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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。
It has been shown that the obvious Klinbenberg effect exists in the seepage of gas in coal seams. Establishing the coupling model of gas seepage stress in coal considering the Klinbenberg effect is the key to the numerical simulation of gas drainage in coal seams. The relationship between gas permeability and gas pressure and confining pressure has been studied through experiments. The fitting analysis of test data shows that Zhao Yangsheng formula can well simulate the Klinkenberg effect of gas seepage and the influence of confining pressure on coal permeability. The Zhao Yangsheng formula is introduced into the established elastic-plastic coupling model of gas seepage in coal seam. A mathematic model of seepage-stress elasto-plastic coupling of coal seam considering Klinkenberg effect is established, which is implemented in the numerical calculation program Coupling Analysis. The reliability of the program was verified. The numerical calculation was performed with and without considering the “Klinbenberg” effect. The results show that according to the former calculation of gas pressure drop is greater than the latter. This is consistent with the conclusion of the theoretical study, which shows that the established model considering the Klinbenberg effect has theoretical and engineering value.