Electrical properties of sedimentary rocks having interconnected water‐saturated pore spaces

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1093-1097 ◽  
Author(s):  
Pham Duc Chinh
Keyword(s):  
Electrical Conductivity ◽  
Sedimentary Rocks ◽  
Open Water ◽  
Effective Medium ◽  
Multiphase Model ◽  
Archie’S Law ◽  
Effective Media ◽  
Self Similar ◽  
Model Components ◽  
Water Saturated

Permeable sedimentary rocks can often be modeled as an impermeable rock matrix cut by a system of an irregular system of interconnected, irregularly shaped, water‐saturated pore spaces. I represent this system by a multiphase effective medium that is compatible with Archie’s Law for electrical conductivity. My effective medium is an extention of the self‐similar Sen, Scalar, and Cohen model which characterizes sedimentary rocks as a water suspension of spherical solid grains. My generalized multiphase model includes two important components: open water spherelike pockets, which significantly increase the porosity but add little to the electrical conductivity, and thin films surrounding the grains and water‐filled cracks, which contribute little to the porosity but significantly to the electrical conductivity. By perturbing the relative balance between these two model components, I am able to represent a range of aggregates for which I can construct effective media that are consistent with the electrical conductivity predicted by Archie’s Law.

Cross-property relations between electrical conductivity and the seismic velocity of rocks

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. E193-E204 ◽  
Author(s):  
José M. Carcione ◽  
Bjørn Ursin ◽  
Janniche I. Nordskag
Keyword(s):  
Electrical Conductivity ◽  
Constitutive Equations ◽  
Seismic Velocity ◽  
Refraction Index ◽  
Rock Properties ◽  
Index Method ◽  
Archie’S Law ◽  
Property Relations ◽  
Backus Averaging ◽  
Self Similar

Cross-property relations are useful when some rock properties can be measured more easily than other properties. Relations between electrical conductivity and seismic velocity, stiffness moduli, and density can be obtained by expressing the porosity in terms of those properties. There are many possible ways to combine the constitutive equations to obtain a relation, each one representing a given type of rock. The relations depend on the assumptions to obtain the constitutive equations. In the electromagnetic case, the equations involve Archie’s law and its modifications for a conducting frame, the Hashin-Shtrikman (HS) bounds, and the self-similar and complex refraction-index method (CRIM) models. In the elastic case, the stress-strain relations are mainly based on the time-average equation, the HS bounds, and the Gassmann equation. Also, expressions for dry rocks and for anisotropic media, using Backus averaging, are analyzed. The relations are applied to a shale saturated with brine (overburden) and to a sandstone saturated with oil (reservoir). Tests with sections of a North Sea well log show that the best fit is given by the relation between the Gassmann velocity and the CRIM, self-similar, and Archie models for the conductivity.

A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 781-795 ◽  
Author(s):  
P. N. Sen ◽  
C. Scala ◽  
M. H. Cohen
Keyword(s):  
Dielectric Constant ◽  
External Field ◽  
Sedimentary Rocks ◽  
Glass Beads ◽  
The Self ◽  
Similar Model ◽  
Archie’S Law ◽  
Self Consistent ◽  
Self Similar ◽  
Coated Spheres

We develop a theory for dielectric response of water‐saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron‐micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water‐coated grains is obtained by a self‐consistent effective medium theory. In the dc limit, this gives Maxwell’s relation for conductivity σ of the rock [Formula: see text], where [Formula: see text] is the conductivity of water. In order to include the local environmental effects around a grain, a self‐similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coated spheres. The self‐consistent complex dielectric constant [Formula: see text] is given in this model in terms of that of water [Formula: see text] and of rock [Formula: see text], by [Formula: see text] for spherical particles. This gives, in the dc limit, [Formula: see text]. For nonspherical particles, the exponent m in Archie’s law [Formula: see text] is greater than 3/2 for the plate‐like grains or cylinders with axis perpendicular to the external field and smaller than 3/2 for plates or cylindrical particles with axis parallel to the external field. Artificial rocks with a wide range of porosities were made from glass beads. We present data on the glass bead rocks for dc conductivity and the dielectric constant at 1.1 GHz. The data follow the conductivity and the dielectric responses given by the self‐similar model. The present theory fails to explain the salinity dependence of [Formula: see text] at lower frequencies.

Consistent modeling of the electrical and elastic properties of sedimentary rocks

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1236-1243 ◽  
Author(s):  
Ping Sheng
Keyword(s):  
Effective Medium Theory ◽  
Sedimentary Rocks ◽  
Fluid Phase ◽  
Compressional Wave ◽  
Effective Medium ◽  
Dielectric Behavior ◽  
Unified Framework ◽  
Medium Theory ◽  
Archie’S Law ◽  
Component Material

An effective medium theory is formulated which reproduces many of the observed electrical and elastic characteristics of sedimentary rocks within a unified framework. The effective medium consists of fluid, solid, and cement components, with the component material properties related to those of the composite through a differential effective medium (DEM) scheme. The resulting microstructure of the composite both conducts electricity through the fluid phase and supports shear. Besides deriving Archie’s law, the theory gives an excellent account of the shear‐wave and compressional‐wave velocity correlations, and predicts corrections to the Wyllie equation that are consistent with observed deviations. The three‐component DEM also accommodates clay conductivity and finite‐frequency dielectric behavior.

scholarly journals Effective-medium theory of sedimentary rocks

1990 ◽  
Vol 41 (7) ◽  
pp. 4507-4512 ◽  
Author(s):  
Ping Sheng
Keyword(s):  
Effective Medium Theory ◽  
Sedimentary Rocks ◽  
Effective Medium ◽  
Medium Theory

scholarly journals Automatic Surface Water Mapping Using Polarimetric SAR Data for Long-Term Change Detection

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 872
Author(s):  
Wen Zhang ◽  
Baoxin Hu ◽  
Glen S. Brown
Keyword(s):  
Surface Water ◽  
Open Water ◽  
Polarimetric Sar ◽  
Dynamic Events ◽  
Term Change ◽  
Microwave Signals ◽  
Timely Fashion ◽  
Sar Data ◽  
Accuracy Of Results ◽  
Water Saturated

Mapping the distribution and persistence of surface water in a timely fashion has broad value for tracking dynamic events like flooding, and for monitoring the effects of climate and human activities on natural resource values and biodiversity. Traditionally, surface water is mapped from optical imagery using semi-automatic approaches. However, this process is time-consuming and the accuracy of results can vary among image interpreters. In recent years, Synthetic Aperture Radar (SAR) images have been increasingly used. Microwave signals sensitive to water content make SAR systems useful for mapping surface water, saturated soils, and flooded vegetation. In this study, a fully automatic method based on robust stepwise thresholding was developed to map and track the change in the extent of surface water using Polarimetric SAR data. The application of this method in both Radarsat-2 and Sentinel-1 data in central Ontario, Canada demonstrates that the developed robust stepwise thresholding approach could facilitate rapid mapping of open water areas with a promising accuracy of over 95%. In addition, the time-series extent of surface water extracted from May 2008 to August 2016 reveals the dynamic nature of surface inundation, and the trend was consistent with the local precipitation data.

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