Computers and Chemical Engineering 29 (2005) 1457–1471 A robust strategy for optimizing complex distillation columns Filipe J.M. Neves, Dulce C.M. Silva, Nuno M.C. Oliveira ∗ GEPSI-PSEGroup,DepartmentofChemicalEngineering,UniversityofCoimbra,P´ oloII,PinhaldeMarrocos,3030-290Coimbra,Portugal Available online 16 March 2005 Abstract This work introduces a strategy for the optimal design of distillation systems based on continuous optimization. The approach is similar to the one proposed earlier by [Lang, Y. -D., & Biegler, L. T. (2002). A distributed stream method for tray optimization. AIChEJournal, 48, 582], avoiding the need of solving extremely large and non-linear discrete optimization problems. When used with complex distillation units, it can identify interesting design configurations not considered by other continuous formulations, and also relieve some of the numerical difficulties associated with the use of distribution functions for the optimal location of feed and side-streams. The method considers a relaxation of the original problem, where the streams are initially split to several trays in the column, not necessarily adjacent. The optimal location of each stream is converged by constraining the optimization problem, using adjustable parameters that control the minimum amount of aggregation allowed. The methodology is illustrated with the application to several industrial case studies, including sets of distillation columns. Models up to 17,000 variables/equations were solved, revealing large economic benefits in the design of new units and optimization of sets of existing ones. © 2005 Published by Elsevier Ltd. Keywords: Distillation; Optimization; Continuous formulations; Relaxation 1. Introduction The topic of optimization of distillation columns has re- ceived significant attention in the past decades due, at the same time, to its economical importance and the numeri- cal difficulties associated with the solution of this type of problems. Among the difficulties usually encountered, it is possible to emphasize: (a) The complexity of the models required to adequately de- scribe the equilibrium phenomenon that takes place. The use of detailed non-ideal equilibrium models, such as the UNIFAC group contribution method, is often neces- sary (Reid, Prausnitz, & Poling, 1987). When the non- ideality of the vapor and liquid phases is simultaneously considered, the corresponding models can require up to 50 scalar variables per component per equilibrium stage, leading easily to overall unit models with tens of thou- ∗ Corresponding author. Tel.: +351 239 798700; fax: +351 239 798703. E-mail addresses: fneves@eq.uc.pt (F.J.M. Neves), dulce@eq.uc.pt (D.C.M. Silva), nuno@eq.uc.pt (N.M.C. Oliveira). sands of non-linear algebraic equations, and highly non- linear behavior. (b) The need to incorporate discrete decisions in the so- lution process, related to the optimal location of the feed and product streams, and the total number of equilibrium stages. These problems are usually ad- dressed as mixed-integer non-linear programs—MINLP (Barttfeld & Aguirre, 2002; Barttfeld, Aguirre, & Gross- mann, 2003; Bauer & Stilchmair, 1998; Viswanathan & Grossmann, 1990, 1993) or general disjunctive programs—GDP (Barttfeld et al., 2003; Yeomans & Grossmann, 2000). A common difficulty associated with the use of MINLP formulations is the need to satisfy each model constraint, even in cases where a particular equilibrium stage is elimi- nated from the correspondent superstructure. This can lead to models of large size, where singularities can be encoun- tered during the integer solution phase, especially associated with linearizations at zero flows. These characteristics affect adversely the robustness of MINLP approaches and consti- tuted the main motivation for the development of alternative 0098-1354/$ – see front matter © 2005 Published by Elsevier Ltd. doi:10.1016/j.compchemeng.2005.02.002