Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning

Abstract

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 tractable 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 modelsavoiding the utilization of inaccurate approximations through heuristics or shortcut 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.

Effect of pH on Total Volume Membrane Charge Density in the Nanofiltration of Aqueous Solutions of Nitrate Salts of Heavy Metals

“…Kingsbury and co-authors [ 56 ] used the solution-diffusion model as a common framework to compare the permeability, partition and diffusion coefficients, water permeance, and salt rejection of twenty commercial ion exchange membranes. Despite the modelling approaches presented above, the novel computational methodology was developed by Rall et al [ 57 ], who integrated accurate physical models of ion transport—valid on the nano-scale—into the large-scale superstructure optimization of the membrane. Nevertheless, none of these models are fully predictive, due to the difficulties associated with the identification of certain model parameters [ 58 ].…”

A Neural Network Based Superstructure Optimization Approach to Reverse Osmosis Desalination Plants

“…Using the phenomenological transport equations for RO membranes to derive operational desalination plant parameters, results in a complex system of equations, which is computationally expensive to solve, especially within the context of optimization [24,25]. To overcome these drawbacks, linear surrogate models are employed to capture the operational RO plant behavior.…”

“…Generally, the optimization of RO systems requires modeling the mass transfer of the employed membrane modules [21], which may result in a complex mathematical model if first order principles are employed [22][23][24]; often a computationally expensive task [25]. Data-driven surrogate models can be utilized to capture the complex mass transfer behavior of membrane systems [26], utilizing machine learning (ML) methods [27].…”

Challenges and Opportunities to Enhance Flexibility in Design and Operation of Chemical Processes

“…So far, only a few methods are available to deal with this challenge. Recent work uses, e.g., artificial neural networks to set up a surrogate model enabling multi-scale optimization exemplified with a membrane process [91] or thin film growth processes [92]. Other solutions proposed to deal with multiscale problems are model reduction methods or surrogate modeling approaches to reduce computational effort for complex nonlinear systems to allow for efficient control and scheduling [93][94][95][96].…”