Optimal feeding strategy of diafiltration buffer in batch membrane processes

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 the 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.

Graphical abstractOptimal operation of general batch membrane process. Left plot shows concentration diagram with two general initial (∘) and terminal (×) points and optimal concentration curve S. Right plot shows corresponding optimal control α. Figure optionsDownload full-size imageDownload high-quality image (76 K)Download as PowerPoint slideHighlights► Optimal control is investigated for a general filtration process. ► Analytical solution is provided for the most common class of processes. ► Simple numerical approach is proposed to treat the general case. ► Obtained optimal operation is compared with the standard control techniques.