The kinetic population balance model (PBM) is widely used to predict the particle size distributions of grinding products. However, the model may not be solved if the rate of particle accelerates or decelerates in the mill hold-up, i.e., non-first-order breakage. This study presents a computational algorithm coupled with a pseudo-matrix model to simulate the product size distributions (PSDs) of successive breakage events at grinding. The algorithm's applicability and accuracy were validated

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... nst PSDs taken from different grinding equipment. The advantages of the algorithm are as follows—(i) time can be implicitly or explicitly added to the algorithm. (ii) The parameters required to run the algorithm are quite few. (iii) The proposed algorithm can predict PSDs in the normal or abnormal breakage region. Even a short-time grinding test will be sufficient to estimate the parameters if abnormal breakage effects are reduced or eliminated. (iv) The algorithm can work with arbitrary sets of parameters that are irrelevant to the mill feed and mill type. Also, the algorithm's framework shows that grinding is not a chaotic process; yet it may be due to the surface/gravitational attraction forces between particles and grinding media.