An MIQCP Reformulation for the Optimal Synthesis of Thermally Coupled Distillation Networks

Superstructure based approaches have long been employed for optimal process synthesis problems. Due to the difficulties of using rigorous process models and simultaneous solutions, shortcut calculations have been the preferred means of modeling unit operations within larger process network problems. However, even with the use of shortcut equations to model the behaviour of unit operations, the resulting mixed-integer programs can be challenging to solve. Furthermore, generating the problem superstructure has often been done manually, presenting issues for scaling to larger problems. We demonstrate the use of an algorithmic approach to generate network superstructures for synthesis problems coupled with equation reformulations to yield an MIQCP (Mixed-Integer Quadratically Constrained Program) for networks of thermally coupled distillation columns. The combination of rapid problem generation with the ability to leverage recent advances in the performance of QCP (Quadratically Constrained Program) solvers enables efficient and scalable solutions for these process synthesis applications.