Nondimensional analysis and application of gas desorption and diffusion driven by density gradient in coal particles

An in-depth understanding of gas diffusion characteristics in coal is of great value to coalbed methane (CBM) production planning and coal mine safety management. However, the mechanism and model of gas diffusion is still unclear, and some methods for determining diffusion coefficients are not accurate enough. Accordingly, a free gas density gradient (FGDG)–driven coal particle gas desorption and diffusion model was established in this work, and numerical solutions were performed via finite difference method (FDM) and dimensionless method. The variation rules of dimensionless gas pressure, gas content, desorption capacity, and desorption rate were obtained. Finally, the application of the dimensionless method in diffusion modeling and diffusion coefficient inversion was discussed. The results show that the dimensionless method can simplify mathematical equation processing and analyze the common phenomena of desorption and diffusion under different parameters. The gas desorption diffusion in coal particles is from the surface to the inside, and there is obvious desorption hysteresis effect. The larger the dimensionless radius or dimensionless time, the smaller the dimensionless gas pressure, gas content, and dimensionless desorption rate. The dimensionless cumulative gas desorption amount increased rapidly first and then tended to flat with dimensionless time. The simulated curve can be easily converted into the variation curves of several different measured parameters, and the diffusion coefficient can be calculated accurately. The prediction curve of the FGDG diffusion model is in good agreement with the experimentally measured data, which verifies its reasonableness. The research content aims to provide some ideas for modeling gas desorption and diffusion behavior.