Comparison of PBM and ANPM models for predicting grinding product size distributions

Abstract

Grinding is a very important industrial operation that draws up to 4% of the global electricity consumption. It is imperative to predict accurately the appropriate retention times necessary for a given size reduction to minimize the wasted energy invested in overgrinding. However, the most common models for scaling, such as Bond, could lead to a design risk on the order of ± 20% due to their assumption that a single particle size can describe the entire particle size distribution. Thus, different approaches (both phenomenological and non- phenomenological) need to be explored.

In the present work, a population balance model is compared with an algebraic statistical model, to predict the evolution of particle size distribution over time, assessing them in terms of accuracy, robustness, and computational complexity. Even though the population balance model had a lower accuracy and higher mathematical complexity its predictions were physically coherent, which made it a more robust model for extrapolating to different initial conditions and milling times. It is important to note that due to the 2020 COVID-19 pandemic, experimental information was limited, which inhibited an independent validation of the models, and an overfitting analysis for the ANPM.