Design of integrated batch processes with discrete and continuous equipment sizes

This paper presents a mathematical programming approach for the integrated design of batch processes involving multiple processing steps. Detailed dynamic models are used to describe the behaviour of individual batch operations. The mathematical formulation regards both the design (e.g. equipment items with discrete sizes) and operational characteristics (i.e. control variable profiles such as reflux ratio, cooling water flowrate) of each task as degrees-of-freedom, the values of which are selected to optimise a particular objective function (e.g. profit). The solution may be restricted by inequality constraints which hold throughout the task (e.g. reactor temperature violation) or at the end of the task (e.g. end-product purity specification). The sizes of the equipment items are treated as discrete decisions and are chosen from a selection of standard sizes. The mathematical formulation leads to a mixed integer dynamic optimisation problem and is solved using the outer approximation/augmented penalty (OA/AP) algorithm.