During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

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瓦斯煤层水力压裂驱甲烷数学模型

在含气煤的水力压裂过程中，甲烷是由水力压裂驱动的。但其数学模型尚未建立。以“双孔双渗”流体渗流理论为基础，同时考虑割理构造、主要水力裂缝和水力压裂驱动的甲烷，建立了数学模型。借助 COMSOL Multiphysics 软件，得到数学模型的数值解。此外，还得到了水和甲烷饱和度、孔隙压力及其梯度的时空规律。得出结论：（1）沿水力压裂驱动甲烷的方向，割理处的孔隙压力呈现先减小后增大的趋势。孔隙压力梯度沿水力压裂驱动甲烷的方向呈现出一定的区域特征。(2) 沿水力压裂驱动甲烷方向，含水饱和度呈下降趋势；然而，在割理或水力裂缝附近，含水饱和度先升高后降低。煤基质块中央区域的含水饱和度小于其周围区域的含水饱和度，而整个基质块的含水饱和度大于基质块周围割理或水力裂缝中的含水饱和度。同一空间点的含水饱和度随着时间的推移逐渐增加。甲烷饱和度的时空分布规律与水饱和度的时空分布规律相反。(3) 水力压裂驱动的游离甲烷包括原始游离甲烷和吸附甲烷解吸的游离甲烷。吸附甲烷的还原率大于游离甲烷的还原率。