Schlumberger-Doll Research, 1 Hampshire Street, Cambridge, MA 02139, United States.
J Colloid Interface Sci. 2018 Sep 1;525:62-75. doi: 10.1016/j.jcis.2018.04.048. Epub 2018 Apr 11.
In this work, we establish an effective medium model to describe the low-frequency complex dielectric (conductivity) dispersion of dilute clay suspensions. We use previously obtained low-frequency polarization coefficients for a charged oblate spheroidal particle immersed in an electrolyte as the building block for the Maxwell Garnett mixing formula to model the dilute clay suspension. The complex conductivity phase dispersion exhibits a near-resonance peak when the clay grains have a narrow size distribution. The peak frequency is associated with the size distribution as well as the shape of clay grains and is often referred to as the characteristic frequency. In contrast, if the size of the clay grains has a broad distribution, the phase peak is broadened and can disappear into the background of the canonical phase response of the brine. To benchmark our model, the low-frequency dispersion of the complex conductivity of dilute clay suspensions is measured using a four-point impedance measurement, which can be reliably calibrated in the frequency range between 0.1 Hz and 10 kHz. By using a minimal number of fitting parameters when reliable information is available as input for the model and carefully examining the issue of potential over-fitting, we found that our model can be used to fit the measured dispersion of the complex conductivity with reasonable parameters. The good match between the modeled and experimental complex conductivity dispersion allows us to argue that our simplified model captures the essential physics for describing the low-frequency dispersion of the complex conductivity of dilute clay suspensions.
在这项工作中，我们建立了一个有效的介质模型来描述稀粘土悬浮液的低频复介电（电导率）色散。我们使用先前获得的在电解质中浸入带电荷的扁长球体的低频极化系数作为 Maxwell Garnett 混合公式的构建块，来对稀粘土悬浮液进行建模。当粘土颗粒具有较窄的尺寸分布时，复电导率的相位色散会出现近共振峰。峰频率与颗粒的尺寸分布以及形状有关，通常被称为特征频率。相比之下，如果粘土颗粒的尺寸分布较宽，相位峰会变宽并可能消失在卤水的典型相位响应的背景中。为了对我们的模型进行基准测试，使用四点阻抗测量法测量了稀粘土悬浮液的复电导率的低频色散，该方法可以在 0.1 Hz 至 10 kHz 的频率范围内可靠地校准。通过在模型输入中使用可靠信息并仔细检查潜在的过度拟合问题时，仅使用最小数量的拟合参数，我们发现我们的模型可以用于用合理的参数拟合复电导率的实测色散。复电导率的模拟和实验色散之间的良好匹配使我们能够认为我们的简化模型捕捉到了描述稀粘土悬浮液的复电导率低频色散的基本物理原理。
