Abstract The widely distributed microfractures play an important role in shale gas production. However, limited studies focus on gas flow behavior in microfractures, and ignore the complex transport mechanisms, leading to a large error for gas permeability evaluation. In this work, a newly dynamic apparent permeability (AP) model, coupling poromechanics, sorption-induced strain, and gas slippage, has been proposed to effectively reveal the gas flow mechanisms through microfractures of shale. Specifically, a dynamic aperture is innovatively incorporated into the Navier-Stokes (N–S) equation using the second-order slip boundary condition to calculate the gas velocity and volume flux in single microfracture. Based on that, the gas transport model for microfracture networks considering the distributions of aperture and tortuosity is derived using the fractal theory. The newly developed model is verified well with experimental data and network simulation. Results indicate that the gas conductance highly depends on the structure of microfracture networks (i.e., the maximum aperture and fractal dimensions). There are three different AP evolutions under various boundary conditions (i.e., constant confining pressure ( P c ), constant pore pressure ( P p ), and constant effective stress ( σ e f f )) resulting from the coupling transport mechanisms. The AP presents a similar shape of “V” at reservoir conditions (i.e., constant P c ), indicating the “negative contribution” of poromechanics at an early stage, and the “positive contribution” for both gas slippage and sorption-induced strain at the late stage should be underlined during gas production. Moreover, the “negative factor” of poromechanics is positively correlated with fracture compressibility coefficient but negatively associated with Biot's coefficient at high pressures (>15 [MPa]). Increasing gas desorption capacity, fracture spacing, and internal swelling coefficient can enhance the “positive factor” of sorption-induced strain at low pressures (

中文翻译：

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页岩微裂缝的动态表观渗透率模型：耦合孔隙力学、流体动力学和吸附诱导应变

摘要 广泛分布的微裂缝在页岩气生产中发挥着重要作用。然而，有限的研究集中在微裂缝中的气体流动行为，而忽略了复杂的输运机制，导致气体渗透率评价存在较大误差。在这项工作中，提出了一种新的动态表观渗透率 (AP) 模型，耦合孔隙力学、吸附诱导应变和气体滑移，以有效地揭示通过页岩微裂缝的气体流动机制。具体而言，使用二阶滑移边界条件将动态孔径创新地纳入纳维-斯托克斯 (N-S) 方程，以计算单个微裂缝中的气体速度和体积通量。基于此，利用分形理论推导出考虑孔径分布和曲折度分布的微裂缝网络气体输运模型。新开发的模型通过实验数据和网络模拟得到了很好的验证。结果表明，气体电导高度依赖于微裂缝网络的结构（即最大孔径和分形维数）。由于耦合输运机制，在各种边界条件下（即恒定围压（Pc）、恒定孔隙压力（Pp）和恒定有效应力（σeff））存在三种不同的AP演化。AP 在储层条件下呈现出类似的“V”形状（即常数 P c ），表明早期孔隙力学的“负贡献”，在产气过程中应强调后期气体滑脱和吸附诱导应变的“积极贡献”。此外，孔隙力学的“负因子”与裂缝压缩系数呈正相关，但与高压（>15 [MPa]）下的 Biot 系数呈负相关。增加气体解吸能力、裂缝间距和内部膨胀系数可以增强低压下吸附诱导应变的“正因子”。