Phenomenological Modeling of Supercritical CO <sub>2</sub> Extraction for Critical Metal Recovery from NMC Black Mass
Bibliographic record
Abstract
The rapid growth of electric vehicle adoption is intensifying demand for lithium-ion batteries (LIBs), resulting in a rising volume of spent batteries and the need for efficient recycling strategies to recover critical metals. Supercritical fluid extraction (SCFE) using supercritical carbon dioxide (sc-CO 2 ) offers a sustainable route for metal recovery, particularly when combined with chelating and reducing agents. This study develops a phenomenological modeling framework by integrating Sovová’s broken and intact cell (BIC) model with the shrinking-core model to describe the extraction kinetics of Li, Co, Mn, and Ni from real NMC111 black mass. The BIC model successfully predicted extraction curves with deviations below 1.1%, identifying a Type A pattern dominated by rapid surface extraction followed by intraparticle diffusion. Shrinking-core analysis confirmed ash-layer diffusion as the rate-determining step, with apparent activation energies ranging from 4.8 to 14.9 kJ/mol. Comparison with Chrastil empirical solubility modeling validated the predictive accuracy of the BIC approach, highlighting stable solubility behavior for Li and Co and stronger sensitivity for Mn and Ni. By bridging macroscopic kinetics with mechanistic insights, this work establishes a predictive framework for optimizing SCFE processes, advancing environmentally responsible and scalable recycling of strategic metals from end-of-life LIBs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".