In Part I of this series, we presented a new theoretical approach for computing the effective permeability of porous media that are under deformation by a hydrostatic pressure P. Beginning with the initial pore-size distribution (PSD) of a porous medium before deformation and given the Young’s modulus and Poisson’s ratio of its grains, the model used an extension of the Hertz–Mindlin theory of contact between grains to compute the new PSD that results from applying the pressure P to the medium and utilized the updated PSD in the effective-medium approximation (EMA) to estimate the effective permeability. In the present paper, we extend the theory in order to compute the electrical conductivity of the same porous media that are saturated by brine. We account for the possible contribution of surface conduction, in order to estimate the electrical conductivity of brine-saturated porous media. We then utilize the theory to update the PSD and, hence, the pore-conductance distribution, which is then used in the EMA to predict the pressure dependence of the electrical conductivity. Comparison between the predictions and experimental data for twenty-six sandstones indicates agreement between the two that ranges from excellent to good.

在本系列的第一部分中，我们提出了一种新的理论方法，用于计算在静水压力P变形下多孔介质的有效渗透率。从变形前多孔介质的初始孔径分布 (PSD) 开始，并给定其晶粒的杨氏模量和泊松比，该模型使用 Hertz-Mindlin 晶粒之间接触理论的扩展来计算新的 PSD施加压力P 的结果到介质并利用有效介质近似 (EMA) 中更新的 PSD 来估计有效渗透率。在本文中，我们扩展了理论以计算被盐水饱和的相同多孔介质的电导率。我们考虑了表面传导的可能贡献，以估计盐水饱和多孔介质的电导率。然后，我们利用该理论来更新 PSD，从而更新孔隙电导分布，然后在 EMA 中使用该分布来预测电导率的压力依赖性。26 个砂岩的预测和实验数据之间的比较表明两者之间的一致性从优秀到良好。