(596e) De-Risking the Scale-up of Novel Critical Minerals Separation

The demand for critical minerals and materials (CMM) is expected to increase approximately 6-fold by 2050 [1]. CMMs (e.g., lithium, cobalt, rare earth elements), which are critical to the economic security of the US, are vulnerable to global supply chain disruptions. By 2030, only about 50% of the demand for lithium is expected to be met [2]. A 2022 report by the International Energy Agency showed that less than 3% of CMMs are recycled [1]. Therefore, to address the demand deficit of CMMs, recycling technologies must be developed and deployed on an industrial scale. Membrane-based separations are promising due to their avoidance of expensive chemical solvents used in conventional separation systems and minimal energy consumption. Our collaborators at the University of Notre Dame (UND) have installed a novel diafiltration apparatus for CMM recycling with the goal of building a three-stage bench-top experiment to achieve 95% lithium recovery [2, 3]. Wamble et al. (2022) developed the model for the three-stage diafiltration membrane [2]. In the model, the separation performance is captured in the Sieving Coefficients (SC), which measure the membrane’s ability to retain or allow the passage of a solute (i.e., lithium and cobalt).

Accurately estimating the SCs of the membrane system is critical to enable the successful demonstration of this process on a pilot plant, ensuring that this is achieved with the lowest capital investment. However, this is a difficult task. Biegler et al. (1986) showed that parameter estimation in general can be challenging as the assumed model may be incorrect and the error structure unknown, all of which require experimental data to estimate [4]. Experimentation can be expensive and time-consuming. Design of experiment (DoE) techniques reduce this cost by using models to identify the most impactful experimental conditions. Conventional DoE methods (e.g., factorial design) evaluate the impact of a selected level of factors on responses without process knowledge [5]. This may produce experiments with low information content. Shahmohammadi and McAuley (2019) used science-based DoE (SBDoE), which leverages process-based models, to identify the most informative experiments for pharmaceutical production [6]. Wang and Dowling (2022) developed Pyomo.DoE, an open-source Python package for SBDoE in Pyomo [5]. This work aims to address the following question: Can SBDoE reliably identify the experiments needed to estimate the SCs of the three-stage membrane?

In this work, we used SBDoE in Pyomo.DoE to identify the next best experiments that maximize the information gained in the SCs of the three-stage diafiltration apparatus for lithium and cobalt separation. The information gained in the SCs was measured using four metrics of the Fisher information matrix: trace (A-optimality), determinant (D-optimality), minimum eigenvalue (E-optimality), and condition number (ME-optimality). Preliminary data from the apparatus were generated using a full-factorial design (FFD) to sample experimental conditions at the high and low levels of four decision variables: feed flowrate, diafiltrate flowrate, and feed lithium and cobalt concentrations. The predictions of the measured variables from FFD were scaled with Gaussian noise, with a mean of 0 and a standard deviation of 2% for flow rate and 3% for concentration. SC estimates were evaluated from the preliminary data using the weighted least squares objective, and their uncertainty was calculated using first-order error propagation and Monte Carlo simulation. The calculated uncertainty in the lithium SC was significant. Given a fixed feed concentration, SBDoE identified high feed and low diafiltrate flowrates as the next experimental conditions to increase the information gained in the lithium SC.

Finally, our experimental collaborators at UND have developed plans to build this three-stage diafiltration bench-top experiment. Upon completion, the experimentalists plan to conduct three experiments to estimate the SCs. Based on this planned experimental campaign, we identified low feed and diafiltrate flowrates at the high-high, high-low, and low-high concentrations of lithium and cobalt as the best three experiments for them to perform from the eighteen available options (sixteen FFD experiments and two from SBDoE).

References

1. International Energy Agency. The Role of Critical Minerals in Clean Energy Transitions. World Energy Outlook Special Report 2022. https://www.iea.org/reports/the-role-of-critical-minerals-in-clean-energy-transitions
2. 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 Sustain. Chem. Eng. 2022, 10 (37), 12207–12225. https://doi.org/10.1021/acssuschemeng.2c02862
3. Ouimet, J. A.; Liu, X.; Brown, D. J.; Eugene, E. A.; Popps, T.; Muetzel, Z. W.; Dowling, A. W.; Phillip, W. A. DATA: Diafiltration Apparatus for High-Throughput Analysis. Journal of Membrane Science 2022, 641, 119743. https://doi.org/10.1016/j.memsci.2021.119743
4. Biegler, L. T.; Damiano, J. J.; Blau, G. E. Nonlinear Parameter Estimation: A Case Study Comparison. AIChE J. 1986, 32 (1), 29–45. https://doi.org/10.1002/aic.690320105
5. Wang, J.; Dowling, A. W. Pyomo.DOE: An Open‐Source Package for Model‐Based Design of Experiments in Python. AIChE Journal 2022, 68 (12), e17813. https://doi.org/10.1002/aic.17813
6. Shahmohammadi, A.; McAuley, K. B. Sequential Model-Based A- and V-Optimal Design of Experiments for Building Fundamental Models of Pharmaceutical Production Processes. Chem. Eng. 2019, 129, 106504. https://doi.org/10.1016/j.compchemeng.2019.06.029

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 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.