Project ForgeAn equi-molar mixture of four hydrocarbons (1,2,3,4) with relative volatilities K1=6, K2=3, K3=2.5, K4=1.1 is to be separated into high purity individual components using a sequence of simple distillation columns. Scheme P removes {4} first (leaving {1,2,3}), then splits off {1} (leaving {2,3}), then finally splits {2} from {3}. Using the Ki values, the optimal scheme is
- Scheme P
- BScheme Q (first split is between 2 and 3)
- CScheme R (direct sequence, lightest off first each time)
- DScheme S (indirect sequence, heaviest off first each time)
Explanation
The hardest split (smallest relative volatility ratio) is between components 2 (K=3) and 3 (K=2.5), ratio 1.2. Standard sequencing heuristics favor performing the most difficult separation LAST, on the smallest remaining stream, to minimize overall cost. Scheme P defers the 2-vs-3 split to its final column (operating on just the 2-component stream), while the other schemes perform this hard split earlier, on larger multi-component streams — making Scheme P the heuristically optimal choice.
Source: GATE CH 2009 (2009)
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