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Authors: Ivar J. Halvorsen and Sigurd Skogestad

Published in Ind.Eng. Chem.Res., Volume 42 (2003), page 596-604 (part 1), page 605-615 (part 2), page 616-629 (part 3).

Part 1: Vmin-diagram for a two-product column
Abstract. The Vmin-diagram is introduced to effectively visualize how the minimum energy consumption is related to the feed component distribution for all possible operating points in a two-product distillation column with a multicomponent feed. The classical Underwood equations are used to derive analytical expressions for the ideal case with constant relative volatility and constant molar flows. However, the diagram can also be used for non-ideal mixtures. The Vmin-diagram is very insightful for assessing multicomponent separation in a single column, and is even more powerful for complex column arrangements, such as Petlyuk columns (Part II and III).

Part 2: Three-product Petlyuk Arrangements
Abstract. We show that the minimum energy requirement for separation of a multicomponent mixture in a three-product Petlyuk arrangement is equal to the minimum energy for most difficult of the two separations (top/ middle- or middle/bottom product) in a conventional single column. In the Vmin-diagram (part I) this is simply the highest peak. These results are based on an analytical solution for columns with infinite number of stages, assuming constant relative volatilities and constant molar flows. The previous analytical results for the Petlyuk column are extended to include non-sharp separations, multicomponent feeds, and any feed quality.

Part 3: More than Three Products and Generalized Petlyuk Arrangements
Abstract. We consider separation of ideal multicomponent mixtures with constant relative volatility 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 2-product column. This extends the results for the 3-product Petlyuk arrangement from Part II to a generalized arrangement with any number of products and feed components. The solution is very simple to visualize in the Vmin-diagram (Part I), 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.