Optimal synthesis of liquid-liquid multistage extractors

• Published in: Computer Aided Chemical Engineering Vol. 9; pp. 487 - 492
• Main Authors: Reyes-Labarta, Juan A., Grossmann, Ignacio E.
• Format: Book Chapter
• Language: English
• Published: 2001
• ISBN: 0444507094; 9780444507099
• ISSN: 1570-7946
• DOI: 10.1016/S1570-7946(01)80076-6

This chapter discusses the optimal synthesis of liquid–liquid countercurrent extractor systems. The method calculates the optimum number of equilibrium stages and flowrates to obtain a specified product separation and recovery. Based on a superstructure representation, the problem is formulated as a Generalized Disjunctive Programming (GDP) model to minimize the total cost of the process subject to design specifications. The robustness and computational efficiency of the model is illustrated. The proposed GDP model is solved with a modification of the Logic-Based Outer Approximation (OA) algorithm. This decomposition algorithm solves the problem by iterating between reduced Non Linear Programming (NLP) subproblems and a Mixed-Integer Linear Programming (MILP) master problem that consists of linear approximations in all solution points given for all the NLPs solved previously, using the big-M formulation to relax the linear approximations of the disjunctions. The proposed design model is tested with an example that involves the separation of a quaternary mixture, using a countercurrent extractor.