瓦斯压力场方程的研究

Research on the equation of gas pressure field

掌握瓦斯压力分布对采掘工作面瓦斯灾害的防治至关重要。利用理论推导和软件模拟的方法,对单一巷道(钻孔)瓦斯压力场方程进行了分析。根据Darcy定律、质量守恒定律和流体力学中微分形式的运动方程,建立了两个瓦斯流动的偏微分方程并联立求解,得出了煤层中径向不稳定流和球向不稳定流的瓦斯压力场方程。根据瓦斯压力场方程和达西定律推导出了半径为r的圆上的单位面积瓦斯流量方程和煤层透气性系数λ的方程,它们都是关于时间t和距钻孔(或巷道)中心距离r的函数。利用λ的方程和矿山压力理论解释了煤层中打钻时出现的喷孔现象。瓦斯压力场方程的得出有助于掌握瓦斯在煤层的赋存状况,进而采取有效的瓦斯灾害防治措施。

The present paper intends to introduce our research results over the equation of the gas pressure field, which is very important to grasp the distribution of the gas pressure for the prevention of coal-gas blasts and explosion disasters in coal mining. It is for this purpose that we have analyzed and established a theoretical derivation and a computer simulation model. In our work, we have focused our attention on the analysis and the equation of the gas pressure field through a single roadway or a single borehole. We have also tried two partial differential equations about the gas flow in accordance with Darcy＇s law, the law of conservation of mass and hydrodynamic equations of motion based on the differential formulas. The above said equations can then be combined to solve the the equation problem. The equation of the gas flow in the unit area from a circle whose radius is r and the equation of the coal seam permeability coefficient λ can thus be deduced according to the equation of the gas pressure field and Darcy＇s law. Both of equations are functions of time t and distance r from the center of borehole or tunnel. At the same time, the gas spray from the borehole during drilling in coal seam can be explained properly by means of equation of λ and theory of rock pressure. Therefore, the equation of gas pressure field established in this article can help the coal mine managers to grasp the regularity of methane incidence in the coal seams. What＇s more, it can also help to provide a sound theoretical basis and effective technical support for coal mines managers to adopt effective countermeasures to prevent and control gas disasters.