The role of particle-scale effects on coal spontaneous combustion: A multi-scale mathematical model based on analytical solution

Abstract

Coal spontaneous combustion (CSC) is a well-documented phenomenon in coal mining and represents a significant cause of mine fires. Extensive numerical studies have been conducted to explore the mechanisms and behavior of CSC. However, existing numerical models often fail to adequately address the multi-scale characteristics inherent to this process. This study develops a mathematical model to describe the distribution of gas concentration and temperature within an individual coal particle, deriving analytical solutions under third-type boundary conditions and constructing a multi-scale mathematical framework based on the effectiveness factor. Key findings demonstrate that the analytical solutions accurately characterize temperature and concentration distributions within the particle. Additionally, the effectiveness factor proves instrumental in evaluating the significance of particle-scale effects. The multi-scale model significantly enhances the representation of CSC phenomena. Results reveal a temperature difference of 16.6 K between the conventional model and the multi-scale model, and an 8.2 K difference between the center and surface of the particle. Variations in particle diameter and porosity resulted in temperature differences of 31.8 K and 43.7 K, respectively. The unique contribution of this work lies in the development of the multi-scale model that integrates a derived effectiveness factor to bridge particle-scale and macroscopic behaviors.