Abstract Permeability measurements show that unconventional rock is considerably stress sensitive because the matrix permeability is likely controlled by micro cracks and bedding structures in unconventional reservoirs. While there are a number of laboratory studies in the literature on the dependency of core-scale permeability on effective stress for unconventional rocks, how to determine the corresponding large-scale stress-dependency relationship (of more interest to practical applications) from the laboratory measurements has not been systematically investigated. This work proposes a method to estimate such a large-scale relationship from laboratory measurements. Based on the stochastic approach commonly used for parameter upscaling, we derived relationships between the large-scale effective permeability and the stress for the two- and three-dimensional isotropic porous media. The development is based on the empirical observation that at core scale permeability is an exponential function of effective stress. The developed large-scale relationships can be written in terms of the same mathematical form as the local-scale relationship except parameters in the large-scale relationships correspond to effective ones. The effective stress sensitivity parameter (that characterizes the stress-dependency) is simply the expected value of that at the local scale, or the arithmetic average of local values, for the two-dimensional flow problem and a function of effective stress for the three-dimensional problem. Because of its dominant two-dimensional flow along beddings (resulting from the fact that vertical permeability is significantly smaller than the horizontal one), the relationship for the two-dimensional flow case is valid for unconventional rocks. Nevertheless, we demonstrate that for typical local-scale parameter values from unconventional rocks (e.g., Barnett shale and a carbonate source rock), the relationships obtained for two- and three-dimensional problems give the essentially same results.

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非常规岩石有效渗透率与应力之间的关系：实验室测量的分析估计

摘要 渗透率测量表明，非常规岩石对应力相当敏感，因为基质渗透率可能受非常规储层中微裂缝和层理结构的控制。虽然文献中有许多关于岩心渗透率对非常规岩石有效应力的依赖性的实验室研究，但如何从实验室测量中确定相应的大尺度应力依赖性关系（对实际应用更感兴趣）没有系统地研究过。这项工作提出了一种从实验室测量中估计这种大规模关系的方法。基于常用于参数放大的随机方法，我们推导出了二维和三维各向同性多孔介质的大尺度有效渗透率与应力之间的关系。该开发基于经验观察，即在岩心尺度渗透率是有效应力的指数函数。除了大规模关系中的参数对应于有效参数外，开发的大规模关系可以用与局部规模关系相同的数学形式写成。有效应力敏感参数（表征应力依赖性）只是局部尺度的期望值，或局部值的算术平均值，对于二维流动问题和有效应力的函数，对于三维流动问题。维度问题。由于其沿层理的二维流占主导地位（由于垂直渗透率明显小于水平渗透率），二维流情况的关系对于非常规岩石是有效的。然而，我们证明，对于来自非常规岩石（例如 Barnett 页岩和碳酸盐岩源岩）的典型局部尺度参数值，二维和三维问题获得的关系给出了基本相同的结果。