Time-optimal Diafiltration in the Presence of Membrane Fouling

This paper is a preliminary study that deals with time-optimal control of a batch membrane diafiltration processes where fouling of the equipped membrane is pronounced. We account for the membrane fouling by its dynamic model where the pore blocking mechanism applies. It is assumed that due to the deposit of foulants, the radius of membrane pores decreases and the part of membrane surface becomes unavailable for the filtration. We apply Pontryagin’s minimum principle to solve the time-optimal control problem in an analytical fashion. It is found that the analytical approach enables to fix the control structure into sequence of arcs. It is further shown that once the sequence of control arcs is fixed, the optimal solution is determined by identification of switching times between the control arcs using a simple numerical technique. The method is demonstrated by its application to some of the most commonly used models of diafiltration processes.