Particle Size Distribution Models for Metallurgical Coke Grinding Products

Abstract

Six different particle size distribution (Gates–Gaudin–Schuhmann (GGS), Rosin–Rammler (RR), Lognormal, Normal, Gamma, and Swebrec) models were compared under different metallurgical coke grinding conditions (ball size and grinding time). Adjusted R2, Akaike information criterion (AIC), and the root mean of square error (RMSE) were employed as comparison criteria. Swebrec and RR presented superior comparison criteria with the higher goodness-of-fit and the lower AIC and RMSE, containing the minimum variance values among data. The worst model fitting was GGS, with the poorest comparison criteria and a wider results variation. The undulation Swebrec parameter was ball size and grinding time-dependent, considering greater b values (b > 3) at longer grinding times. The RR α parameter does not exhibit a defined tendency related to grinding conditions, while the k parameter presents smaller values at longer grinding times. Both models depend on metallurgical coke grinding conditions and are hence an indication of the grinding behaviour. Finally, oversize and ultrafine particles are found with ball sizes of 4.0 cm according to grinding time. The ball size of 2.54 cm shows slight changes in particle median diameter over time, while 3.0 cm ball size requires more grinding time to reduce metallurgical coke particles.

Relation between Scale-Up and Life Cycle Assessment for Wet Grinding Process of Pumice

“…The experiments conducted in a wet stirred media mill showed that increasing the grinding time decreases the median particle size of pumice with a simultaneous increase in the unit energy demand (Table 2 and Figure 2). A similar observation for the stirred ball mill was presented in the author's previous study for limestone [24] and other types of mills, for instance, ball mills [58], beater mills [59,60], and hammer mills [61]. The analysis of the results presented in Figure 2 suggests that grinding of pumice in the analyzed laboratory stirred mill (solid mass concentration: 20%, mill filling ratio: 70%) becomes inefficient after 5 min, as the further increase in grinding time results in only a small median particle size decrease and a very high rise in the energy consumption (Table 2).…”

Dynamic mechanical response and crack evolution law of raw coal loaded by dynamic-static coupling under three-dimensional constraints

“…The crushing effect of coal specimens under three-dimensional dynamic and static combined loading reflects the force state of coal specimens, and through the properties of fractal theory, the crushing block size distribution can be used, to evaluate the crushing effect of coal rock, and in the previous studies, the statistical function of crushing block size distribution with R–R (Rosin–Rammler) distribution and G-G-S (Gate-Gaudin-Schuhmann) distribution 43 – 45 has been used relatively frequently. In this paper, the G-G-S distribution function is used to fracture the coal samples into dimensions.…”

Experimental study on dynamic mechanical properties of multidirectional constrained water-bearing coal samples under dynamic-static coupling loading

“…The crushing effect of coal samples under three-dimensional dynamic and static combined loading reflects the force state of coal samples, and by the characteristics of fractal theory, the crushing block size distribution can be used to evaluate the crushing effect of coal rock, and in the previous studies, the statistical function of crushing block size distribution is relatively widely used with R-R (Rosin-Rammler) distribution and G-G-S (Gate-Gaudin-Schuhmann) distribution [42][43][44] widely used . In this paper, the G-G-S distribution function is used to fracture the coal samples into dimensions.…”