煤屑瓦斯扩散系数时间响应规律研究

Study on time response law of methane diffusion coefficient of coal cuttings

为探讨煤屑瓦斯扩散系数随时间变化的响应规律,选取典型煤样进行煤屑瓦斯解吸扩散实验,建立了扩散系数随时间变化的球形煤屑瓦斯扩散微分方程,通过变量代换方法将得到的微分方程转化为经典的扩散方程,并运用分离变量法得到了煤屑时变扩散系数的理论解;基于扩散规律理论解对煤屑瓦斯解吸实验实测解吸数据进行分析,利用Matlab软件编制程序进行解算,得出瓦斯扩散系数的时间响应规律。研究结果表明:煤屑瓦斯等效扩散系数随时间响应规律符合幂函数关系,采用瓦斯扩散系数时间响应模型比经典瓦斯扩散模型和煤屑瓦斯扩散实验吻合度更高;煤屑瓦斯扩散系数时间响应模型描述煤层的瓦斯运移过程更合理、更准确。

In order to investigate the response law of methane diffusion coefficient of coal cuttings,the typical coal samples were chosen to carry out desorption diffusion experiment of coal cuttings. The differential equation of spherical coal cuttings was established,in which the diffusion coefficient changed with time. By variable substitution method,the differential equation was transformed into the classical diffusion equation and the theoretical solution of the time-varying diffusion coefficient of the coal was obtained by using the separation variable method. Based on the diffusion law theory,the desorption data of the coal desulfurization experiment were analyzed,and the program was compiled by Matlab software,and the time response of the methane diffusion coefficient was obtained. The results show that the equivalent diffusion coefficient of coal is consistent with the power function decay trend with time response,and the methane diffusion coefficient time response model is higher than that of classical methane diffusion model and coal cuttings diffusion experiment. Therefore,it is the coal methane diffusion coefficient time response model to describe the coal seam methane migration process that is more reasonable and more accurate.