Multi-objective optimal control of ultrafiltration/diafiltration processes

This paper deals with multi-objective optimal operation of a general batch ultrafiltration/diafiltration (UF/DF) process. We consider the optimization criterion consisting of two parts as combination of two classical optimization problems, namely the minimum time problem and the problem of minimum diluant consumption. We apply Pontryagin´s minimum principle for obtaining the necessary conditions for optimality. Based on these, we show how to obtain a Pareto front and how to derive multi-objective optimal operation for considered type of processes. The presented methodology will be applied to the most commonly used model in membrane filtration - the limiting flux case and to another experimentally derived membrane model.