Important advances have been made in the last 60 years or so in the modeling of ball mills using mathematical formulas and models. One approach that has gained popularity is the population balance model, in particular, when coupled to the specific breakage rate function. The paper demonstrates the application of this methodology to optimize solids concentration in ball milling of an iron ore from Brazil. The wet grinding experiments were conducted in bench (0.25 m diameter) and pilot-scale mills (0.42 m diameter), and surveys in a full-scale industrial (5.2 m diameter) mill. It is first demonstrated that the successful application of the model required recognizing the non-normalizable nature of the breakage function of the particular ore. It is then demonstrated how the model can be used to predict results of pilot-scale grinding tests under different conditions (overflow/grate discharge) based on data from batch grinding tests. Finally, the model is used to predict the effect of changing solids concentration inside the industrial mill, with good correspondence between the pilot plant and full-scale results, which demonstrated the benefit of reducing solids concentration to values between 76 and 80% in weight for the ore of interest from the 83% that was originally used in the operation.
The process of particle size reduction by grinding is inherently inefficient and involves high capital and operating costs. In particular, ball milling is one of the important unit operations in the iron ore pelletizing process. The mill product, due to its physical properties, determines the efficiency of subsequent stages of classification, filtration and pelletizing, thus impacting the quality of iron ore pellets. The work demonstrates the application of the population balance model in the optimization of a full-scale ball mil circuit grinding pellet fines with the aim to evaluate the optimal solids concentration to improve iron ore pellet quality. Initially, detailed experimentation was carried out in a 25.4 cm diameter batch mill and a relationship for mill scale-up using a linear population balance model in wet grinding systems was established. The selection and breakage parameters and the specific selection functions were determined for pellet feed iron ore. It was possible to identify the non-normalizable nature of the breakage functions of the ore studied, which were modeled properly. Afterwards, as a result of incorporating the specific selection functions and breakage functions into the linear population balance model, it was possible to predict product size distributions in the pilot and plant scale mills (0.416 and 5.18 m diameter, respectively) from data obtained in the 25.4 cm diameter mill. Finally, with this scaleup procedure it was possible to appraise the plant scale optimization via laboratory scale grinding mill tests. The effects of changing percent solids were assessed in order to improve the industrial mill performance and the optimal value should be in the range from 76 to 80%.
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