Economically viable water treatment process plants for drinking water purification are a prerequisite for sustainable supply of safe drinking water in the future. However, modern membrane process development experiences a disconnect in this domain: the synthesis of the membrane and the design of the process are decoupled. We propose an optimization strategy to simultaneously design the performance of layer-by-layer nanofiltration membrane modules along with the separation process. This approach achieves overall optimal performance by extending the search space and thus exploiting synergies. Better separation performances at a lower cost as compared to conventional optimization strategies can be achieved. The key feature of this optimization framework is the integration of artificial neural networks. This machine-learning technique describes the membrane performance as a function of its synthesis protocol. We optimize the design problem rigorously by a deterministic global nonlinear optimization method. Thus, this framework yields membrane synthesis protocols and membrane processes that are optimally tailored to the desired separation task. In a showcase, the simultaneous membrane synthesis and process optimization design achieve immediately favorable results with lower impurities at comparable costs. The process investment and operation costs are compared to a state of the art commercially available membrane for nanofiltration.

Innovative membrane technologies optimally integrated into large separation process plants are essential for economical water treatment and disposal. However, the mass transport through membranes is commonly described by nonlinear differential-algebraic mechanistic models at the nano-scale, while the process and its economics range up to large-scale. Thus, the optimal design of membranes in process plants requires decision making across multiple scales, which is not possible using standard tools. In this work, we embed artificial neural networks (ANNs) as surrogate models in the deterministic global optimization to bridge the gap of scales. This methodology allows for deterministic global optimization of membrane processes with accurate transport models – avoiding the utilization of inaccurate approximations through heuristics or short-cut models. The ANNs are trained based on data generated by a one-dimensional extended Nernst-Planck ion transport model and extended to a more accurate two-dimensional distribution of the membrane module, that captures the filtration-related decreasing retention of salt. We simultaneously design the membrane and plant layout yielding optimal membrane module synthesis properties along with the optimal plant design for multiple objectives, feed concentrations, filtration stages, and salt mixtures. The developed process models and the optimization solver are available open-source, enabling computational resource-efficient multi-scale optimization in membrane science.

Synthetic membranes for desalination and ion separation processes are a prerequisite for the supply of safe and sufficient drinking water as well as smart process water tailored to its application. This requires a versatile membrane fabrication methodology. Starting from an extensive set of new ion separation membranes synthesized with a layer-by-layer methodology, we demonstrate for the first time that an artificial neural network (ANN) can predict ion retention and water flux values based on membrane fabrication conditions. The predictive ANN is used in a local single-objective optimization approach to identify manufacturing conditions that improve permeability of existing membranes. A deterministic global multi-objective optimization is performed in order to identify the upper bound (Pareto front) of the delicate trade-off between ion retention characteristics and permeability. Ultimately, a coupling of the ANN into a hybrid model enables physical insight into the influence of fabrication conditions on apparent membrane properties.