A Convex Hull Formulation for the Design of Optimal Mixtures

Abstract

The design of mixtures plays an important role in improving process and product performance but is challenging because it requires finding the optimal number, identities and compositions of mixture components and using nonlinear property models. To address this, a general modeling framework for mixture design problems is presented. It integrates Generalized Disjunctive Programming (GDP) into Computer-Aided Mixture/blend Design via Hull Reformulation (HR). The design methodology is applied successfully to a case study involving solid-liquid equilibrium calculations to find an optimal solvent mixture that dissolves ibuprofen. The results show that the proposed GDP-based approach appears very promising for the design of mixture problems. The HR approach is used to solve mixture problems successfully. Its overall computational efficiency is found to be better than that of Big-M approach. Numerical difficulties arising from the absence of components in the final mixture can be avoided, leading to computationally efficient solutions.