Numerical solution of three mathematical models of gas adsorption in coal particle based on finite difference method. (15th January 2022) - Qin, Yueping; Zhao, Zhengduo; Xu, Hao; Liu, Wei; Wu, Fan; Zhou, Yujun; Duan, Wenpeng
Graphical abstract: Highlights: Free gas density gradient models for spherical, cylindrical and flat coal particle. Microchannel diffusion coefficients varies with coal particles in different shapes. The simulation results have a high degree of matching with the experimental data. Abstract: At present, coal particles are commonly used as a substitute for coal matrix in gas diffusion studies, and are usually simplified to regular spheres when modeling. However, the shapes of coal particles in actual coal seams are so varied that only treating coal particles as spheres may cause some deviations and bring up some suspicions. Based on this, this work firstly carried out the coal particle gas adsorption experiments under constant pressure conditions. Then, the coal particles were regarded as sphere, cylinder and flat respectively, and the three mathematical models of free gas density gradient diffusion (FGDGD) in coal matrix were established and numerically solved by finite-difference method (FDM). Finally, the simulation results of the three shapes of coal particles were verified. The results indicated that whether the coal particles were regarded as sphere, cylinder or flat, the simulation results were well matched with the experimental data. FGDGD model in coal matrix is reliable, and the coal particles can be simplified to sphere, cylinder or flat in the gas adsorption modeling. Furthermore, the microchannel diffusion coefficients ( Km ) of the three shapes of coal particles are different, which are shown as: Km (flat) > Km (cylindrical) > Km (spherical). This may be due to the different structures of the internal pores in the different shaped coal particles, which leads to the different effective diffusion cross-sectional areas of gas in coal particles. Although simplifying the actual coal particles to these three different shapes is acceptable to some extent, the spherical model is relatively simpler than the cylindrical and flat ones. Therefore, we propose the concept of sphere equivalent diameter and suggest the application of simplified spherical particles to model gas diffusion in coal matrix.