Development of a Non-linear Framework for the Prediction of the Particle Size Distribution of the Grinding Products "Mining, Metallurgy & Exploration (2021)"

The main objective of batch grinding modeling is the estimation of the product particle size distribution over time or specific energy input to the mill. So far, the developed analytical methods require often complicated calculations which are timeconsuming. Thus, more simple approaches that allow the reliable prediction of the complete product size distribution need to be developed. In the present paper, an approach, based on the population balance model (PBM), that reliably predicts the product size distribution is proposed. In order to enable this, the simplified form of the fundamental batch grinding equation was transformed into the well-known Rosin–Rammler (R-R) distribution, thus allowing the determination of the breakage rate for each grinding period. A time-dependent breakage rate framework was developed where the traditional linear theory of the PBM is considered a partial case. This approach allows the deviations from the linear theory to be categorized and the degree of the acceleration-deceleration of the breakage rate to be predicted. Modeling results were validated by laboratory grinding studies using two homogeneous materials, quartz and marble, and one heterogeneous, a limonitic laterite. The experimental data revealed that grinding exhibits non-first-order behavior and the degree of deviation from the linear theory depends on the tested material. The reliability of the proposed model was validated with the use of the distribution modulus n, the a value of the breakage rate parameter, and the optimum n values that minimize the sum of the differences between the experimental and estimated particle size distributions.