Investigation on the ultra-fine grinding of coals based on a matrix population balance model

The ultra-fine grinding kinetic model for pulverized coal based on the mechanism of grinding process can be used to predict the particle size distribution of the products in the grinding process,provide a guidance for optimizing the mill efficiency,and reduce the process energy consumption. It is very important for the preparation of ultra-clean coal powder with low ash content. In this paper,by using an orthogonal design of Taguchi plan,the effects of the physical parameters of different coals,the size of grinding medium and the specific load of pulverized coal on the ultra-fine grinding process are investigated by using a 1. 5 L vertical stirred ball mill in the laboratory. A mechanistic approach based model,matrix population balance model (M-PBM),is proposed to predict the particle size distribution of the ul- tra-fine grinding products by the stirred ball mill,and by combining the Rosin-Rammler particle size distribution mod- el,the particle size corresponding to any cumulative content under sieve can be accurately predicted. By range analy- sis,the influences of coal ash content,the size of grinding medium and the specific load of pulverized coal on the ener- gy consumption and specific flux of ultra-fine grinding are discussed. Based on the analysis of coal-ash dissociation process in the ultra-fine grinding of pulverized coal and by combining Tomoyoshi’s energy consumption formula rela- ting specific surface area of particles,the relationship between coal ash content and energy consumption is discussed, and the formulas relating coal ash content,grinding medium size,the specific load of pulverized coal with specific grinding flux and with energy consumption are further established. It is found that the particle size reduction during the ultra-fine wet grinding process of stirring ball mill conforms to the first-order linear kinetic hypothesis. Under a fixed rotating speed of agitating shaft and within the considered particle size reduction range,the ash content of coal has the greatest influence on the specific flux and energy consumption of the stirring ball mill. Within the ultrafine grinding size range which is below 10 μm (p50 ),the established formulas of specific flux and energy consumption show that the increase in ash content,decrease in grinding medium size (0. 3-1. 8 mm) and increase in the specific load of pulver- ized coal will lead to the decrease in energy consumption and increase in specific flux,respectively.