(123c) Modeling Multi-Component Critical Material Feed Streams to Enable Design and Optimization of Multi-Stage Diafiltration Cascades

The U.S. Department of Energy acknowledges 68 critical materials with high-risk supply chains that are essential to national security [1]. These critical minerals and materials can be harvested from primary sources, such as mineral ore, or from unconventional, secondary sources. These unconventional and secondary sources include a broad range of materials ranging from recycled sources, such as spent consumer electronic waste, to post-industrial waste, such as coal combustion residuals (e.g., coal ash). With the concentrations of critical materials within primary ore declining, there is increased focus on securing the supply chains of critical materials via facilitating recovery from unconventional and secondary sources [2]. Regardless of the source, the conventional pathways for harvesting many critical materials (i.e., acid leaching, solvent extraction, pH adjustment, and precipitation) have opportunities for improvement [2]. Thus, we propose implementing membrane separations to recover critical materials to improve process efficiency and reduce process costs [2,3].

In this work, we consider a feedstock of lithium-ion battery leachate as a case study for the recovery of critical materials using a multi-stage diafiltration cascade modeled using the IDAES-PSE framework [4], which is built on Pyomo [5]. Previous work shows that superstructure optimization of the diafiltration cascade model is capable of efficiently designing robust, cost-optimal membrane systems to meet product specifications for lithium and cobalt products [6,7]. However, realistic critical material feed streams are more complex (i.e., contain multiple species with varying concentrations) [2] and higher fidelity models are required to accurately capture transport phenomena and inform process design.

We propose a multi-component model for diafiltration cascades to recovery critical materials from complex feed streams such as lithium-ion battery leachate. Specifically, we use the extended Nernst-Plank equation, which accounts for convection, diffusion and electromigration, to derive the appropriate cross-diffusion relationships. Combined with additional constraints to describe ion partitioning at the membrane-solution interface and fluid convection through the cascade, the model can capture the effect of ion-ion interactions on the overall recovery of the system. We extend the modeling framework [7] to generate cost-optimal diafiltration cascades to meet product purity specifications for these complex streams. Using the high-fidelity model developed in this work, we present design strategies for recovering multiple high-value products from a mixed feed stream using multi-stage diafiltration cascades.

Acknowledgements: This effort was funded by the U.S. Department of Energy’s Process Optimization and Modeling for Minerals Sustainability (PrOMMiS) Initiative, supported by the Office of Fossil Energy and Carbon Management’s Office of Resource Sustainability.

Disclaimer: This project was funded by the United States Department of Energy, National Energy Technology Laboratory, in part, through a support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, or any of their contractors.

References

[1] What are critical materials and critical minerals? https://www.energy.gov/cmm/what-are-critical-materials-and-critical-min…

[2] Laurianne Lair, Jonathan Aubuchon Ouimet, Molly Dougher, Bryan W Boudouris, Alexander W Dowling, and William A Phillip. Critical mineral separations: Opportunities for membrane materials and processes to advance sustainable economies and secure supplies. Annual Review of Chemical and Biomolecular Engineering, 15:243–266, 2024.

[3] Molly Dougher, Laurianne Lair, Jonathan Aubuchon Ouimet, William Phillip, Thomas Tarka, and Alexander Dowling. Opportunities for process intensification with membranes to promote circular economy development for critical minerals. Systems and Control Transactions, 3:711–718, 2024.

[4] Andrew Lee, Jaffer H Ghouse, John C Eslick, Carl D Laird, John D Siirola, Miguel A Zamarripa, Dan Gunter, John H Shinn, Alexander W Dowling, Debangsu Bhattacharyya, et al. The IDAES process modeling framework and model library—flexibility for process simulation and optimization. Journal of advanced manufacturing and processing, 3(3):e10095, 2021.

[5] Michael L Bynum, Gabriel A Hackebeil, William E Hart, Carl D Laird, Bethany L Nicholson, John D Siirola, Jean-Paul Watson, David L Woodruff, et al. Pyomo-optimization modeling in python, volume 67. Springer, 2021.

[6] Noah P Wamble, Elvis A Eugene, William A Phillip, and Alexander W Dowling. Optimal diafiltration membrane cascades enable green recycling of spent lithium-ion batteries. ACS Sustainable Chemistry & Engineering, 10(37): 12207-12225, 2022.

[7] Jason L Yao, Molly Dougher, Andrew Lee, Alexander W Dowling, Chrysanthos E Gounaris. Robust Optimization of Flexible Diafiltration Systems for Critical Mineral Separations. In Preparation.