t_2=2\tau,t_3=3\tau,t_4=4\tau$
  2. $t_1=\tau/2,t_2=\tau,t_3=3\tau/2,t_4=2\tau$
  3. $t_1=\tau/2,t_2=\tau/4,t_3=\tau/8,t_4=\tau/16$
  4. $t_1=\tau/3,t_2=2\tau/3,t_3=\tau,t_4=4\tau/3$

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Correct answer: (B) $t_1=\tau/2,t_2=\tau,t_3=3\tau/2,t_4=2\tau$

Explanation

Let fresh volumetric feed be q. Recycle R = 1 makes the reactor flow 2q, while the fresh-feed space time is τ = V/q. Each plug-flow transit therefore takes V/(2q) = τ/2. With no recycle-loop delay, successive tracer returns emerge at τ/2, τ, 3τ/2 and 2τ. Recycling reduces pulse areas geometrically but not their equal time spacing. Select B.

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