Optimal operation guidelines for direct recovery of high‐purity precursor from spent lithium‐ion batteries: hybrid operation model of population balance equation and data‐driven classifier

The direct resynthesis of precursor from spent lithium‐ion batteries (LIBs) via co‐precipitation is a crucial step in closed‐loop cathode recycling systems. However, design and operation strategies for producing high‐purity precursors have not been comprehensively explored or optimized. Herein, we propose the optimization of co‐precipitation during the recovery of spent LIBs to achieve impurity‐free precursor resynthesis. By incorporating the thermodynamic equilibrium model of the leaching solution of spent LIBs into a population balance equation (PBE) model, we identified the operating ranges that prevented the formation of impurities. Bayesian optimization was employed within the screened operating ranges to determine the optimal operating conditions for minimizing both operation time and maximum particle size. This optimization was performed for both unseeded batch and semi‐batch systems. The results demonstrate that the selection of an optimal semi‐batch operation can reduce the operation time by 23.33% and increase the particle size by 54.75%, owing to the high nucleation and particle growth rate during the initial time step. By employing an optimization approach based on the PBE model, this study provides detailed operational guidelines for batch and semi‐batch co‐precipitation, enabling the production of high‐purity precursor materials from spent LIBs, while minimizing both operating time and maximum particle size. This study proposes an operation optimization framework for impurity‐free recycling of spent lithium‐ion batteries. Using a hybrid population balance equation integrated with a data‐driven condition classifier, the study firstly identifies the optimal batch and semi‐batch operation conditions that significantly reduce the operation time with 100% purity of product; detailed guidelines are given for industrial applications.