Numerical modelling of the IP effect at the pore scale
Numerical modelling of the IP effect at the pore scale
复制标题
孔隙尺度 IP 效应的数值模拟
DOI：
10.3997/1873-0604.2009030
复制
发表时间：
2008
影响因子：
1.6
通讯作者：
A. Hördt
中科院分区：
文献类型：
--
作者：
R. Blaschek;A. Hördt
地球物理学家已经尝试了很长一段时间，以相关的激发极化数据与孔隙几何形状的参数，通常与总体目标，以估计的重要参数的水力传导性。然而，到目前为止，还没有发现适用于少数特殊情况的相关性。使用经验关系和等效电路往往忽略了描述
孔隙中的过程。原因之一是控制低频的机制
两极分化仍然没有完全被理解。只有少数现有的模型试图解释的过程，并得出与几何的关系，大多数模型需要强有力的假设。
在这里，我们的目标是通过数值模拟的主要过程负责IP效应更深入的了解。我们的方法是基于20世纪50年代末的一维解决方案，给出了简化的几何形状的最大频率效应的表达式。该模型依赖于活性区和钝化区的长度和相应的离子迁移率在每个区域的阴离子和阳离子分别。该理论描述了离子沿着浓度梯度的扩散、外加电场的影响以及两者之间的耦合。
我们首先通过与解析解的比较来验证我们的数值结果，然后将该方法扩展到灵活的几何形状，包括更高的维度。这构成了一个相当大的进步，从一维模型限制到两个交替介质与固定长度。除了任意的几何形状，
我们还可以模拟全光谱行为。一个相对简单的模型是能够解释频率依赖的幅度和相位的行为，通常是在现场测量。Cole-Cole模型可以被认为是不同长度的孔隙网络的结果。从我们的建模研究中，我们推导出流动性和几何形状的比例律，并提出了一个经验方程
研究了被动孔隙长度与最大相移时间的关系。
Geophysicists have tried for a long time to correlate induced polarization data with parameters of the pore geometry, often with the overall aim to estimate the important parameter of hydraulic conductivity. However, no correlation has been found so far that is applicable to more than just a few special cases. Using empirical relationships and equivalent circuits often neglects the description
of the processes in the pore space. One reason is that the mechanisms controlling the low-frequency
polarization are still not completely understood. Only a few existing models try to explain the processes and derive relationships with geometry and most models need strong assumptions.
Here, we aim at a deeper understanding by numerical modelling of the main processes responsible for the IP effect. Our approach is based on a 1D solution of the late 1950s that gives an expression for the maximum frequency effect for simplified geometries. The models depend on the lengths of active and passive zones and the corresponding ion mobilities in each zone for anions and cations respectively. The theory describes the ion diffusion along concentration gradients, the influence of an external electric field and the coupling between the two.
We first verify our numerical results by comparison with analytical solutions and then extend the approach to flexible geometry, including higher dimension. This constitutes a considerable progress from 1D models restricted to two alternating media with fixed lengths. Apart from arbitrary geometry,
we can also simulate the full spectral behaviour. A relatively simple model is able to explain frequency-dependent magnitude and phase behaviour that is typically measured in the field. The Cole-Cole model can be considered as the result of a network of pores of varying lengths. From our modelling studies, we derive scaling laws for mobility and geometry and suggest an empirical equation
for the relationship between the length of passive pores and the time of maximum phase shift.