Optimal feeding strategy of diafiltration buffer in batch membrane processes

Abstract

This work addresses the optimal control strategy of diafiltration buffer utilisation in discontinuous membrane processes that are designed to fulfil the twin aims of concentration and fractionation. The problem of optimal process operation is formulated using a general membrane response model that encounters concentration-dependent flux and rejections. We consider two problems, operation time minimisation and diluant consumption minimisation, and we apply theory of optimal control and derive necessary conditions of optimality. Through selected case studies from literature, we demonstrate how to apply the proposed methodology to determine optimal time-dependent wash-water feeding policy. The analytical results are confirmed by numerical computations, using numerical methods of dynamic optimisation. The presented methodology allows decision makers to analyse suboptimality of conventional diafiltration strategies in terms of processing time and diluant consumption. Results show that depending on the complexity of the membrane response model, it may be attractive to implement optimal trajectory.

Time-optimal operation of multi-component batch diafiltration

“…The duration of the steps is fully determined from the initial and final conditions on concentrations. More details on these results can be found in our previous study (Paulen et al, 2012).…”

Economically optimal control of batch diafiltration processes

“…The membrane transport model was experimentally verified in [1]. Timeoptimal and minimum diluant operations of this process were studied in [8]. The goal is to process 0.0666 m 3 of solution with 15 kg/m 3 of albumin and 194.3 kg/m 3 of ethanol.…”

“…2 shows resulting transitions in the state diagram (top plot) and optimizing control (bottom plot) for the economically optimal (red curve), the minimum time (blue curve), and the minimum diluant (green curve) operations. The minimum time and the minimum diluant control strategies are shown for comparison and are in accord with [8].…”

“…The singular surface (8) depends only on the concentration of radiopaque. This predicts constant concentration of radiopaque on the singular arc which is maintained by using CVD operation, α = 1.…”

Economically optimal diluant addition for batch ultrafiltration/diafiltration processes

“…• minimum diluant problem (w T = 0 and w D ≥ 0) Resulting minimum diluant control strategy was previously shown in [17] to be physically unattainable since it gives q = 0 during the CVD step which implies infinite processing time. A practically realizable scenario was proposed that involves certain back-off from condition (8).…”