A PBM framework based on DEM modelling and particle breakage kinetics to investigate continuous grinding in ball mills

Abstract

Grinding is an important size reduction process in many industries. Current grinding devices have very low energy efficiency with only less than 20% of the total energy contributing to particle breakage. Therefore, developing a reliable grinding model is important for optimisation and scale-up of mills for improved efficiency and reduced operating costs. In this study, a framework based on population balance model (PBM) was developed to investigate continuous grinding in ball mills. The framework was able to predict particle size distribution (PSD) by incorporating the information obtained from the simulations using the discrete element method (DEM) (e.g. particle flow pattern, collision energy, collision frequency and residence time distribution) with particle breakage kinetics obtained from physical experiments (i.e. particle breakage rate and breakage function). The model was verified by comparing the predicted results with the data from experiments. The predicted PSD for batch and continuous process were also compared. The effect of operating variables such as rotation speed, inclination angle and ground particle loading on grinding performance was studied. Increasing rotation speed increase collision energy between grinding media and ground particles but reduced the mean residence time, resulting reduced product sizes. Smaller particle size was also obtained by increasing particle loading due to the increase in residence time of particles inside the mill even the collision energy profile was slightly higher for lower loadings. On the other hand, coarser particles were produced as the inclination angle increases due to the shorter mean residence times at higher inclination angles while the collision energy profile was almost the same. The effects of design parameters such as the number of lifters, lifter shape, ball size and particle size were also investigated. By increasing the ball size, the collision energy was increased while the mean residence time was reduced. However, the product size was reduced with increasing ball size, indicating that optimal grinding performance can only be achieved by balancing residence time and collision energy. On the other hand, the study showed that the number of lifters and lifter shape had optimal values that must be designed precisely based on the other variables. The effects of these parameters on Peclet number (Pe) which is the parameter that describes the RTD curve shape have also been studied. A relation between the mass fraction passing half of the original size (T2) and Pe was identified. This relation was affected by mean residence time and mean collision energy. It was found that higher Pe, mean residence time and mean collision energy lead to better grinding performance. So the Peclet number along with mean collision energy and mean residence time can be used as criterions in scale-up processes of continuous ball mills. In summary, a PBM framework has been successfully developed and applied to modelling continuous grinding in ball mills under different grinding conditions. The study has demonstrated that the framework is a useful tool for the design and optimization of the continuous grinding systems.