Membrane network synthesis for metal recovery: An optimization-based framework

High-value metals, including critical metals and rare earth elements, are essential for a wide range of modern applications. Recovering these metals from wastewater provides a sustainable alternative to extracting them from finite natural resources. Membrane-based technologies, particularly nanofiltration, offer significant benefits such as high separation efficiency and low energy requirements. However, designing membrane networks is intricate due to the vast array of potential membrane materials that are available and network configurations that can be utilized. In this work, we first present a rich superstructure representing multiple network configurations. We then develop a mixed-integer nonlinear programming (MINLP) model, which incorporates an accurate membrane unit model, which is solvable to global optimality. The proposed framework determines network configuration, membrane materials, and operating conditions to minimize total annualized operating costs. This novel framework enables the synthesis of membrane networks for recovering multiple high-value metals from wastewater. Finally, we demonstrate the effectiveness of the proposed framework in achieving globally optimal solutions through various case studies.