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

Authors: Yan Xie; Laibin Wang; Dongjia Liu; Haijian Xie

Addresses: School of Earth and Environment, Anhui University of Science and Technology, Huainan, 232001, China ' School of Earth and Environment, Anhui University of Science and Technology, Huainan, 232001, China ' School of Resources and Environmental Engineering, Hefei University of Technology, Hefei, 230009, China ' Institute of Hydrology and Water Resources Engineering, Zhejiang University, Hangzhou, 310058, China

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.

Keywords: mathematical modelling; seepage instability; coal and gas outburst; numerical simulation; outburst intensity; penetration stability failure; gaseous coal; fluid dynamics; porous media; seepage damage law; coal seams; finite difference method; coal bed instability; coal permeability; pressure dissipation rate.

Progress in Computational Fluid Dynamics, An International Journal, 2017 Vol.17 No.1, pp.27 - 33

Published online: 23 Jan 2017 *