Integration of hierarchical decomposition and mathematical programming for the synthesis of process flowsheets

Two of the main methods for performing the conceptual design of process flowsheets are (1) the mathematical programming approach using Mixed-Integer Nonlinear Programming (MINLP) techniques and (2) hierarchical decomposition. The objective of this paper is to develop a combined approach for flowsheet synthesis that exploits the advantages of each of these methods, while maintaining consistency with their fundamental tenets. In the proposed approach, the idea is to solve the entire flowsheet at each step of the decomposition using a multilevel tree search. Aggregated models, based on black-box (input-output) representations of the downstream subsystems, are used to account for interactions with the detailed MINLP model of the subsystem at the current level of decomposition. Thus a simultaneous optimization of the entire flowsheet is performed with a combination of simple and detailed models. This provides for better designs, tighter bounds, and a monotonic decrease in the profit as decomposition proceeds. The procedure continues until the entire flowsheet has been decomposed to the level of the detailed models. The profit of every alternative is compared to the base-case profit at each node in the multilevel tree search, allowing for early fathoming of uneconomical alternatives, through which exhaustive enumeration is avoided. Application of the proposed methodology is illustrated with one large example. (C) 1997 Elsevier Science Ltd.