Machine Learning-Based Prediction of Elemental Distribution Rates in Pyrometallurgical Copper Production

Understanding elemental distribution among slag, dust, and copper-bearing products during pyrometallurgical copper production is critical for minimizing valuable metal losses, controlling potentially hazardous elements, and improving resource recovery. However, prediction of elemental distribution rates under diverse industrial conditions remains challenging. In this study, multiple machine learning (ML) models were developed and compared for predicting elemental distribution rates based on output-stream descriptors, elemental properties, feed compositions, and process-technology descriptors, using a dataset comprising 370 samples. The ML models were trained and optimized using Bayesian optimization (BO), and permutation importance was used to identify the variables contributing most to the model predictions. The results showed that the optimized CatBoost model achieved the best predictive performance on the independent testing set, with a coefficient of determination (R2) of 0.672, a root mean square error (RMSE) of 12.955, and a mean absolute error (MAE) of 9.312. Permutation importance analysis indicated that output-stream descriptors mainly provided conditional information for distinguishing prediction scenarios, while elemental descriptors contributed to differentiating element-specific distribution behaviors. Predictions based on constrained virtual samples further revealed distinct element-specific distribution patterns across the five output streams. Zn and Co showed stronger tendencies to report to slag, whereas Hg, As, Bi, and Cd were preferentially enriched in dust; Ni was mainly distributed between converting slag and blister copper. Despite the relatively high importance of elemental properties, no individual elemental descriptor exhibited a consistent monotonic relationship with distribution behavior. These results demonstrate the potential of the proposed framework for predicting elemental distribution rates under heterogeneous industrial conditions, while further improvement in prediction is required for high-precision process control or quantitative mass-balance applications.