A simple, effective‐medium model for water saturation in porous rocks

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1070-1080 ◽  
Author(s):  
Charles R. Berg
Keyword(s):  
General Equation ◽  
Water Saturation ◽  
Effective Medium Theory ◽  
Complex Refractive Index ◽  
Low Frequency ◽  
Frequency Equation ◽  
Effective Medium ◽  
Porous Rocks ◽  
Rock Types ◽  
Wide Range

A general equation for water saturation is derived from effective‐medium theory. A simpler low‐frequency equation is also derived. Both equations are directly solvable for water saturation. The model should be applicable to any granular, water‐wet formation. Additional relationships are derived specifically for application to shaly sandstones, but the model should be applicable to a wide range of rock types, water conductivities, and tool frequencies. In the derivation, hydrocarbons are included in the matrix component of the equation and the combined “matrix” elements are treated as resistors in parallel. The low‐frequency equation is compared to various approaches to calculation of water saturation, such as Dual‐Water, Waxman‐Smits, and Bussian. The general equation is compared to three‐component effective medium, porosity index, and complex refractive index models (CRIM). The model is proven to work on experimental data under a wide range of frequencies and water conductivities. It is recommended that the new saturation model be used for nearly all types of electrical saturation calculation, whether the measurements are from standard resistivity tools or from dielectric tools.

Experimental determination of bulk dielectric properties and porosity of porous asphalt and soils using GPR and a cyclic moisture variation technique

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. K93-K102 ◽  
Author(s):  
W. L. Lai ◽  
W. F. Tsang ◽  
H. Fang ◽  
D. Xiao
Keyword(s):  
Water Saturation ◽  
Complex Refractive Index ◽  
Large Mass ◽  
Small Mass ◽  
Time Domain Reflectometry ◽  
Water Permeation ◽  
Moisture Variation ◽  
Wide Range ◽  
Test Materials ◽  
Variation Technique

This paper describes a new method for determining porosities in two porous construction and geologic materials (asphalt and soil) by using ground-penetrating radar (GPR) over a wide range of controlled degrees of water saturation [Formula: see text]. We call this method a cyclic moisture variation technique (CMVT). Freshwater is used as an enhancer or a tracer to allow GPR to easily detect and differentiate amounts of water or other moisture in these materials. The CMVT is based on measuring the changes of real permittivity [Formula: see text] and [Formula: see text] in the test materials as they transition from partially saturated states to a fully saturated state via cycles of water permeation and dewatering. This method does not disturb the test materials, as do the methods associated with traditional laboratory testing on cored samples. It also tests a large mass of in situ material, compared with the small mass tested by the conventional or electromagnetic coaxial transmission line (EMCTL) method (also known as a dielectric cell) and the time-domain reflectometry (TDR) method. Porosity values of asphalt [Formula: see text] and of soils [Formula: see text] were determined by fitting the data into the complex refractive index model (CRIM). Dielectric hysteresis of both soils and asphalt also is observable during the tests and shows that the pathways of water-ingress and water-egress processes are not identical in the plot of [Formula: see text] versus degrees of water saturation [Formula: see text].

Ultrasonic velocity‐porosity relationships for sandstone analogs made from fused glass beads

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 108-119 ◽  
Author(s):  
Patricia A. Berge ◽  
Brian P. Bonner ◽  
James G. Berryman
Keyword(s):  
Upper Bound ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Glass Beads ◽  
Composite Medium ◽  
Host Material ◽  
Consistent Theory ◽  
Medium Theory ◽  
Wide Range ◽  
Self Consistent

Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P‐ and S‐wave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the Hashin‐Shtrikman bounds, a differential effective medium approach, and a self‐consistent theory known as the coherent potential approximation. The self‐consistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background (host) material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the Hashin‐Shtrikman upper bound overestimate the observed velocities of the sandstone analogs because these theories assume the microgeometry is represented by isolated pores embedded in a host material that remains continuous even for high porosities. We also demonstrate that the differential effective medium theory and the Hashin‐Shtrikman upper bound correctly estimate bulk moduli of porous glass foams, again because the microstructure of the samples is consistent with the implicit assumptions of these two theoretical approaches.

High-Throughput Screening of Aperiodic Superlattice for Minimum Thermal Conductivity Based on Atomistic Simulation-Informed Effective Medium Theory and Genetic Algorithm

2021 ◽  
Author(s):  
Shangchao Lin ◽  
Yixuan Liu ◽  
Zhuangli Cai
Keyword(s):  
Thermal Conductivity ◽  
Genetic Algorithm ◽  
High Throughput ◽  
High Throughput Screening ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Correction Function ◽  
Stable Range ◽  
Medium Theory ◽  
Wide Range

Abstract Superlattices with suppressed thermal conductivity are of great significance in the field of thermoelectricity and can improve the thermoelectric conversion efficiency of materials. Due to Anderson localization of coherent phonons, aperiodic superlattices have lower thermal conductivity than their periodic counterparts. At present, the thermal conductivity of superlattices is mostly predicted through ab initio or molecular dynamics simulations, which is computationally expensive and limits the size of the system. Meanwhile, there are many layered structural combinations for aperiodic superlattices, making it difficult to efficiently screen through all the combinations to search structures with the minimum thermal conductivity. In this work, based on a modified series thermal resistance model (STRM), a new effective medium theory (EMT) is established to predict the thermal conductivity of periodic and aperiodic superlattices. An adjacency factor near the maximum-resistance layers and a correction function, respectively, are introduced to account for the phonon coherence effect and the degree of randomization in the layer thickness. Combined with the genetic algorithm, EMT enables high-throughput screening of millions of aperiodic superlattice structures. This work demonstrates that the thermal conductivities of aperiodic superlattices at a wide range of system size can be constantly reduced to 1.4∼1.8 W/(m·K), which occurs at averaged periodic thicknesses in a stable range of 2.0∼2.5 nm.

The Attenuation of Very Low Frequency Brain Oscillations in Transitions from a Rest State to Active Attention

2009 ◽  
Vol 23 (4) ◽  
pp. 191-198 ◽  
Author(s):  
Suzannah K. Helps ◽  
Samantha J. Broyd ◽  
Christopher J. James ◽  
Anke Karl ◽  
Edmund J. S. Sonuga-Barke
Keyword(s):  
Brain Activity ◽  
Sampling Rate ◽  
Low Frequency ◽  
Future Research ◽  
Adhd Symptoms ◽  
Default Mode ◽  
Very Low Frequency ◽  
Wide Range ◽  
Interference Hypothesis ◽  
Mode Interference

Background: The default mode interference hypothesis ( Sonuga-Barke & Castellanos, 2007 ) predicts (1) the attenuation of very low frequency oscillations (VLFO; e.g., .05 Hz) in brain activity within the default mode network during the transition from rest to task, and (2) that failures to attenuate in this way will lead to an increased likelihood of periodic attention lapses that are synchronized to the VLFO pattern. Here, we tested these predictions using DC-EEG recordings within and outside of a previously identified network of electrode locations hypothesized to reflect DMN activity (i.e., S3 network; Helps et al., 2008 ). Method: 24 young adults (mean age 22.3 years; 8 male), sampled to include a wide range of ADHD symptoms, took part in a study of rest to task transitions. Two conditions were compared: 5 min of rest (eyes open) and a 10-min simple 2-choice RT task with a relatively high sampling rate (ISI 1 s). DC-EEG was recorded during both conditions, and the low-frequency spectrum was decomposed and measures of the power within specific bands extracted. Results: Shift from rest to task led to an attenuation of VLFO activity within the S3 network which was inversely associated with ADHD symptoms. RT during task also showed a VLFO signature. During task there was a small but significant degree of synchronization between EEG and RT in the VLFO band. Attenuators showed a lower degree of synchrony than nonattenuators. Discussion: The results provide some initial EEG-based support for the default mode interference hypothesis and suggest that failure to attenuate VLFO in the S3 network is associated with higher synchrony between low-frequency brain activity and RT fluctuations during a simple RT task. Although significant, the effects were small and future research should employ tasks with a higher sampling rate to increase the possibility of extracting robust and stable signals.

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