Fig. 7. The tree structure of quaternary separation.

2.2. Design and synthesis of TCD

For a TV-component mixture, the minimum number of columns in a separation sequence is:

Consequently, we can understand the source of Eq. (11), in which the numerator reflects the total distinguishable sites that are occupied by both pure components (N sites) and the mixtures (N - 1 sites), and the denominator reflects the N undistinguishable sites occupied by pure components and N - 1 undistinguishable sites occupied by the mixture. Only until this combination is finished, we can distinguish the N pure components by the series of A, B, C, etc.

Actually, Eq. (11) is only suitable for simple distillation sequences, excluding complex distillation sequence, such as TCD. Unfortunately, up to date, there isn't an uniform formulation to account for the number of TCD separation sequences.

Based on the above background knowledge, we can understand TCD more easily. Then what is TCD? The most significant characteristics in TCD configuration is that at least one end of a distillation column has both liquid and vapor exchange with another column, and thus either the reboiler or the condenser is eliminated from this end of the distillation column. For ternary component mixtures, there are only three feasible thermally coupled configurations called the side stripping (SS), the side rectifying (SR) and the fully coupled (FC) (or Petlyuk configuration), respectively [20, 21]. However, in the whole FC configuration there is only one condenser and one reboiler.

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