煤与瓦斯突出过程中瓦斯流动规律的理论模型及数值解法

Theoretical model and numerical method on the law of gas flow in coal and gas outburst

煤与瓦斯突出是发生在煤炭开采过程中的一种地质灾害,其机理复杂且破坏性强,是煤矿安全生产的极大威胁。至今,对煤与瓦斯突出机理的研究仍然处于不断探索认识的阶段,学者们普遍认为地应力,瓦斯压力以及煤体物理性质共同导致了突出的发生,瓦斯作为三要素之一,在突出中起着重要作用。因此,研究突出过程中的瓦斯在煤样中的流动规律,对研究突出机理具有重要意义。煤与瓦斯突出是一个动力学过程,因此从力学的角度研究突出过程中瓦斯流动规律,可以分析瓦斯在突出过程中的主要作用。基于多孔介质渗流理论,建立了突出过程中瓦斯流动的控制方程,该方程为一个非稳态非线性偏微分方程,利用有限体积法对控制方程离散后得到该方程的离散形式为一个非线性方程组,利用拟牛顿法求解该方程组并得到其数值解。利用二分法原理和试验数据分析确定了突出过程中试验所用煤样的近似渗透率,该渗透率远大于实验室测得的煤样静态渗透率。通过试验验证了该数值解的正确性。基于建立的控制方程,进一步分析了突出过程中瓦斯状态,如瓦斯压力,瓦斯压力梯度以及瓦斯流动速度的变化规律。整个突出过程中,最大的瓦斯压力梯度始终出现在孔口附近且瓦斯压力梯度快速衰减,结合试验现象,可以表明瓦斯压力梯度是主导煤与瓦斯突出发生和终止的一个关键因素。

Coal and gas outburst,which is a kind of disaster in coal mines and has a great threat to the safety of coal production,has complex mechanical mechanism and strong destructiveness.Up to now,the study on coal and gas mechanism is still in the stage of exploration.Scholars generally believe that in-situ stress,gas pressure and physical properties of coal lead to the outburst initiation.As one of these three elements,gas plays an important role in coal and gas outburst.Therefore,it is of great significance to study the rule of gas flow in coal and gas outburst.It is generally known that coal and gas outburst is a dynamic process.Hence,the understanding on the rule of gas flow in coal and gas outburst from a mechanical point of view can better explain the main role of gas in coal and gas outburst.Based on the percolation theory of porous media,the governing equation,which is an unsteady and nonlinear partial differential equation,is developed in outburst process.This governing equation is discretized by the finite volume method,the discrete form of which is a system of nonlinear equations.The numerical solution obtained by a quasi-Newton method is agreed with experimental data well.The permeability of the coal sample in outburst process is determined by the bisection method and experimental data.With respect to the permeability measured in the laboratory,the permeability increases dramatically in outburst process.Based on this governing equation,the change laws of gas pressure,gas pressure gradient and gas velocity in coal and gas outburst are analyzed.In the whole process of outburst,the maximum gas pressure gradient always appears near the hole and the gas pressure gradient decays rapidly.Combined with the experimental phenomenon,it can be shown that gas pressure gradient is a key factor dominating the outburst initiation and termination.