(211b) Non-Pinched Minimum Energy Solutions in Distillation

Distillation is still an important unit operation for the separation of chemicals, and due to its versatility, it will continue to be used in the forseeable future. Very good techniques for finding minimum energy requirements for distillation, like the McCabe-Thiele and Underwood methods, have existed for quite some time. More recently, methods like the boundary value of Doherty and co-workers, the Vmin method of Halvorsen and Skogestad, and the rectifying body method of Urdaneta et al. have been proposed to handle multicomponent mixtures that exhibit azeotropes and multiple column configurations. For the most part, these methods exclusively find minimum energy requirements for distillations with pinched column profiles. There are no methods that can find non-pinched minimum energy designs for distillations in a rigorous and systematic way ? either for single distillation columns or for multi-unit processes in which distillation is a part. In this presentation, non-pinched solutions of single distillation columns and multi-unit chemical processes are studied. It is shown that the recent approach proposed by Lucia and co-workers based on the shortest stripping line distance can be used to find non-pinched solutions. This new methodology consists of a Mixed Integer NonLinear Programming (MINLP) strategy in which pinched solutions are determined by 1) First solving a NonLinear Program (NLP) for the boil-up ratio that gives the feasible column with the shortest stripping line distance from the desired bottoms composition to the stripping pinch point curve. 2) Subsequently solving an integer program (IP) for a finite number of stages to further reduce the stripping line distance under the conditions that the column is feasible and the boil-up ratio is fixed at the solution provided by the NLP. A number of interesting example problems are presented that show that the shortest stripping line methodology is capable of finding minimum energy requirements with non-pinched distillations. Many geometric illustrations for three and four component mixtures are used to highlight key attributes of the shortest stripping line approach.