Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery

Abstract

To decarbonize our global energy system, sustainably harvesting metals from diverse sourcewaters is essential. Membrane-based processes have recently shown great promise in meeting these needs by achieving high metal ion selectivities with relatively low water and energy use. An example is nanofiltration, which harnesses steric, dielectric, and Donnan exclusion mechanisms to perform size- and charge-based fractionation of metal ions. To further optimize nanofiltration systems, multicomponent models are needed; however, conventional methods necessitate large amounts of data for model calibration, introduce substantial uncertainty into the characterization process, and often yield poor results when extrapolated. In this work, we develop a new computational architecture to alleviate these concerns. Specifically, we develop a framework that: (1) reduces the data requirement for model calibration to only charged species measurements; (2) eliminates uncertainty propagation problems present in conventional characterization processes; (3) enables exploration of pH optimization for enhancing metal ion selectivities; and (4) enables uncertainty quantification to assess the sensitivity of partition coefficients and ion driving forces to learned pore size distributions. Our framework captures eight independent datasets comprising over 500 measurements to within ±15%. Our studies also suggest that the expectation-maximization algorithm can effectively learn pore size distributions and that optimizing pH can improve metal ion selectivities by a factor of 3-10×. Our findings also reveal that image charges appear to play a less pronounced role in dielectric exclusion under the studied conditions and that ion driving forces are more sensitive to pore size distributions than partition coefficients.

Keywords: Bilevel optimization; Donnan exclusion; Ion selectivity; Metal recovery; Nanofiltration; Transport models.