再论阿尔奇定律：用弯曲度和收缩度描述电导
Re-examining Archie's law: Conductance description by tortuosity and constriction
摘要：
在这篇文章中，我们研究了绝缘多孔介质（例如，沉积岩）填充有电解质（例如，盐水），通常使用阿尔奇胶结指数描述。我们展示了如何电导取决于漂移速度和电场线的长度的变化，除了多孔性和电解质的电导。我们的特点是电场线的曲折度和漂移速度的变化由收缩因子的长度。弯曲度和收缩因子都是孔隙微观结构的描述符。我们定义了一个电导减少因子来衡量的孔隙微结构的局部贡献的全球电导。它示出的全球电导降低因子是弯曲度的平方除以收缩因子的产品，从而证明弯曲度和收缩的组合效果，除了电解质的孔隙率和电导率，充分描述了多孔介质的有效电导。我们表明，我们的曲折度，收缩因子和电导减少因子重现理想化的多孔介质的电导。他们也适用于Bentheimer砂岩，在那里我们描述了一个微观结构相关的孔隙度和电导率之间的相关性，使用全球电导率降低因子和弯曲度和收缩的不同贡献。总的来说，这项工作表明，经验阿尔奇胶结指数可以取代更多的描述性，物理参数，无论是全球电导率降低因子或弯曲度和收缩。
英文摘要：
In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g., brine), usually described using the Archie cementation exponent. We show how the electrical conductance depends on changes in the drift velocity and the length of the electric field lines, in addition to the porosity and the conductance of the electrolyte. We characterized the length of the electric field lines by a tortuosity and the changes in drift velocity by a constriction factor. Both the tortuosity and the constriction factor are descriptors of the pore microstructure. We define a conductance reduction factor to measure the local contributions of the pore microstructure to the global conductance. It is shown that the global conductance reduction factor is the product of the tortuosity squared divided by the constriction factor, thereby proving that the combined effect of tortuosity and constriction, in addition to the porosity and conductance of the electrolyte, fully describes the effective electrical conductance of a porous medium. We show that our tortuosity, constriction factor, and conductance reduction factor reproduce the electrical conductance for idealized porous media. They are also applied to Bentheimer sandstone, where we describe a microstructure-related correlation between porosity and conductivity using both the global conductance reduction factor and the distinct contributions from tortuosity and constriction. Overall, this work shows how the empirical Archie cementation exponent can be substituted by more descriptive, physical parameters, either by the global conductance reduction factor or by tortuosity and constriction.
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