Economically optimal diluant addition for batch ultrafiltration/diafiltration processes

Presented work deals with the cost optimal operation of batch ultrafiltration/diafiltration (UF/DF) processes. The economic optimization problem comprises two classical optimization criteria, namely minimum time and minimum diluant (solvent) consumption. In order to reflect the varying prices of individual parts of operational cost to the economically optimal process on longer time horizon, we treat the resulting optimization problem as a multi-objective one. We use analytical solution to this problem, obtained by applying Pontryagin´s minimum principle, which provides conditions for switching of optimal control structure and for evaluation of economically optimal diluant utilization strategy. The here developed methodology is applied to the examples of UF/DF processes taken from the literature and economical benefits of using such advanced control strategy are discussed.