A petrophysical model that accurately relates bulk electrical conductivity (σ) to pore fluid conductivity (σ_w) is critical to the interpretation of geophysical measurements. Classical models are either only applicable over a limited salinity regime or incorrectly explain the nonlinear-to-linear behavior of the σ(σ_w) relationship. In this study, asymptotic limits at zero and infinite salinity are first established in which, σ is expressed as a linear function of σ_w with four parameters: cementation exponent (m), the equivalent value of volumetric surface electrical conductivity (σ_s), the volume fraction of overlapped diffuse layer (ϕ_od) and parameter χ representing the ratio of the volume fraction of the water phase to that of the solid phases in the surface conduction pathway. Subsequently, we bridge the gap between the two extremes by employing the Padé approximant (PA). Given that parameter χ exhibits a marginal influence on the σ(σ_w) curve, based on measurements for 15 samples, we identify its optimal value to be 0.4. After setting the optimal value of χ, we proceed to evaluate the performance of the PA model by comparing its estimates and estimates made by two existing models to measured values from 27 rock samples and eight sediment samples. The comparison confirms that the PA model estimates are more accurate than estimates made by existing models, particularly at low salinity and for samples with higher cation exchange capacity. The PA model is advantageous in scenarios involving the interpretation of electrical data in freshwater environments.

中文翻译：

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使用 Padé 近似模拟饱和多孔介质中本体和孔隙水电导率之间的非线性关系


将体电导率 （σ） 与孔隙流体电导率 （σ_w） 准确关联的岩石物理模型对于地球物理测量的解释至关重要。经典模型要么仅适用于有限的盐度状态，要么错误地解释了 σ（σ_w） 关系的非线性到线性行为。在本研究中，首先建立了零和无限盐度的渐近极限，其中 σ 表示为 σ_w 的线性函数，具有四个参数：胶结指数 （m）、体积表面电导率的等效值 （σ_s）、重叠扩散层的体积分数 （φ_od） 和参数 χ 表示表面传导途径中水相的体积分数与固相的体积分数之比。随后，我们通过使用 Padé 近似 （PA） 来弥合两个极端之间的差距。鉴于参数 χ 对 σ（σ_w） 曲线表现出边际影响，根据 15 个样品的测量，我们确定其最佳值为 0.4。在设定了 χ 的最优值后，我们通过将 PA 模型的估计值和两个现有模型的估计值与 27 个岩石样本和 8 个沉积物样本的测量值进行比较，继续评估 PA 模型的性能。比较证实，PA 模型的估计值比现有模型的估计值更准确，尤其是在低盐度和阳离子交换容量较高的样品下。PA 模型在涉及淡水环境中电气数据解释的场景中是有利的。