Project ForgeChemical Reaction Engineering
Ideal Reactor Design
GATE 2010
Hard
Two reactors (reactor 1 and reactor 2) with average residence times, τ1 and τ2 respectively, are placed in series. Reactor 1 has zero dispersion and reactor 2 has infinite dispersion. The residence-time distribution, E(t), of this system is given by
- 0 for t≤τ1; (1/τ2)exp(−(t−τ1)/τ2) for t>τ1
- B0 for t≤τ2; (1/τ1)exp(−(t−τ2)/τ1) for t>τ2
- C0 for t≤τ1; (1/τ1)exp(−(t−τ1)/τ2) for t>τ1
- D0 for t≤τ2; (1/τ2)exp(−t/τ1) for t>τ2
Explanation
Zero dispersion = ideal PFR (pure time delay of τ1, no spreading). Infinite dispersion = ideal CSTR (with its own E(t)=(1/τ2)e^(−t/τ2)). In series, the PFR simply delays the CSTR's response by τ1: E(t)=0 for t≤τ1, and (1/τ2)exp(−(t−τ1)/τ2) for t>τ1.
Source: GATE CH 2010 (2010)
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