气体在煤层中渗流的稳定性分析

The stability of the seepage flow of gas in coal seam

基于瓦斯突出本质在于气体在煤层中渗流失稳的假设,建立了气体渗流的一种非线性动力学模型,讨论了系统平衡态的存在性。用Chebyshev配点法将系统的控制方程简化成含12个相变量的常微分方程组,计算了系统的动力学响应,得到了系统失稳的条件。研究表明,由于气体的压缩性,煤层中气体非Dar-cy渗流系统平衡态的绝对压力的平方成线性分布;系统存在跨临界Hopf分岔和切分岔。

Based on the hypothesis that gas outburst is, in nature, the loss of stability of seepage flow of gas in coal strata, a nonlinear dynamic model suitable for gas seepage is established, and the existence of steady state is discussed. By using Chebyshev's collocation method, the partial equations which dominate the evolution of the system are reduced into a set of ordinary differential equations involving twelve state variables. The dynamic responses are computed before the bifurcation conditions are summed up. This study shows that the square of absolute pressure under the steady state is linearly distributed owing to the compressibility of gas; trans-critical hopf's bifurcation and tangential bifurcation exist in the system.