(311g) Designing Operationally Flexible Diafiltration Membrane Systems for Critical Mineral Separations

Society’s transition toward clean energy technologies and growing consumption of high technology products is driving a major increase in demand for critical minerals (CMs)—designated in the United States as elements serving essential functions in energy technologies with high risk for supply chain disruption [1]. However, the fact that CMs are highly concentrated in a small number of geographical regions, the decline in quality of primary resources, and concerns with environmental harm from current processes all make novel, sustainable processes for CM recovery extremely desirable [2]. Membrane processes are a promising advanced technology for recovering CMs from mining waste streams and have seen success in other wastewater treatment applications [3]. The design and deployment of these systems require rigorous mathematical modeling and optimization, as well as a reduction of technical risks caused by process uncertainties.

To enable equation-oriented optimization in this context, we have developed a flowsheet-level model of a multi-stage, multi-period diafiltration membrane system using the IDAES Integrated Platform (IDAES-IP) [4]. The model is based on a lumped parameter model for convectively driven transport that uses solute sieving coefficients and solvent flux to characterize membrane performance, as proposed in the literature for CM separations using membrane cascades of this sort [5]. Our membrane cascades are designed as multiple skids, each containing several membrane tubes (i.e., modules) in series, where the model can be initialized with any number of membrane unit stages and tubes. We consider a hierarchy of process superstructures for feed, diafiltrate, recycle, and product streams: (i) a base case with fixed inlet and outlet flows; (ii) a superstructure that introduces degrees of freedom for feed, diafiltrate, and recycle flows into different stages, flow of a mixed stage inlet into different tubes, and flows of products from each stage; and (iii) a more generalized superstructure allowing for freedom in choosing inlet flows at any stage and tube and outlet flows from any stage. The membrane model is extended to include precipitators for downstream product recovery and recycling of water with dilute CMs as diafiltrate.

We demonstrate the use of this model for the downstream separation and recovery of cobalt and lithium leached from recycled lithium-ion batteries. We first obtain hierarchies of deterministically cost-optimal designs for varying the number of stages, the number of tubes in each stage, and the process superstructure. We also investigate case studies of changing process conditions, such as varying feed flow rates and decreasing membrane flux with time due to fouling. These results help us elucidate the process recovery performance gains expected from employing more sophisticated membrane cascades that offer greater operational flexibility.

To reduce technical risks associated with our membrane system designs, we also apply robust optimization using the Pyomo Robust Optimization Solver (PyROS) [6,7]. Here, we consider major process uncertainties in feedstock quality and membrane performance. In our robust optimization framework, we partition our variables into design (membrane area) and operational (inlet flows at different locations and diafiltrate recycle flowrates) degrees of freedom. A suite of uncertainty sets available in PyROS can be used to model uncertainty, where, for example, a continuous set can represent the uncertainty in feedstock concentration, while a discrete scenario set can model various situations of membrane underperformance due to manufacturing defects. With such a setup, PyROS yields robust optimal solutions that remain feasible across all realizations of uncertainty along with insights into the worst-case performance of the system, which can, in turn, lead practitioners to develop risk mitigation strategies.

Our work designing operationally flexible diafiltration membrane cascades offers new perspectives on superstructure configuration and choice of inlet/outlet flow locations for membrane system operation over multiple periods. Our model helps us explore the designs necessary for satisfactory performance under changing operating conditions, and through robust optimization, these designs can perform satisfactorily despite model uncertainties. Our results help to further initiatives in deploying and operating sustainable CM recovery processes and demonstrate the successful application of PyROS to consider uncertainty in the context of membrane cascade process design.

[1] Notice of Final Determination on 2023 DOE Critical Materials List. Federal Register. https://www.federalregister.gov/documents/2023/08/04/2023-16611/notice-of-final-determination-on-2023-doe-critical-materials-list (accessed 2024-03-18).

[2] Executive summary – The Role of Critical Minerals in Clean Energy Transitions – Analysis. IEA. https://www.iea.org/reports/the-role-of-critical-minerals-in-clean-energy-transitions/executive-summary (accessed 2024-03-18).

[3] Sarker, S. K.; Haque, N.; Bhuiyan, M.; Bruckard, W.; Pramanik, B. K. Recovery of Strategically Important Critical Minerals from Mine Tailings. Journal of Environmental Chemical Engineering 2022, 10 (3), 107622. https://doi.org/10.1016/j.jece.2022.107622.

[4] Lee, A.; Ghouse, J. H.; Eslick, J. C.; Laird, C. D.; Siirola, J. D.; Zamarripa, M. A.; Gunter, D.; Shinn, J. H.; Dowling, A. W.; Bhattacharyya, D.; Biegler, L. T.; Burgard, A. P.; Miller, D. C. The IDAES Process Modeling Framework and Model Library—Flexibility for Process Simulation and Optimization. Journal of Advanced Manufacturing and Processing 2021, 3 (3), e10095. https://doi.org/10.1002/amp2.10095.

[5] Wamble, N. P.; Eugene, E. A.; Phillip, W. A.; Dowling, A. W. Optimal Diafiltration Membrane Cascades Enable Green Recycling of Spent Lithium-Ion Batteries. ACS Sustainable Chem. Eng. 2022, 10 (37), 12207–12225. https://doi.org/10.1021/acssuschemeng.2c02862.

[6] Isenberg, N. M.; Akula, P.; Eslick, J. C.; Bhattacharyya, D.; Miller, D. C.; Gounaris, C. E. A Generalized Cutting-Set Approach for Nonlinear Robust Optimization in Process Systems Engineering. AIChE Journal 2021, 67 (5), e17175. https://doi.org/10.1002/aic.17175.

[7] Isenberg, N. M.; Sherman, J. A.; Siirola, J. D.; Gounaris, C. E. PyROS: The Pyomo Robust Optimization Solver. Forthcoming. 2024.

Acknowledgments

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 Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a support contract. Neither the United States Government nor any agency thereof, nor any of its 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.