Study on mathematical relationship of classical diffusion models of coal containing methane

The diffusion models of coal containing methane have various forms, but the mathematical relationship between the models remains to be clarified. Twenty classical diffusion models of coal containing methane are studied, which are divided into conventional diffusion model, dynamic diffusion model and empirical diffusion model according to their characteristics. Through equivalent and approximate mathematical transformation, it is found that there is a mathematical relationship between similar diffusion models. In order to explore the relationship between the three types of diffusion models, a dynamic diffusion coefficient model was established based on the conventional diffusion model and the fractal pore structure characteristics of coal. The dynamic diffusion coefficient model was derived by observing the relationship between the diffusion coefficient and time, and the mathematical relationship between the dynamic diffusion model and the conventional diffusion model was established. Based on the cubic geometry model of coal matrix, Fick’s law and dynamic diffusion model, the empirical diffusion model is derived, and the relationship between the empirical diffusion model and dynamic diffusion model is established.