Theoretical Model of Early Diffusion in Coal Particles Containing Methane and Its Analytical Solution

In order to study the early gas diffusion laws, on the basis of assuming that the pre-diffusion coefficient of coal particle methane is constant, according to the second law of Fick in the spherical coordinate system, the mathematic model was established, and its analytical solution was obtained by mathematical and physical method. The new model and the classical model are applied to calculate the methane diffusion experimental data under different equilibrium pressure, coal ranks, particle sizes and deformed coal, respectively. The results show that: the new model could describe the early diffusion more exactly than the classical model. Generally, the diffusion coefficients calculated by the new model are more than that by the classical model. When the uniformity of coal particles approaches to 1, the new model would agree with the classical model. The diffusion coefficient has a positive correlation with equilibrium pressure, coal rank, particle size and deformed type, and the methane amount in early diffusion stage has a positive correlation with the deformed type and equilibrium pressure, but a negative correlation with particle size and coal rank.