Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery.

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.

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration.

Membranes offer a scalable and cost-effective approach to ion separations for lithium recovery. In the case of salt-lake brines, however, the high feed salinity and low pH of the post-treated feed have an uncertain impact on nanofiltration's selectivity. Here, we adopt experimental and computational approaches to analyze the effect of pH and feed salinity and elucidate key selectivity mechanisms. Our data set comprises over 750 original ion rejection measurements, spanning five salinities and two pH levels, collected using brine solutions that model three salt-lake compositions. Our results demonstrate that the Li+/Mg2+ selectivity of polyamide membranes can be enhanced by 13 times with acid-pretreated feed solutions. This selectivity enhancement is attributed to the amplified Donnan potential from the ionization of carboxyl and amino moieties under low solution pH. As feed salinities increase from 10 to 250 g L-1, the Li+/Mg2+ selectivity decreases by ∼43%, a consequence of weakening exclusion mechanisms. Further, our analysis accentuates the importance of measuring separation factors using representative solution compositions to replicate the ion-transport behaviors with salt-lake brine. Consequently, our results reveal that predictions of ion rejection and Li+/Mg2+ separation factors can be improved by up to 80% when feed solutions with the appropriate Cl-/SO42- molar ratios are used.

Monovalent selective electrodialysis: Modelling multi-ionic transport across selective membranes.

Monovalent selective electrodialysis (MSED) is a variant of conventional electrodialysis (ED) that employs selective ion exchange membranes to preferentially remove monovalent ions relative to divalent ions. This process can be beneficial when the divalent rich stream has potential applications. In agriculture, for example, a stream rich in calcium and magnesium is deemed beneficial for crops and can decrease the use of fertilizers that would otherwise need to be re-introduced to the source water prior to irrigation. MSED has been used for salt production, brine concentration, and irrigation. An experimentally validated computational model to predict its performance, however, is not available in the literature. The present work uses concepts from conventional ED modelling to build a high-resolution predictive model for the performance of MSED. The model was validated with over 32 experiments at different operating conditions and observed to fit the data to within 6% and 8% for two different types of membranes. All voltage predictions were within 10% of experiments conducted. The model was then used to predict permselectivity across different salinities and compositions. These values were extended to investigate the economic benefits of using MSED to save fertilizers for greenhouses across the U.S. Results showed an average of $4991 saved per hectare when employing MSED technology. These values aligned with predictions from two previous techno-economic studies conducted investigating MSED for agriculture.

Novel Positively Charged Metal-Coordinated Nanofiltration Membrane for Lithium Recovery.

Nanofiltration (NF) with high water flux and precise separation performance with high Li+/Mg2+ selectivity is ideal for lithium brine recovery. However, conventional polyamide-based commercial NF membranes are ineffective in lithium recovery processes due to their undesired Li+/Mg2+ selectivity. In addition, they are constrained by the water permeance selectivity trade-off, which means that a highly permeable membrane often has lower selectivity. In this study, we developed a novel nonpolyamide NF membrane based on metal-coordinated structure, which exhibits simultaneously improved water permeance and Li+/Mg2+ selectivity. Specifically, the optimized Cu-m-phenylenediamine (MPD) membrane demonstrated a high water permeance of 16.2 ± 2.7 LMH/bar and a high Li+/Mg2+ selectivity of 8.0 ± 1.0, which surpassed the trade-off of permeance selectivity. Meanwhile, the existence of copper in the Cu-MPD membrane further enhanced anti-biofouling property and the metal-coordinated nanofiltration membrane possesses a pH-responsive property. Finally, a transport model based on the Nernst-Planck equations has been developed to fit the water flux and rejection of uncharged solutes to the experiments conducted. The model had a deviation below 2% for all experiments performed and suggested an average pore radius of 1.25 nm with a porosity of 21% for the Cu-MPD membrane. Overall, our study provides an exciting approach for fabricating a nonpolyamide high-performance nanofiltration membrane in the context of lithium recovery.

The Need for Accurate Osmotic Pressure and Mass Transfer Resistances in Modeling Osmotically Driven Membrane Processes.

The widely used van 't Hoff linear relation for predicting the osmotic pressure of NaCl solutions may result in errors in the evaluation of key system parameters, which depend on osmotic pressure, in pressure-retarded osmosis and forward osmosis. In this paper, the linear van 't Hoff approach is compared to the solutions using OLI Stream Analyzer, which gives the real osmotic pressure values. Various dilutions of NaCl solutions, including the lower solute concentrations typical of river water, are considered. Our results indicate that the disparity in the predicted osmotic pressure of the two considered methods can reach 30%, depending on the solute concentration, while that in the predicted power density can exceed over 50%. New experimental results are obtained for NanoH2O and Porifera membranes, and theoretical equations are also developed. Results show that discrepancies arise when using the van 't Hoff equation, compared to the OLI method. At higher NaCl concentrations (C > 1.5 M), the deviation between the linear approach and the real values increases gradually, likely indicative of a larger error in van 't Hoff predictions. The difference in structural parameter values predicted by the two evaluation methods is also significant; it can exceed the typical 50-70% range, depending on the operating conditions. We find that the external mass transfer coefficients should be considered in the evaluation of the structural parameter in order to avoid overestimating its value. Consequently, measured water flux and predicted structural parameter values from our own and literature measurements are recalculated with the OLI software to account for external mass transfer coefficients.