Mathematical model of one-dimensional penetration stability failure for gaseous coal

Abstract

Based on the theory of fluid dynamics in porous media, combined with the gas state equation, Darcy's law and the discriminant equation of one-dimensional seepage instability, a mathematical model of one-dimensional penetration stability failure is established to study the seepage damage law of coal seam. Assuming that the background pressure of the coal wall is attenuated according to the exponential law, the mathematical equation is solved by using the finite difference method. Furthermore, the process of coal bed instability which is supposed as a form of a 'sublayer' pushing forward was analysed. That is, the coal bed loses its stability layer by layer. The calculation results showed that the thickness of the failure sublayer decreases with the reduction of coal permeability and the acceleration of dissipation rate of the background pressure. The model provides a method which can analyse the outburst process and its intensity quantitatively.