Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model is expressed in terms of the porosity, electrical conductivity of the pore liquid and the microstructural parameters of porous media. It takes into account the interface properties between minerals and pore water by introducing a surface conductivity. Expressions for the formation factor and hydraulic tortuosity are also obtained from the model derivation. The model is then successfully compared with published data and performs better than previous models. The proposed approach also permits to relate the electrical conductivity to other transport properties such as the hydraulic conductivity.

中文翻译：

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部分饱和多孔介质电导率的物理模型

电导率是储层和环境研究中最常用的地球物理方法之一。它的主要兴趣在于它对多孔介质中存储和传输的关键特性的敏感性。因此，它的定量使用取决于将它们联系起来的岩石物理关系的效率。在这项工作中，我们开发了一种新的基于物理的模型来估计饱和多孔介质的电导率。该模型假设多孔介质由一束具有分形孔径分布的曲折毛细管表示。该模型用孔隙液体的孔隙率、电导率和多孔介质的微观结构参数表示。它通过引入表面电导率来考虑矿物和孔隙水之间的界面特性。地层系数和水力弯曲度的表达式也从模型推导中获得。然后将该模型成功地与已发布的数据进行比较，并且其性能优于以前的模型。所提出的方法还允许将电导率与其他传输特性（例如水力传导率）相关联。