基于真实气体的瓦斯径向不稳定流动模型及其解析解

A Radial Unstable Gas Flow Model Based on Real Gas and its Analytical Solution

基于达西定律、质量守恒定律、真实气体状态方程建立了瓦斯流动数学模型,利用分离变量法,求出径向不稳定流场瓦斯压力分布规律的解析解;通过该解析解得出了不同时间、不同抽采距离的瓦斯压力分布演化规律;基于此提出一种计算抽采半径的理论方法,并利用COMSOL Multiphysics进行了数值模拟验证。结果表明:根据瓦斯压力径向分布规律,抽采钻孔周围分为降压区、转折区及稳定区,抽采难度依次增加。瓦斯压力随时间空间变化规律主要由压力准数r^(2)/4ψt决定,压力准数越小,瓦斯压降越大,抽采效果越好,缩小抽采间距或延长抽采时间都可以减小压力准数;由于瓦斯压力与抽采距离为平方的关系,因此相对于抽采时间,瓦斯压力对抽采距离更加敏感;当压力准数大于4,则煤体瓦斯压力几乎不受抽采影响。

A mathematical model of gas flow was established based on the Darcy's law,the law of conservation of mass,and the real gas state equation.Using the separation variable method,the analytical solution of the gas pressure distribution law in the radially unstable flow field was obtained.Through the obtained analytical solution,the evolution law of gas pressure distribution at different time and different extraction distance was obtained.Based on this,a theoretical method to calculate the extraction radius was proposed,and numerical simulation was carried out by COMSOL Multiphysics.The results show that according to the radial distribution law of gas pressure,the surrounding area of drainage drilling is divided into depression-relief zone,transition zone and stable zone,and the drainage difficulty increases successively.The variation of gas pressure with time and space is mainly determined by the pressure criterion r^(2)/4ψt.The smaller the pressure criterion,the greater the gas pressure drop and the better the drainage effect.The pressure criterion can be reduced by reducing the drainage interval or prolonging the drainage time.Due to the relationship between gas pressure and drainage distance is square,the impact of drainage distance is greater on the gas pressure than the drainage time.When the pressure criterion is greater than 4,the gas pressure of coal body is hardly affected by drainage.