Study of the stochastic dynamics of particles in the coal screening based on the Markov process

Abstract

The model of the stochastic dynamics for the screening and screen-penetration processes was developed based on the Markov process to reveal the mechanism of the coal screening effect. As a partial differential equation, the model of the stochastic dynamics describes the relationship between particle position in the y direction, screening time, and particle screen-penetration probability. The obtained model for stochastic dynamics can calculate the screen-penetration probability of a specific particle size at any given time. Moreover, two coefficients, a1 and a2, are defined where a1 represents the average velocity of particles, and a2 represents the combined effect of orderly segregation and mixing of particles in chaotic motion. These coefficients of the stochastic dynamics model were obtained by regression analysis. Additionally, the statistical analysis showed that the fitting errors were all <1. The proposed statistical dynamics model works for all particle sizes. A necessary coefficient, a1, was calculated based on screen-penetration coefficients k, a, and b. A large value of a1 means a high average velocity of particles and a greater screen-penetration probability. The value of a1 for particles smaller than 6 mm declines as the feed mass increases. Moreover, it initially decreases, followed by an increase, in response to a rising proportion of particles <6 mm. In contrast, the a1 value for particles ranging between 6 mm and 13 mm undergoes minimal changes when subjected to variations in feed mass and the proportion of particles <6 mm.