Generalized effective-medium theory of induced polarization

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. F197-F211 ◽  
Author(s):  
Michael Zhdanov
Keyword(s):  
Mathematical Model ◽  
Arbitrary Shape ◽  
Effective Conductivity ◽  
Effective Medium Theory ◽  
Induced Polarization ◽  
Effective Medium ◽  
Matrix Composition ◽  
Medium Theory ◽  
Rock Formations ◽  
The Matrix

A rigorous physical-mathematical model of heterogeneous conductive media is based on the effective-medium approach. A generalization of the classical effective-medium theory (EMT) consists of two major parts: (1) introduction of effective-conductivity models of heterogeneous, multiphase rock formations with inclusions of arbitrary shape and conductivity using the principles of the quasi-linear (QL) approximation within the framework of the EMT formalism and (2) development of the generalized effective-medium theory of induced polarization (GEMTIP), which takes into account electromagnetic-induction (EMI) and induced polarization (IP) effects related to the relaxation of polarized charges in rock formations. The new generalized EMT provides a unified mathematical model of heterogeneity, multiphase structure, and the polarizability of rocks. The geoelectric parameters of this model are determined by the intrinsic petrophysical and geometric characteristics of composite media: the mineralization and/or fluid content of rocks and the matrix composition, porosity, anisotropy, and polarizability of formations. The GEMTIP model allows one to find the effective conductivity of a medium with inclusions that have arbitrary shape and electrical properties. One fundamental IP model of an isotropic, multiphase, heterogeneous medium is filled with spherical inclusions. This model, because of its relative simplicity, makes it possible to explain the close relationships between the new GEMTIP conductivity-relaxation model and an empirical Cole-Cole model or classical Wait’s model of the IP effect.

Modifying the generalized effective-medium theory of induced polarization model in compacted rocks

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR245-MR255
Author(s):  
Tong Xiaolong ◽  
Yan Liangjun ◽  
Xiang Kui
Keyword(s):  
Maxwell Equations ◽  
Effective Medium Theory ◽  
Induced Polarization ◽  
Effective Medium ◽  
High Resistivity ◽  
Hydraulic Permeability ◽  
Mineral Particle ◽  
Polarization Model ◽  
Rock Composition ◽  
Medium Theory

The generalized effective-medium theory of the induced polarization model (GEMTIP) is a mathematical-physical model derived from the Maxwell equations based on the effective-medium approach. Compared to the Cole-Cole model, the GEMTIP parameters are better related to the structural parameters of reservoir rocks, such as rock composition, mineral particle size, porosity, and specific surface; therefore, it can better describe the induced polarization (IP) characteristics of tight oil and gas reservoirs. However, GEMTIP is not suitable for high-resistivity perturbed media, and it does not account for interfacial polarization, which occurs between two media that share the same resistivity. Starting from the theoretical assumptions of the GEMTIP model, we derived an extended GEMTIP model (MGEMTIP) by adding an equivalent surface current term into the Maxwell equations for a heterogeneous medium. The complex resistivity parameters predicted by two models are compared through numerical simulation, and the results demonstrate that MGEMTIP can more accurately predict the DC resistivity and the chargeability of heterogeneous media. MGEMTIP is suitable for characterizing the polarization phenomena of rock with high salinity, low porosity, low hydraulic permeability, and a disseminated perturbed medium. Furthermore, the testing of rock samples for the inversion of IP parameters with MGEMTIP revealed that the predicted chargeability is higher than the inverted chargeability from the experimental data. This difference is strongly correlated with rock hydraulic permeability. MGEMTIP provides a petrophysical basis for the forward modeling and inversion of IP parameters of compacted rocks. The quantitative relationships between model IP parameters and reservoir parameters also provide a theoretical foundation for predicting reservoir permeability using electromagnetic methods.

scholarly journals Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

Materials ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1243 ◽  
Author(s):  
Andrei A. Snarskii ◽  
Mikhail Shamonin ◽  
Pavel Yuskevich
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Effective Conductivity ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Effective Parameters ◽  
Two Phase ◽  
Medium Theory ◽  
Percolation Thresholds ◽  
Conductive Properties

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.

Parametric Study on Mechanical, Thermal and Electrical Properties of Graphene Reinforced Composites by Effective Medium Theory

2021 ◽  
Vol 13 (01) ◽  
pp. 2150008
Author(s):  
Zhilin Tong ◽  
Yu Wang ◽  
Chuang Feng ◽  
Dong Zhu ◽  
Sujing Jin
Keyword(s):  
Dielectric Properties ◽  
Electrical Properties ◽  
Material Properties ◽  
Parametric Study ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Reinforced Composites ◽  
Medium Theory ◽  
The Matrix ◽  
Thermal And Electrical Properties

This paper conducts theoretical study on the mechanical, thermal and electrical properties of graphene reinforced composites by effective medium theory (EMT). Considering the imperfect bonding between the reinforcing fillers and the matrix, an interphase surrounding the graphene fillers is introduced during the EMT modeling. The coated graphene fillers are homogenized as effective reinforcements dispersed in a matrix. The EMT model is validated by comparing the predicted material properties with previously reported results. Parametric study is carried out to investigate the influences of several parameters, including concentration and geometry of graphene fillers, the attributes of the introduced an interphase and the alternating current (AC) frequency, upon the effective material properties of the reinforced composites. The results demonstrate that the increase of the thickness of the interphase results in the decrease of Young’s modulus, thermal conductivity and electrical conductivity of the composites while it is favorable to enhance the dielectric properties of the composites. The increase in the aspect ratio of the graphene filler enhances all material properties involved. Percolation behaviors are observed for the dielectric properties of the composites. Moreover, the dielectric properties of the composites are very sensitive to the change of the AC frequency within a certain range, which suggests the achievement of active tuning of material properties.

An Effective Unit Cell Approach to Compute the Thermal Conductivity of Composites With Cylindrical Particles

2003 ◽  
Author(s):  
Deepak Ganapathy ◽  
Kulwinder Singh ◽  
Patrick E. Phelan ◽  
Ravi S. Prasher
Keyword(s):  
Thermal Conductivity ◽  
Effective Conductivity ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Unit Cell ◽  
Spherical Particles ◽  
Medium Theory ◽  
Volume Fractions ◽  
Finite Differences Method ◽  
Cylindrical Particles

This paper introduces a novel method to model the effective thermal conductivity of cylindrical-particle-laden composite materials. This modeling methodology is a combination of the effective medium theory and the finite differences method. Typically the curvature effects of cylindrical or spherical particles are ignored while calculating the thermal conductivity of composites containing such particles through numerical techniques. These particles are modeled as cuboids or cubes. Numerical modeling of circular/spherical geometries as cubes or cuboids will lead to wrong conclusions due to two reasons: (i) It does not capture the effect of curvature on heat flow, i.e., constriction of heat flux lines near the particles due to shape, (ii) It assigns higher effective conductivity to the particles as the cubes or the cuboids have larger volume and surface area. An alternative approach to mesh the particles into small volumes is just about impossible as it leads to highly intensive computational algorithms to get accurate results. On the other hand, effective medium theory takes the effect of curvature into account but it cannot be used at high volume fractions because it does not take into account the effects of percolation. In this paper, a novel model is proposed where the cylindrical particles are still treated as squares (cuboids) but to capture the effect of curvature, an effective conductivity is assigned to the particles by using the effective medium approach. The authors call this the effective unit cell approach. Results from this model for different volume fractions, on average, have been found to lie within ±5% of experimental thermal conductivity data.

Anisotropy of induced polarization in the context of the generalized effective‐medium theory

2008 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Alexander Gribenko ◽  
Vladimir Burtman ◽  
Vladimir I. Dmitriev
Keyword(s):  
Effective Medium Theory ◽  
Induced Polarization ◽  
Effective Medium ◽  
Medium Theory
Sign in / Sign up

Export Citation Format

Share Document