Model-based optimization approaches for pressure-driven membrane systems

Membrane technology is commonly used within food, bio- and pharmaceutical processes. Beside single-stage membranes, multi-stage membrane systems are become more popular to improve separation performance. In this review, we present a unified four-phase model-based optimization framework to optimize these systems, using mechanistic models, empirical models including machine learning models, or a combination of them. We begin by providing a general overview and outlining the steps to construct each phase in the framework. The importance of each stage and critical points to consider are discussed. We then provide detailed information for each phase, including the governing equations from known literature models. Finally, we explore the platform's potential applications and outlook. Despite the great potential of an integrated approach, studies thus far focus either on extensive membrane modeling with brute-force optimization via simple comparison or on meticulous optimization using an oversimplified membrane model. We believe that the integrated framework can bridge the well justified approaches in both filtration modeling and mathematical optimization and help in designing multi-unit processes.