Second-Order Correlation of Klinkenberg-Corrected Permeability and its Experimental Verification on Heterogeneously-Stressed Gas Shale

Yufei Chen, Changbao Jiang, J. Leung, A. Wojtanowicz, Dongming Zhang, Chuanyao Zhong
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引用次数: 1

Abstract

Shale is an extremely tight and fine-grained sedimentary rock with nanometer-scale pore sizes. The nanopore structure within a shale system contributes not only to the low to ultra-low permeability coefficients (10−18 to 10−22 m2), but also to the significant gas slippage effect. The Klinkenberg equation, a first-order correlation, offers a satisfying solution to describe this particular phenomenon for decades. However, in recent years, several scholars and engineers have found that the linear relation from the Klinkenberg equation is invalid for most gas shale reservoirs, and a need for a second-order model is, therefore, proceeding apace. In this regard, the purpose of this study was to develop a second-order approach with experimental verifications. The study involved a derivation of a second-order correlation of the Klinkenberg-corrected permeability, followed by experimental verifications on a cubic shale sample sourced from the Sichuan Basin in southwestern China. We utilized a newly developed multi-functional true triaxial geophysical (TTG) apparatus to carry out permeability measurements with the steady-state method in the presence of heterogeneous stresses. Also discussed were the effects of two gas slippage factors, Klinkenberg-corrected permeability, and heterogeneous stress. Finally, based on the second-order slip theory, we analyzed the deviation of permeability from Darcy flux. The results showed that the apparent permeability increased more rapidly as the pore pressure declined when the pore pressures are relatively low, which is a strong evidence of the gas slippage effect. The second-order model could reasonably match the experimental data, resulting in a lower Klinkenberg-corrected permeability compared with that from the linear Klinkenberg equation. That is, the second-order approach improves the intrinsic permeability estimation of gas shales with the result being closer to the liquid permeability compared with the Klinkenberg approach. Analysis of the experimental data reported that both the first-order slippage factor A and the second-order slippage factor B increased with increasing stress heterogeneity, and that A was likely to be more sensitive to stress heterogeneity compared with B. Interestingly, both A and B first slightly increased and then significantly as the permeability declined. It is recommended that when the shale permeability is below 10−18 m2, the second-order approach should be taken into account. Darcy’s law starts to deviate when Kn > 0.01 and is invalid at high Knudsen numbers. The second-order approach seems to alleviate the problem of overestimation compared with the Klinkenberg approach and is more accurate in permeability evolution.
非均质应力页岩klinkenberg校正渗透率二阶相关及其实验验证
页岩是一种非常致密和细粒的沉积岩,具有纳米级的孔隙大小。页岩系统中的纳米孔隙结构不仅对低至超低渗透系数(10−18 ~ 10−22 m2)有贡献,而且对显著的气滑效应也有贡献。Klinkenberg方程,一阶相关性,提供了一个令人满意的解决方案来描述几十年来的这种特殊现象。然而,近年来,一些学者和工程师发现,Klinkenberg方程的线性关系对大多数页岩气储层来说是无效的,因此,对二阶模型的需求正在迅速发展。在这方面,本研究的目的是发展二阶方法与实验验证。该研究首先推导了klinkenberg校正渗透率的二阶相关性,然后对来自中国西南部四川盆地的立方页岩样品进行了实验验证。我们利用新开发的多功能真三轴地球物理(TTG)仪器,在非均质应力存在的情况下,用稳态方法进行渗透率测量。还讨论了两个气滑因素,klinkenberg校正渗透率和非均质应力的影响。最后,基于二阶滑移理论,分析了磁导率与达西通量的偏差。结果表明,当孔隙压力较低时,表观渗透率随孔隙压力的降低而增加得更快,这是气体滑移效应的有力证据。二阶模型能较好地拟合实验数据,与线性Klinkenberg方程相比,得到了较低的Klinkenberg校正渗透率。也就是说,二阶方法提高了页岩固有渗透率的估计,与Klinkenberg方法相比,其结果更接近液体渗透率。对实验数据的分析表明,随着应力非均质性的增加,一阶滑移因子A和二阶滑移因子B均增大,且A对应力非均质性的敏感性可能高于B。有趣的是,随着渗透率的降低,A和B均先略有增大,后显著增大。当页岩渗透率低于10 ~ 18 m2时,建议采用二阶法。达西定律在Kn > 0.01时开始偏离,在高Knudsen数时失效。与Klinkenberg方法相比,二阶方法似乎减轻了过高估计的问题,并且在渗透率演化方面更准确。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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