Minimum energy consumption in multicomponent distillation. 3. More than three products and generalized Petlyuk arrangements

We consider separation of ideal multicomponent mixtures with constant relative volatilities and constant molar flows and at constant pressure. The exact analytical solution of minimum energy in a generalized Petlyuk arrangement for separation of N-component feed into M products has been derived. Interestingly, the minimum-energy solution in a complex integrated Petlyuk arrangement is equal to the most difficult split between any pair of the products, as if each single split was to be carried out in an ordinary two-product column. This extends the results for the three-product Petlyuk arrangement from part 2 of the series to a generalized arrangement with any number of products and feed components. The solution is very simple to visualize in the V-min diagram (part 1 of the series), simply as the highest peak. In addition, we obtain detailed flow rates and component distribution inside the arrangement. We also conjecture that the minimum energy requirement for the generalized extended Petlyuk arrangement is lower than the minimum-energy requirement for any distillation configuration when we consider conventional adiabatic sections and no internal heat exchange. The Vmin diagram may thus be used to obtain a target value for the energy requirements.