A generic dynamic model incorporating a 4d appearance function for tumbling mills

A mill model structure based on the population mass balance framework incorporating breakage characteristics, slurry and solids transport, product classification and discharge and energy consumption was reported in XXVII IMPC and named the Generic Tumbling Mill Model Structure Version I (GTMMS I). In this work, a new 4D (four dimensional) appearance function sub-model based on the experimental results of the JK Rotary Breakage Tester (JK RBT) was developed to describe the breakage characteristics and was applied to this new model structure. The newly developed 4D appearance function model has fewer fitting parameters and is more generic in nature. Most importantly, it is applicable to both high and low energy impact breakage. It is therefore much more versatile in comparison to the existing JKMRC t₁₀t_n appearance function and the size-dependent JK M-p-q t₁₀-t_n appearance function. In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. With DEM results providing energy distribution information inside the mill directly, the selection function and the back-calculation method used in the existing JKSimMet modelling method are not needed in this model structure. With the above two revolutionary innovations, the previous model structure was upgraded to the Generic Tumbling Mill Model Structure Version II (GTMMS II). Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation. A case of the dynamic grinding of a SAG mill was studied to validate the GTMMS II. The model simulation results agreed well with the plant data. With the newly developed 4D appearance function model, the incorporation of DEM energy distribution and transport function, the GTMMS II is an important step forward towards mechanistic modelling of tumbling mills.