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首页> 外文期刊>Journal of natural gas science and engineering >Second-order correction of Klinkenberg equation and its experimental verification on gas shale with respect to anisotropic stress
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Second-order correction of Klinkenberg equation and its experimental verification on gas shale with respect to anisotropic stress

机译：Klinkenberg方程的二阶校正及其对各向异性应力气体的实验验证

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摘要

Shale is an extremely tight and fine-grained sedimentary rock with nanometer-scale pore sizes. The internal nanopore structure gives rise to not merely the ultra-low permeability of shale, but also the significant slip flow (non-Darcy) phenomenon. This study involves a second-order correction of the traditional Klinkenberg equation and its experimental verification, in consideration of the effect of anisotropic stress, using cube-sized shale samples sourced from a typical Chinese sedimentary basin. The effects of two gas slippage factors, Klinkenbergcorrected permeability, and anisotropic stress were also discussed. The results showed an increasing trend of apparent permeability with decreasing pore pressure when the pressures are relatively low, due to the gas slippage effect. The second-order model results in a lower Klinkenberg-corrected permeability compared with that from the traditional Klinkenberg equation and yields a better match with the experimental data. Analysis of the experimental data showed that both the first-order slippage factor A and the second-order slippage factor B rose as stress anisotropy increased, and that A was more sensitive to stress anisotropy compared with B. Interestingly, both A and B first increased slightly and then dramatically as the permeability declined. It is recommended that when the shale permeability is below 10-3 mD, the second-order approach should be taken into consideration. Darcy?s law starts to deviate when Kn > 0.01 and is invalid at high Knudsen numbers. The secondorder approach alleviates the problem of permeability overestimation compared with the traditional Klinkenberg equation. When subjected to effective stress, shale pores become constricted and the degree of this constriction decreases gradually as the effective stress continues to increase.
机译：页岩是一种极为致密的细粒沉积岩，具有纳米级的孔径。内部纳米孔结构不仅导致页岩的超低渗透性，还导致显著的滑移流（非达西）现象。本研究涉及对传统克林肯伯格方程进行二阶修正，并在考虑各向异性应力影响的情况下，使用来自中国典型沉积盆地的立方体大小的页岩样品进行实验验证。还讨论了克林肯伯格校正渗透率和各向异性应力两种气体滑移因素的影响。结果表明，当压力较低时，由于气体滑移效应，表观渗透率随孔隙压力的降低而增加。与传统的克林肯伯格方程相比，二阶模型的克林肯伯格校正渗透率更低，并且与实验数据更匹配。对实验数据的分析表明，一阶滑移系数A和二阶滑移系数B都随着应力各向异性的增加而增加，而A对应力各向异性的敏感性比B更高。有趣的是，随着渗透率的降低，A和B都先略有增加，然后急剧增加。建议当页岩渗透率低于10-3 mD时，应考虑二阶方法。达西？当Kn>0.01时，s定律开始偏离，在高Knudsen数时无效。与传统的克林肯伯格方程相比，二阶方法缓解了渗透率高估的问题。当受到有效应力时，页岩孔隙会收缩，并且随着有效应力的持续增加，收缩程度逐渐降低。

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