A generic dynamic model structure for tumbling mills

Abstract

In order to develop a common mathematical and simulation platform for tumbling mills, the key aspects of grinding and both slurry and solids transport which are common to all tumbling mills are identified based on a review of existing mechanistic models and milling mechanics. Three versions of generic model structures for tumbling mills (the Generic Tumbling Mill Model Structure Versions 1 to 3: GTMMS I, GTMMS II, and GTMMS III) have been developed based on the population balance framework by incorporating sub-models for breakage characteristics, energy distribution, slurry and solids transport, and discharge. GTMMS I firstly integrates the transport function into a dynamic model structure. As an upgrade of GTMMS I, GTMMS II incorporates a 4D (four dimensional) appearance function sub-model derived from the JK Rotary Breakage Test (JKRBT) data to substitute the existing JK M-p-q t10-tn based appearance function model and applies the Discrete Element Method (DEM) energy distribution model, which can replace the traditional selection function, into the model structure. To obtain a 4D appearance function with wider applicable ranges, the JK Mini drop weight tester (JK Mini DWT) was used to conduct drop weight tests for smaller particles with sizes ranging from 16 mm to 0.45 mm. The test results, together with the existing data from JK Standard Drop Weight Tests (JK DWT), were analysed and the wide-range (Ore particle sizes ranging from 425 mm to 63 mm and the input specific energy from 0.1 kWh/t ~ 2.5 kWh/t) 4D appearance function models, namely the wide-range P80-m based 4D model and the wide-range P80-m-q based 4D model, were developed. All the 4D models have better performance in comparison with other t10 based models. The wide-range 4D appearance function model, together with the DEM energy distribution model corrected by probability-based energy split scheme with both volume ratio and stiffness ratio considered, and the multi-component sub-model were successfully applied to GTMMS III. All three versions of GTMMS were validated against plant data, and the predictions agree well with plant data. GTMMS I, II and III can work independently depending on the availability of plant data. Because of the harmonic integration of the 4D appearance function, DEM energy distribution model, transport function, discharge function, power model, dynamic modelling and multi-component modelling, GTMMS I, II and III are more mechanistic, generic, reliable, scalable and applicable and can be treated as vital milestones towards the goal of mechanistic grinding mill modelling and forming a platform for future models such as the unified comminution models (UCM).