(246b) High Throughput Characterization of Membrane Transport Properties through Data Analytics

Compared to traditional separations, membrane-based systems have demonstrated significant advantages in sustainability and energy applications. Further advances will rely on membranes capable of achieving higher degrees of selectivity, which can be realized through enhanced control over membrane nanostructure and chemical functionality to accentuate desired transport properties. [1],[2] We argue process systems engineering offers untapped capabilities to balance membrane design decisions across molecular, nanostructure, device, and systems scales, and such a multiscale perspective is essential to fully realize the potential of nanoengineering to deliver transformative membrane separation technologies. [3] 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 application is mostly systems, not materials, limited. [4] In another study, we developed a process targeting framework to identify the necessary molecular and materials properties to realize absorptive membranes for environmental remediation. [5] But, an advanced understanding of the molecular separation phenomena that connect nanoengineering and materials informatics to transport properties is needed to better inform these design frameworks. [6],[7] Often, the iterative development and validation of physics-based mathematical models is time-consuming and can be a rate-limiting step in scale-up, design, and optimization. While systems engineering tools such as advanced nonlinear regression and model-based experiments have addressed these modeling challenges in absorption thermodynamics and reaction kinetics[8]-[10] domains, their application to membrane science challenges remains limited.

In this talk, we demonstrate how experimental measurements and data analytics inform each other to discriminate between possible transport mechanisms and accelerate the characterization of membrane transport properties for process design. Dynamic diafiltration experiments are developed by dosing a concentrated dialysate into a stirred cell to achieve a predetermined ramp in concentration. This apparatus design enables membrane characterization under a broad range of conditions, bridging the gaps that exist within conventional filtration experiments. Pressurized with nitrogen gas, permeate product is collected in several scintillation vials. Continuous mass and the final concentration of the permeate product in each scintillation vial are measured. Retentate concentration is monitored through a conductivity probe immersed in the stirred cell. We then postulate a family of differential-algebraic equation models for the system. Weighted least-square estimation is used to successfully calibrate the hydraulic permeability and the solute permeability coefficient that correspond to the membrane transport properties, as well as the reflection coefficient that depends on the thermodynamics of the membrane-solution interface. As a proof of concept, we consider diafiltration experiments for K+ ions across a DuPont NF-90 nanofiltration membrane. Sensitivity analyses over these parameters were performed to explore the impact of the three different experimental observations (i.e., the mass of collected samples, retentate and permeate concentrations). In this talk, we will highlight three specific synergies between mathematical models and experiments:

1. We determined the reflection coefficient is not identifiable in conventional filtration experiments at low concentrations and used the model to inform the diafiltration experiment design that covers high concentration ranges.

2. Through sensitivity analysis of the model, we recommended the collection of time-series retentate concentration measurements, which led to the engineering of an inline conductivity probe enhancement to the experimental apparatus.

3. As anticipated, we found that incorporating the correct physics improves the quality of fit. In the context of these experiments, modeling concentration polarization phenomenon properly is important.

Despite the effort of analyzing a single phenomenon presence in example (3), there still exist major challenges on how to validate among all candidate models that represent different phenomena combinations. As ongoing work, we are exploring the model-based design of experiments techniques for statistical model discrimination as well as experiment adaption[11]-[13] to elucidate transport mechanisms in membrane separations. Ultimately, we expect an automated platform with online data analysis and experiment setup for model identification and membrane characterization.

References

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

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

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

4. 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).

5. 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).

6. 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).

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

8. Floudas, C. A., Niziolek, A. M., Onel, O., & Matthews, L. R. (2016). Multi‐scale systems engineering for energy and the environment: Challenges and opportunities. AIChE Journal, 62(3), 602–623. https://doi.org/10.1002/aic.15151

9. Hasan, M. M. F., Baliban, R. C., Elia, J. A., & Floudas, C. A. (2012). Modeling, Simulation, and Optimization of Postcombustion CO 2 Capture for Variable Feed Concentration and Flow Rate. 1. Chemical Absorption and Membrane Processes. Industrial & Engineering Chemistry Research, 51(48), 15642–15664. https://doi.org/10.1021/ie301571d

10. Vlachos, D. ., Mhadeshwar, A. ., & Kaisare, N. . (2006). Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing. Computers & Chemical Engineering, 30(10), 1712–1724. https://doi.org/10.1016/j.compchemeng.2006.05.033

11. Bonvin, Georgakis, Pantelides, Barolo, Grover, Rodrigues, Schneider, & Dochain. (2016). Linking Models and Experiments. Industrial & Engineering Chemistry Research, 55(25), 6891–6903. https://doi.org/10.1021/acs.iecr.5b04801

12. Franceschini, G., & Macchietto, S. (2008). Model-based design of experiments for parameter precision: State of the art. Chemical Engineering Science, 63(19), 4846–4872. https://doi.org/10.1016/j.ces.2007.11.034

13. Galvanin, F., Cao, E., Al-Rifai, N., Gavriilidis, A., & Dua, V. (2016). A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors. Computers & Chemical Engineering, 95(C), 202–215. https://doi.org/10.1016/j.compchemeng.2016.05.009