Efficient cumulative breakage distribution and breakage rate computation with minimal experiment intervention incorporating optimal time determination for fine grinding simulation

Comminution involves the reduction of materials to the required sizes, from coarser to finer. The population balance method (PBM) is the most frequently used approach to obtain the particle size distribution (PSD) of materials. To numerically obtain the PSD, a semi-empirical approach known as the size-mass balance equation is commonly employed. The existing technique to determine the parameters in the size-mass balance equation is cumbersome as PSD for early grinding times of different feed sizes must be obtained experimentally. Therefore, a new technique using only a limited data to determine the parameters is introduced and examined. In general, the strong capability of the presently proposed technique is evidenced through successfully capturing of the existing experimental PSD. The advantages of using this technique are that only two experimental PSD of any grinding time are needed to predict the PSD using the size-mass balance equation and without the restriction of input from an early grinding time. This study also proposes to use the cumulative PSD rates as an indicator for the limit of particle size reduction of the materials. It is suggested that the grinding of materials should stop before there is a pivotal change in the initial slopes, i.e., before the difference of the cumulative PSD rates between each initial slopes is found to change sign, or when the difference of the cumulative PSD rates is close to 0% in order to prevent agglomeration or over-grinding. The grinding time fulfilling this criterion is considered as optimal