Martin Jelemenský

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

Abstract 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. Pontryagins 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.

Time-optimal operation of multi-component batch diafiltration

Abstract We study the minimum-time operation of batch multi-component diafiltration processes. We employ the technique of Pontryagins minimum principle to derive the candidates for an optimal operation. The optimal operation is defined as a state-feedback strategy. Simulations and numerical optimizations are applied to confirm the optimality of the proposed time-optimal operation. Obtained results are evaluated on two case studies, a typical multi-component diafiltration processes. Standard operational approaches are compared to the optimal operation and the resulting improvements show attractivity of the proposed approach.

Time-optimal Operation of Diafiltration Processes in the Presence of Fouling

Abstract This paper deals with time-optimal operation of a batch diafiltration process in the presence of membrane fouling. Fouling causes a decrease in membrane area and hence, a decrease in permeate flux. Pontryagin’s minimum principle is applied to characterize the structure of the optimal operation. Due to the specific structure of the problem, it is possible to derive and verify an explicit analytic solution. Obtained results are used in a case study where we provide a comparison between traditional operation and the herein developed time-optimal operation.

Time-optimal Diafiltration in the Presence of Membrane Fouling

Abstract 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 Pontryagins 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.

Time-Optimal Control of Batch Multi-Component Diafiltration Processes

Abstract This paper studies the time-optimal operation of batch multi-component diafiltration processes. We employ the technique of Pontryagin’s minimum principle to derive the candidates for optimal operation. Simulations and numerical optimizations are applied to define the time-optimal solution. The obtained results are evaluated on a case study, a typical multi-component diafiltration process. A comparison is provided between standard operational approaches and the newly derived optimal one.

Estimation of membrane fouling parameters for concentrating lactose using nanofiltration

Abstract The paper deals with parameter estimation of permeate flux model with fouling for the nanofiltration process. We propose a new technique towards fouling estimation with fouling model being an explicit function of concentration. The objective is to experimentally concentrate lactose in a lactose-salt solution at constant temperature and pressure using cross-flow nanofiltration. The experimental results show a decrease in the permeate flux over time, as the concentration of lactose increases. The limiting flux model is used to model the experimental permeate flux data without fouling. This limiting flux model parameters and the fouling parameters are then estimated via least-squares method using the experimental flux data.