Phenomenological Modeling of Supercritical CO ₂ Extraction for Critical Metal Recovery from NMC Black Mass

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-CO2) 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.