The dielectric response of rocks results from electric double layer (EDL), Maxwell-Wagner (MW), and dipolar polarizations. The EDL polarization is a function of solid-fluid interfaces, pore water, and pore geometry. MW and dipolar polarizations are functions of charge accumulation at the interface between materials with contrasting impedances and the volumetric concentration of its constituents, respectively. However, conventional interpretation of dielectric measurements only accounts for volumetric concentrations of rock components and their permittivities, not interfacial properties such as wettability. Numerical simulations of the dielectric response of rocks provide an ideal framework to quantify the impact of wettability and water saturation ($S_w$) on electric polarization mechanisms. Therefore, we have developed a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including effects of pore structure, $S_w$, and wettability on permittivity measurements. We solve the quasielectrostatic Maxwell’s equations in 3D pore-scale rock images in the frequency domain using the finite-volume method. Then, we verify simulation results for a spherical material by comparing to the corresponding analytical solution. Additionally, we introduce a technique to incorporate $\alpha$-polarization to the simulation and we verify it by comparing pore-scale simulation results to experimental measurements on a Berea sandstone sample. Finally, we quantify the impact of $S_w$ and wettability on broadband dielectric permittivity measurements through pore-scale numerical simulations. The numerical simulation results show that mixed-wet rocks are more sensitive than water-wet rocks to changes in $S_w$ at sub-MHz frequencies. Furthermore, permittivity and conductivity of mixed-wet rocks have weaker and stronger dispersive behaviors, respectively, when compared to water-wet rocks. Finally, numerical simulations indicate that conductivity of mixed-wet rocks can vary by three orders of magnitude from 100 Hz to 1 GHz. Therefore, Archie’s equation calibrated at the wrong frequency could lead to water saturation errors of up to 73%.

中文翻译：

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沉积岩多频复介电常数色散数值模拟

岩石的介电响应由双电层 (EDL)、麦克斯韦-瓦格纳 (MW) 和偶极极化引起。EDL 极化是固液界面、孔隙水和孔隙几何形状的函数。MW 和偶极极化分别是具有对比阻抗的材料之间界面处的电荷积累及其成分的体积浓度的函数。然而，介电测量的传统解释只考虑了岩石成分的体积浓度及其介电常数，而不是界面特性，如润湿性。岩石介电响应的数值模拟为量化润湿性和含水饱和度的影响提供了理想的框架。${秒}_{瓦}$) 关于电极化机制。因此，我们开发了一种数值模拟方法来计算 100 Hz 至 1 GHz 区间内的孔隙尺度介电色散效应，包括孔隙结构的影响，${秒}_{瓦}$，以及介电常数测量的润湿性。我们使用有限体积方法在频域中求解 3D 孔隙尺度岩石图像中的准静电麦克斯韦方程组。然后，我们通过与相应的解析解进行比较来验证球形材料的模拟结果。此外，我们引入了一种技术来合并$\alpha$-极化模拟，我们通过将孔隙尺度模拟结果与 Berea 砂岩样品的实验测量结果进行比较来验证它。最后，我们量化了影响${秒}_{瓦}$通过孔隙尺度数值模拟测量宽带介电常数的润湿性。数值模拟结果表明，混湿岩石对水湿岩石的变化更为敏感。${秒}_{瓦}$在 sub-MHz 频率。此外，与水湿岩石相比，混合湿岩石的介电常数和电导率分别具有较弱和较强的弥散行为。最后，数值模拟表明，混合湿岩石的电导率可以在 100 Hz 到 1 GHz 的三个数量级内变化。因此，以错误的频率校准的阿奇方程可能导致高达 73% 的水饱和度误差。