China Coal Energy Research Institute Co. ,Ltd.
College of Safety Science and Engineering,Xi’an University of Science and Technology
Key Laboratory of West Mine and Hazard Prevention,Ministry of Education,Xi’an University of Science and Technology

煤矿瓦斯抽采和自然放散过程中,瓦斯在煤层中的运移以Darcy渗流为主,吸附作用导致渗流控制方程变得较为复杂,不得不进行大幅简化。基于渗流理论,推导得出各种坐标系下标准形式的煤层中瓦斯Darcy渗流控制方程。针对煤壁突然暴露后瓦斯单向流动的问题,在不进行过多简化的前提下,利用Crank-Nicolson差分方法推导得出无条件稳定的、具有二阶精度的离散化表征的渗流控制有限差分方程。利用Python语言的SciPy包,选择用于非线性方程组求解的Powell混合法的变体,通过编程实现了对所构建差分方程的数值求解。解算得出不同时刻、距煤壁不同位置的瓦斯含量和瓦斯压力与距离都呈反正切函数关系,给出了在任意位置、不同时间的瓦斯含量计算的综合拟合公式;同时得出煤壁瓦斯涌出速率随时间呈幂函数关系下降的表达式。

In the process of drainage and natural emission of coal mine gas,Darcy seepage is the main pattern of gas transport in coal seam. The presence of adsorption makes the seepage control equations more complicated. The oversimplification had to be performed for this equations. Based on the seepage theory,the normalized form of governing equations of gas Darcy seepage in coal seams for various coordinate systems are derived. Aiming at the problem of unidirectional gas flow after sudden exposure of coal wall,an unconditionally stable seepage governing finite difference equation with second - order accuracy is derived by using Crank-Nicolson difference method without too much simplification. Using Python’s SciPy package and a variant of Powell hybrid method for solving nonlinear equations,numerical solving of the constructed difference equations is implemented through programming. The results show that at different times,both gas content and pressure at different distances from the coal wall,exhibit an arc - tangent function relationship with distance. Therefore, a comprehensive fitting equation for gas content calculation at any position and time could be provided. It is also concluded that the gas emission rate of coal wall decreases as a power function over time.

国家重点研发计划项目(2023YFF0615400);中国中煤能源集团有限公司重点科技项目(21-20)

杨鹏,龚选平,伍国栋.基于Crank-Nicolson差分方法的煤层瓦斯渗流解算[J].矿业安全与环保,2024,51(3):28-35.

YANG Peng,GONG Xuanping,WU Guodong. Solving of coal seam gas seepage based on Crank-Nicolson difference method[J].Mining Safety & Environmental Protection,2024,51(3):28-35.