Predictive pebble flow in SAG mills via DEM–PBM coupling

Semi-autogenous grinding (SAG) mill performance prediction remains limited by empirical calibration requirements in conventional population balance models. This study presents a structured dynamic framework integrating the Reynolds Transport Theorem with a matrix-based Population Balance Model (PBM), explicitly incorporating residence time and two-stage internal classification, coupled with Discrete Element Method (DEM) simulations to predict pebble discharge and fines generation. The methodology combines DEM-derived impact data, a double-Gaussian selection function calibrated via nonlinear regression, and a power-based specific energy model to quantify comminution performance. Six operational cases were evaluated, varying ore competency (Axb) and ball filling level (Jb). The calibrated selection function achieved coefficients of determination (R2) between 0.86 and 0.996. Results indicate that increasing ball filling from 0 to 15% enhances fine particle generation up to 95% and reduces pebble discharge by approximately 50% under high-hardness conditions. Specific energy consumption ranged between 4.39 and 8.42 kWh·t⁻1 across the evaluated scenarios. An efficiency index relating fine mass fraction (< 40 mm) to specific energy consumption is introduced to support performance assessment. The proposed DEM–PBM coupling framework provides a physically consistent approach for SAG mill discharge prediction and energy-performance evaluation.