含瓦斯煤经典扩散模型数学关系研究OA北大核心CSTPCD

The diffusion models of coal containing methane have various forms,but the mathematical relationship between the mod-els remains to be clarified.Twenty classical diffusion models of coal containing methane are studied,which are divided into conven-tional diffusion model,dynamic diffusion model and empirical diffusion model according to their characteristics.Through equival-ent and approximate mathematical transformation,it is found that there is a mathematical relationship between similar diffusion mod-els.In order to explore the relationship between the three types of diffusion models,a dynamic diffusion coefficient model was estab-lished based on the conventional diffusion model and the fractal pore structure characteristics of coal.The dynamic diffusion coeffi-cient 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 em-pirical diffusion model and dynamic diffusion model is established.