Time-optimal control of diafiltration processes in the presence of membrane fouling

This paper deals with time-optimal operation of batch diafiltration processes in the presence of membrane fouling. Fouling causes a decrease in the effective membrane area and, hence, an increase in processing time. In this work we study a time-optimal operation with several fouling models available in literature. Pontryagin's minimum principle is applied to characterize the structure of the optimal operation which voids any further on-line optimization. Due to the specific structure of the problem, it is possible, in several problem setups, to derive and verify an explicit analytic solution. Obtained results are applied in case studies where we provide a comparison between traditional operation and the proposed time-optimal operation. In cases, where the optimal operation cannot be identified analytically, we analyze the performance of sub-optimal control derived from neighboring analytical solution and compare it to optimal operation found via numerical optimization techniques.