Quantitative analysis method for particle scale effect in coal spontaneous combustion

The phenomenon of coal spontaneous combustion necessitates a comprehensive investigation across multiple scales, where the significance of the individual coal particle as a crucial intermediary bridging micro mechanisms and macroscopic attributes is underscored. While existing research has extensively explored both micro and macro scales, a notable gap remains in the quantitative analysis and evaluation of the impact of particle-scale effects on coal spontaneous combustion. Firstly, governing equations were formulated to depict the internal temperature and oxygen concentration diffusion within individual coal particles, employing an equivalent spherical symmetry model and coal oxidation reaction equation under the third type of boundary conditions. By dimensionless processing of the mathematical model, analytical solutions for the dimensionless oxygen concentration and temperature distribution inside single coal particles were obtained, and mathematical expressions for the effectiveness factor used to determine the strength of particle scale effects were defined and derived. Furthermore, by comparing the results obtained from numerical methods with those derived from analytical solutions, the correctness of the analytical solutions has been validated. Subsequently, the influence of several key dimensionless criterion numbers on the internal dimensionless oxygen concentration distribution, temperature distribution, and effectiveness factor of particles was analyzed. The findings revealed that the dimensionless oxygen concentration distribution is intricately linked to two dimensionless criterion numbers, namely the Thiele modulus and the mass transfer Biot number, while the dimensionless temperature distribution involves four dimensionless criterion numbers: the Thiele modulus, the mass transfer Biot number, the heat transfer Biot number, and the newly obtained criterion number. Notably, the effectiveness factor is solely contingent on the Thiele modulus and the mass transfer Biot number. When the Thiele modulus is less than 0.1 and the mass transfer Biot number is greater than 0.1, the effectiveness factor approaches 1.0, and the particle effect can be ignored. When the Thiele modulus is greater than 2.0, the effectiveness factor remains below 0.8, and the influence of particle effects should be considered. Engineers can leverage the proposed effectiveness factor formula to assess the relevance of particle-scale effects. These research outcomes form the cornerstone for a quantitative examination of the influence of micro characteristics of single coal particles on macro characterization, paving the way for the development of subsequent multi-scale simulation models.