Advances on the Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing

The breakage index equation (BIE), or t10 model from drop weight testing (DWT) data for rocks and ores is used in the design of crushers and mills. Such models are becoming increasingly difficult to visualize as the number of variables increases. The so-called double fan BIE, combined with the Swebrec distribution’s accurate description of the sieving curves, is applied to the modelling of drop-weight test fragmentation. The key parameters are geometric properties visible in the fan plot; slopes of straight lines and their point of convergence. The ability of the double fan BIE to reproduce DWT data had been previously established for 8 rocks with 480 DWT data sets. Here the fidelity of the double fan BIE is further evaluated for 18 new materials, based on 281 data sets. The fidelity of the double fan BIE with three fan lines is on par with the fidelity of the current state-of-the-art models for the new materials. Besides the breakage index equation, the new double fan BIE’s t10 equation produces, without additional parameters or fitted constants, the general breakage surface equation tn for an arbitrary n value as a bonus. The specific sieving curve for any combination of particle size and impact energy is also contained in the same formula. The result is an accurate, compact and transparent model.

Use of the Swebrec Function to Model Particle Size Distribution in an Industrial-Scale Ni-Co Ore Grinding Circuit

Mathematical models of particle size distribution (PSD) are necessary in the modelling and simulation of comminution circuits. In order to evaluate the application of the Swebrec PSD model (SWEF) in the grinding circuit at the Punta Gorda Ni-Co plant, a sampling campaign was carried out with variations in the operating parameters. Subsequently, the fitting of the data to the Gates-Gaudin-Schumann (GGS), Rosin-Rammler (RRS) and SWEF PSD functions was evaluated under statistical criteria. The fitting of the evaluated distribution models showed that these functions are characterized as being sufficiently accurate, as the estimation error does not exceed 3.0% in any of the cases. In the particular case of the Swebrec function, reproducibility for all the products is high. Furthermore, its estimation error does not exceed 2.7% in any of the cases, with a correlation coefficient of the ratio between experimental and simulated data greater than 0.99.

Comparison of alumina ball size distribution in two white cement grinding units using Swebrec function

The results of characterizing the alumina ball size distribution in two mills of a crushing and grinding plant are shown. The mills were unloaded and the ball charge was screened in order to establish the ball size distribution. For both mills, the balls retained during the unloading were compared to the balls retained at the beginning of the process, and additionally, they were compared to the results obtained by the Swebrec adjusted distribution model. In both cases, the experimental data have had a good fit with this model. This practice is important in order to establish the best ball charge at the beginning of the operation and the ball recharge in the steady state.