Abstract Accurate prediction of unconventional gas production requires deep understanding of the permeability of complex rock samples. Several predictive expressions of permeability, which include either simplifications of the porous media structure or the flow mechanisms, have been proposed recently. The main objective of this research is to quantify the impact of solid matrix complexity on both intrinsic and apparent permeability. To this end, numerous two-dimensional random porous media structures are constructed using the quartet structure generation set algorithm. Parametric and statistical analysis reveals the importance of the specific surface area of pores, tortuosity, heterogeneity and degree of anisotropy. Special focus is given to the directional dependency of the permeability on isotropic and anisotropic geometries, considering the great impact of anisotropy on the laboratory evaluation of permeability data and the anisotropic nature of shale rocks. Simulation results, for the same value of porosity, clearly indicate the drastic improvement of permeability due to the reduction of specific surface area of pores and their height to width ratio. This suggests that rock matrix complexity has significant impact on permeability and should not be neglected while forming permeability formulations for porous media. Finally, the results of the apparent permeability, obtained by solving the gas kinetic equation, are taken into consideration to demonstrate the enhancement ratio, slip factor and their correlation with the aforementioned parameters. Semi-analytical expressions for intrinsic and apparent permeability, considering continuum and slip flow respectively, are derived. The proposed formulations, suitable for both isotropic and anisotropic structures, have the advantage of not entailing any numerical or experimental data as input.

中文翻译：

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非均质和各向异性超致密多孔介质的本征和表观气体渗透率

摘要 非常规天然气产量的准确预测需要对复杂岩石样品的渗透率有深入的了解。最近提出了几种渗透率的预测表达式，包括多孔介质结构的简化或流动机制。这项研究的主要目的是量化固体基质复杂性对固有渗透率和表观渗透率的影响。为此，使用四重结构生成集算法构建了大量二维随机多孔介质结构。参数和统计分析揭示了孔隙的比表面积、曲折度、不均匀性和各向异性程度的重要性。特别关注渗透率对各向同性和各向异性几何形状的方向依赖性，考虑到各向异性对渗透率数据的实验室评价和页岩岩的各向异性性质的巨大影响。模拟结果，对于相同的孔隙度值，清楚地表明由于孔隙比表面积及其高宽比的降低，渗透率急剧提高。这表明岩石基质的复杂性对渗透率有显着影响，在形成多孔介质渗透率公式时不应忽视。最后，将通过求解气体动力学方程获得的表观渗透率结果考虑在内，以证明增强率、滑移因子及其与上述参数的相关性。固有渗透率和表观渗透率的半解析表达式，分别考虑连续流和滑流，是派生的。所提出的公式适用于各向同性和各向异性结构，其优点是不需要任何数值或实验数据作为输入。