Owing to the characteristics of coal reservoirs, the gas flow capacity and permeability exhibit strong anisotropy. The anisotropy in terms of the magnitude, which corresponds to the permeability in the horizontal direction being several orders of magnitude larger than that in the vertical direction, has been investigated. However, the anisotropy in terms of the mechanical boundaries, specifically, the presence of constant volume and stress boundaries in the horizontal and vertical directions, respectively, has not been examined. Therefore, a coupling model of the gas flow and coal seam deformation was developed, and a model to reflect the permeabilities in the horizontal and vertical directions was established considering the internal swelling factor. The models were verified considering field production data, and a numerical analysis was performed. In the early and later stages of gas production, the gas appeared from the fracture and matrix systems, and it was extracted in different regions in the timescale and synchronously, respectively. Owing to the constant stress boundary condition in the vertical direction of the coal seam, the reduction in the gas pressure in the fractures decreased the horizontal fracture opening, thereby decreasing the permeability in the horizontal direction. Because the horizontal direction exhibited a constant volume boundary condition, the desorption of the adsorbed gas resulted in volumetric shrinkage of the matrix, thereby increasing the permeability in the vertical direction. Non‐Darcy effects reduced the gas flow rate and exerted considerable influence in the early stage of the extraction. Moreover, this effect exhibited anisotropy, which was more pronounced in the horizontal direction. The surface diffusion coefficient continuously increased, which promoted the flow of the adsorbed gas in the matrix. The proposed model can be used to estimate the impact of the permeability anisotropy on the coalbed methane and underground gas extraction.

中文翻译：

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用于研究渗透率各向异性对煤层气提取的影响的内部膨胀因子模型

由于煤储层的特征，瓦斯流量和渗透率表现出很强的各向异性。已经研究了在尺寸方面的各向异性，该各向异性对应于水平方向的磁导率比垂直方向的磁导率大几个数量级。然而，关于机械边界的各向异性，特别是在水平方向和垂直方向上的恒定体积和应力边界的存在，尚未得到检验。因此，建立了瓦斯流动与煤层变形的耦合模型，并考虑了内部溶胀因子，建立了反映水平和垂直方向渗透率的模型。考虑到现场生产数据对模型进行了验证，并进行了数值分析。在天然气生产的早期和后期，天然气从裂缝和基质系统中出现，并分别在不同的时间范围和时间上从不同的区域提取。由于在煤层的垂直方向上恒定的应力边界条件，裂缝中的气压的降低减小了水平裂缝的开口，从而降低了水平方向的渗透率。因为水平方向呈现恒定的体积边界条件，所以吸附气体的解吸导致基质的体积收缩，从而增加了垂直方向的渗透性。非达西效应降低了气体流速，并在提取的早期阶段发挥了相当大的影响。此外，这种效应表现出各向异性，在水平方向上更加明显。表面扩散系数不断增加，从而促进了吸附气体在基体中的流动。所提出的模型可以用来估计渗透率各向异性对煤层气和地下瓦斯抽采的影响。