A New Method for Synthesis of Thermodynamically Equivalent Structures for Petlyuk Arrangements

The Petlyuk arrangement is the mostly studied thermally coupled configuration due to its minimum energy requirement for multicomponent distillation. In this paper, a new method for synthesis of thermodynamically equivalent structures (TES) for the Petlyuk arrangement is presented. The total number of the possible TESs is theoretically calculated with a derived formula a priori. Then, a simple procedure is formulated which generates all of the TESs step-by-step. It is shown that the new method can systematically produce all the known TESs as well as the missing ones for the Petlyuk arrangement of any n-component mixture. It is found that, for any n-component mixture, the Petlyuk arrangement can produce a unique thermodynamically equivalent side column structure by simultaneously moving all of its movable column sections. It constitutes a new mechanism to derive the satellite column superstructure with one reboiler and one condenser. Finally, it is concluded that the Petlyuk arrangement is a superstructure that incorporates all of the known structures as its substructures.