(85b) Dynamic Modeling and Nonlinear Parameter Estimation of Nanofiltration Membranes

Compared to traditional chemical separation techniques, membrane processes offer compact configurations and energy-efficient means to achieve molecular scale separations. Membranes capable of achieving higher degrees of selectivity relies on both the precise control of a membrane’s nanostructure and the identification of chemical functionalities which accentuate desired transport properties. [Hoffman & Phillip, 2020; Sadeghi et al., 2018] We argue process systems engineering offers untapped capabilities to balance membrane design decisions across (macro)molecular, device, and systems scales, and such a multiscale perspective is essential to fully realize the potential of nanoengineering to deliver transformative membrane separation technologies. [Eugene et al., 2019a] For example, we recently developed a superstructure optimization framework to design diafiltration membrane cascades. Our analysis shows that, through optimal systems-scale design, existing membrane materials have the potential to outperform current Li/Co separation methods for lithium-ion battery recycling; in other words, this particular application is mostly systems, not materials, limited. [Eugene et al., 2019b] In another study, we developed a process targeting framework to identify the necessary molecular and materials properties to realize absorptive membranes for environmental remediation. [Eugene et al., 2020] But extending these PSE paradigms to more directly inform nanoengineering requires more detailed and realistic mathematical models. [Geise et al, 2014; Yaroshchuk et al., 2018] Often the iterative creation and validation of said models is time-consuming and can be a rate-limiting step in scale-up, design, and analysis.

In this talk, we present an integrated experimental and data analysis technique to dynamically characterize nanofiltration membranes, resulting in differential-algebraic process models with quantified uncertainty suitable for process design. Experiments were run in a 10 mL dead-end filtration Amicon 8010 stirred cell connected with a dialysate tank. We conducted transport studies by loading both the cell and tank with predetermined concentrations of the desired salt and pressurizing the system with nitrogen gas. This apparatus design allows for continuous monitoring of permeate sample mass. Both retentate and sample concentrations are measured at regular intervals. We then postulate a family of differential-algebraic equation models for the system. Nonlinear regression is used to successfully calibrate hydraulic permeability, solute permeability coefficient, and reflection coefficient parameters in the model. These parameters correspond to the membrane transport properties and depend on the membrane chemistry, membrane nanostructure, and thermodynamics of the membrane-solution interface. As proof of concept, we consider diafiltration experiments for Mg²⁺ and K⁺ ions across an NF-90 nanofiltration membrane. We cast nonlinear parameter estimation as a multi-objective least-squares optimization problem and explore the trade-offs between different experimental observations, i.e., the mass of collected samples and sample concentrations. Through this analysis, we determined reflection coefficient is not identifiable in conventional filtration experiments and used the model to inform the diafiltration experiment design that covers higher concentrations. Finally, we discuss how the proposed dynamic experiments and data analysis technique require much less data than classical steady-state experiments to create and validate a model.

References

Eugene, E., Phillip, W., and Dowling, A., Data science-enabled molecular-to-systems engineering for sustinable water treatment, Current Opinion in Chemical Engineering, 26, 122-130, (2019a).

Eugene, E., Phillip, W., and Dowling, A., Material Property Goals to Enable Continuous Diafiltration Membrane Cascades for Lithium-ion Battery Recycling, Computer Aided Chemical Engineering, 47, 469-474, (2019b).

Eugene, E., Phillip, W., and Dowling, A., Material Property Targets for Emerging Nanomaterials to Enable Point-of-Use and Point-of-Entry Water Treatment Systems, Preprint,
https://doi.org/10.26434/chemrxiv.12526190, (2020).

Geise, G. M., Paul, D. R., Freeman, B. D., Fundamental water and salt transport properties of polymeric materials, Progress in Polymer Science, 39(1), 1-42, (2014)

Hoffman, J. R., and Phillip, W. A., 100^th Anniversary of Macromolecular Science Viewpoint: Integrated Membrane Systems, ACS Macro Letters, 9, 1267-1279, (2020).

Sadeghi, I., Kaner, P., and Asatekin, A., Controlling and Expanding the Selectivity of Filtration Membranes, Mater., 30(21), 7328–7354 (2018).

Yaroshchuk, A., Bruening, M. L., and Zholkovskiy, E., Modelling nanofiltration of electrolyte solutions, Advances in Colloid and Interface Science, 268, 39-63, (2019).