Hierarchical decomposition and mathematical programming: A combined approach for the preliminary screening of processing alternatives

Mathematical Programming, using Mixed-Integer Nonlinear Programming (MINLP) model formulations, is a powerful tool for the synthesis of process flowsheets. Two disadvantages of the MINLP method are that (1) large problems in terms of discrete variables may become intractable, and (2) nonconvexities may cause convergence to poor solutions. To overcome these difficulties, a new framework for the synthesis of process subsystems is first presented that can address the question of how to rigorously combine preliminary screening and MINLP optimization techniques. In the first stage a preliminary screening procedure is developed that avoids solving a single large MINLP containing all the alternatives for a given superstructure, while producing the same result as if the single MINLP had been solved at once. In the second stage a reduced MINLP model is formulated that contains only the alternatives found during the preliminary screening. In addition to the MINLP approach, hierarchical decomposition is a widely-employed technique. It utilizes a sequential approach for the design of complete process flowsheets. A combined approach is proposed in which the entire flowsheet is considered at each step of the decomposition using a multilevel tree search. A simultaneous optimization of the entire flowsheet is performed with a combination of simple and detailed models. The procedure continues until the entire flowsheet has been decomposed to the level of the detailed models. Finally, the relation between simple (thermodynamic) and detailed models for heat-integrated distillation sequences is explored. Thermodynamic analysis suggests alternatives to improve process efficiency. A large MINLP problem was developed to investigate these alternatives, and a multilevel preliminary screening procedure is suggested to make the problem tractable.