考虑Klinbenberg效应的煤中应力-渗流耦合数学模型

已有研究表明，瓦斯在煤层中渗流存在明显的Klinbenberg效应，建立考虑Klinbenberg效应的煤中瓦斯渗流应力耦合模型是煤层瓦斯抽放数值模拟的关键。通过试验研究了煤中的气渗透率与瓦斯压和围压的关系，试验数据的拟合分析表明，赵阳升公式能很好地模拟瓦斯渗流的Klinkenberg效应及围压对煤的渗透率的影响。将赵阳升公式引入到建立的煤层瓦斯渗流应力弹塑性耦合模型中，建立了考虑Klinkenberg效应的煤层渗流-应力弹塑性耦合数学模型，在数值计算程序Coupling Analysis中予以实现，并利用已有解析解对程序的可靠性进行了验证。按考虑和不考虑“Klinbenberg“效应两种工况进行了数值计算。结果表明，按前者计算的瓦斯压降要大于后者。这与理论研究的结论一致，表明所建立的考虑Klinbenberg效应的模型具有理论和工程价值。

Seepage-stress coupled model of coal with Klinbenberg effect

Klinbenberg effect’s existence for gas flow in coal seam has been demonstrated by previous researches. It is a key issue for the numerical simulation of methane recovery to present the model of coupled gas flow and deformation process with Klinbenberg effect. The permeability’s dependence on gas pressure and confining stress in coal seams was studied through experiments. Experimental data’s fitting analysis shows that the fitting result of ZHAO YS formula is perfect, and Klinbenberg effect and the effect of confining stress on permeability can be better considered. The formula was coupled into the established seepage-stress coupled model; and the seepage-stress coupled model with Klinbenberg effect was presented. The corresponding code was developed; and the code was proved to be right with analytical solution. numerical cases with Klinbenberg effect and without Klinbenberg effect were studied. Our main findings are as follows: gas pressure drop with Klinbenberg effect is faster than that without Klinbenberg effect, which is conformable to the theoretical results; and the model with Klinbenberg effect is of marked theoretical and engineering value.