Integrated Modeling of the Kinetic Evolution of True Flotation and Entrainment Species: A Low-Cost Strategy for Grinding–Flotation Optimization

Flotation circuits typically incorporate grinding stages, yet mathematical models for these processes often operate on different principles, leading to misalignment in circuit design. Building on a previously established grinding model for flotation performance, this research introduces significant advances to develop a more comprehensive and industrially relevant framework. The primary innovation is the integration of mechanical entrainment and gangue recovery into the kinetic model, distinguishing between species captured by true flotation and those carried to the surface despite being non-hydrophobic. We developed a robust set of grinding-mill equations based on first-order kinetics to describe the mass-fraction transformation of both true-flotation and entrainment species. To ensure practical applicability, a systematic experimental and modeling methodology for parameter adjustment is introduced, providing a clear sequence for identifying breakage rate constants and flotation kinetic parameters. The proposed strategy was validated using two distinct case studies: an expanded analysis of a copper sulfide ore (ore A) and a new case involving significant gangue entrainment (ore B). The results demonstrate that the model accurately predicts species kinetics, providing a high-fidelity, cost-effective tool to optimize mineral recovery and prevent economic losses from overgrinding in industrial processing plants.