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.

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.

scholarly journals Pressure and fluid saturation prediction in a multicomponent reservoir using combined seismic and electromagnetic imaging

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1580-1591 ◽  
Author(s):  
G. Michael Hoversten ◽  
Roland Gritto ◽  
John Washbourne ◽  
Tom Daley
Keyword(s):  
Electrical Conductivity ◽  
Water Saturation ◽  
Saturation Pressure ◽  
Shear Velocity ◽  
Velocity Shear ◽  
Rock Properties ◽  
Velocity Change ◽  
Archie’S Law ◽  
Fluid Saturation ◽  
Compressional Velocity

This paper presents a method for combining seismic and electromagnetic (EM) measurements to predict changes in water saturation, pressure, and CO2 gas/oil ratio in a reservoir undergoing CO2 flood. Crosswell seismic and EM data sets taken before and during CO2 flooding of an oil reservoir are inverted to produce crosswell images of the change in compressional velocity, shear velocity, and electrical conductivity during a CO2 injection pilot study. A rock‐properties model is developed using measured log porosity, fluid saturations, pressure, temperature, bulk density, sonic velocity, and electrical conductivity. The parameters of the rock‐properties model are found by an L1‐norm simplex minimization of predicted and observed differences in compressional velocity and density. A separate minimization, using Archie's law, provides parameters for modeling the relations between water saturation, porosity, and electrical conductivity. The rock‐properties model is used to generate relationships between changes in geophysical parameters and changes in reservoir parameters. Electrical conductivity changes are directly mapped to changes in water saturation; estimated changes in water saturation are used along with the observed changes in shear‐wave velocity to predict changes in reservoir pressure. The estimation of the spatial extent and amount of CO2 relies on first removing the effects of the water saturation and pressure changes from the observed compressional velocity changes, producing a residual compressional velocity change. This velocity change is then interpreted in terms of increases in the CO2/oil ratio. Resulting images of the CO2/oil ratio show CO2‐rich zones that are well correlated to the location of injection perforations, with the size of these zones also correlating to the amount of injected CO2. The images produced by this process are better correlated to the location and amount of injected CO2 than are any of the individual images of change in geophysical parameters.

scholarly journals Elastic wave velocity and electrical conductivity in a brine-saturated rock and microstructure of pores

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Tohru Watanabe ◽  
Miho Makimura ◽  
Yohei Kaiwa ◽  
Guillaume Desbois ◽  
Kenta Yoshida ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Elastic Wave ◽  
Wave Velocity ◽  
High Pressures ◽  
Seismic Velocity ◽  
Volume Fraction ◽  
Elastic Wave Velocity ◽  
Fluid Volume ◽  
Sem Observation ◽  
Wide Aperture

AbstractElastic wave velocity and electrical conductivity in a brine-saturated granitic rock were measured under confining pressures of up to 150 MPa and microstructure of pores was examined with SEM on ion-milled surfaces to understand the pores that govern electrical conduction at high pressures. The closure of cracks under pressure causes the increase in velocity and decrease in conductivity. Conductivity decreases steeply below 10 MPa and then gradually at higher pressures. Though cracks are mostly closed at the confining pressure of 150 MPa, brine must be still interconnected to show observed conductivity. SEM observation shows that some cracks have remarkable variation in aperture. The aperture varies from ~ 100 nm to ~ 3 μm along a crack. FIB–SEM observation suggests that wide aperture parts are interconnected in a crack. Both wide and narrow aperture parts work parallel as conduction paths at low pressures. At high pressures, narrow aperture parts are closed but wide aperture parts are still open to maintain conduction paths. The closure of narrow aperture parts leads to a steep decrease in conductivity, since narrow aperture parts dominate cracks. There should be cracks in various sizes in the crust: from grain boundaries to large faults. A crack must have a variation in aperture, and wide aperture parts must govern the conduction paths at depths. A simple tube model was employed to estimate the fluid volume fraction. The fluid volume fraction of 10−4–10−3 is estimated for the conductivity of 10−2 S/m. Conduction paths composed of wide aperture parts are consistent with observed moderate fluctuations (< 10%) in seismic velocity in the crust.

Bringing slow slip processes into focus

2020 ◽  
Author(s):  
Rebecca Bell
Keyword(s):  
High Resolution ◽  
Subduction Zones ◽  
Seismic Velocity ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Geophysical Methods ◽  
Rock Properties ◽  
Slow Slip ◽  
Velocity Models ◽  
The North

&lt;p&gt;The discovery of slow slip events (SSEs) at subduction margins in the last two decades has changed our understanding of how stress is released at subduction zones. Fault slip is now viewed as a continuum of different slip modes between regular earthquakes and aseismic creep, and an appreciation of seismic hazard can only be realised by understanding the full spectrum of slip. SSEs may have the potential to trigger destructive earthquakes and tsunami on faults nearby, but whether this is possible and why SSEs occur at all are two of the most important questions in earthquake seismology today. Laboratory and numerical models suggest that slow slip can be spontaneously generated under conditions of very low effective stresses, facilitated by high pore fluid pressure, but it has also been suggested that variations in frictional behaviour, potentially caused by very heterogeneous fault zone lithology, may be required to promote slow slip.&lt;/p&gt;&lt;p&gt;Testing these hypotheses is difficult as it requires resolving rock properties at a high resolution many km below the seabed sometimes in km&amp;#8217;s of water, where drilling is technically challenging and expensive. Traditional geophysical methods like travel-time tomography cannot provide fine-scale enough velocity models to probe the rock properties in fault zones specifically. In the last decade, however, computational power has improved to the point where 3D full-waveform inversion (FWI) methods make it possible to use the full wavefield rather than just travel times to produce seismic velocity models with a resolution an order of magnitude better than conventional models. Although the hydrocarbon industry have demonstrated many successful examples of 3D FWI the method requires extremely high density arrays of instruments, very different to the 2D transect data collection style which is still commonly employed at subduction zones.&lt;/p&gt;&lt;p&gt;&amp;#160;The north Hikurangi subduction zone, New Zealand is special, as it hosts the world&amp;#8217;s most well characterised shallow SSEs (&lt;2 km to 15 km below the seabed).&amp;#160; This makes it an ideal location to collect 3D data optimally for FWI to resolve rock properties in the slow slip zone. In 2017-2018 an unprecedentedly large 3D experiment including 3D multi-channel seismic reflection, 99 ocean bottom seismometers and 194 onshore seismometers was conducted along the north Hikurangi margin in an 100 km x 15 km area, with an average 2 km instrument spacing. In addition, IODP Expeditions 372 and 375 collected logging-while drilling and core data, and deployed two bore-hole observatories to target slow slip in the same area. In this presentation I will introduce you to this world class 3D dataset and preliminary results, which will enable high resolution 3D models of physical properties to be made to bring slow slip processes into focus. &amp;#160;&lt;/p&gt;

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.

Anisotropic velocity tomography: A case study in a near‐surface rock mass

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1748-1763 ◽  
Author(s):  
R. G. Pratt ◽  
W. J. McGaughey ◽  
C. H. Chapman
Keyword(s):  
Rock Mass ◽  
Fault Zone ◽  
Seismic Velocity ◽  
Anisotropic Media ◽  
Rock Properties ◽  
Initial Assessment ◽  
Borehole Data ◽  
Near Surface ◽  
Crown Pillar ◽  
Velocity Tomography

Cross‐borehole data were acquired in the surface crown pillar of a massive sulfide ore mine. The data consist of five, two‐dimensional (2-D), cross‐borehole panels, each with approximately 900 source‐receiver pairs. The panels were located within the crown pillar at either side of and within a major subvertical fault zone that intersects the orebody. An initial analysis of the data indicates that the bedrock containing the orebody is seismically anisotropic. A rigorous analysis of the traveltimes using anisotropic velocity tomography confirms the initial assessment that anisotropy exists within the crown pillar rock mass. Anisotropic velocity tomography is the generalization of tomographic methods to anisotropic media. As in any geophysical problem, the data are insufficient to completely resolve the distributions of the rock properties at all scale lengths; we use external constraints on the roughness of the final solution to ensure an algebraically well‐posed problem. Plots of the data residuals (the “traveltime surfaces”) are an essential tool in determining an optimal level of constraint. Of equal importance are plots of the relationship between the solution roughness and the rms level of the residuals. The final results of anisotropic velocity tomography are a set of images (tomograms) of the velocity and selected anisotropy parameters for the five panels. Our images do not contain the distortions typically exhibited when using isotropic tomography in anisotropic media. The velocity tomograms clearly show the geometry of the overburden contact at the top of the bedrock. The anisotropy tomograms show a decrease in anisotropy with depth on two of the panels. They also show a decrease in anisotropy with proximity to the fault zone. These features of the seismic velocity anisotropy are consistent with observations of fracture orientation and distribution. The results of the crosshole data interpretation contribute to the overall site investigation and provide a reliable interrogation of the bulk properties of the rock mass.

Recent advances in rock physics

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2480-2491 ◽  
Author(s):  
David P. Yale
Keyword(s):  
Electrical Properties ◽  
Seismic Waves ◽  
Seismic Velocity ◽  
Pore Space ◽  
Rock Physics ◽  
Rock Properties ◽  
Bright Spot ◽  
Geometrical Parameters ◽  
S Wave ◽  
Velocity Models

The need to extract more information about the subsurface from geophysical and petrophysical measurements has led to a great interest in the study of the effect of rock and fluid properties on geophysical and petrophysical measurements. Rock physics research in the last few years has been concerned with studying the effect of lithology, fluids, pore geometry, and fractures on velocity; the mechanisms of attenuation of seismic waves; the effect of anisotropy; and the electrical and dielectric properties of rocks. Understanding the interrelationships between rock properties and their expression in geophysical and petrophysical data is necessary to integrate geophysical, petrophysical, and engineering data for the enhanced exploration and characterization of petroleum reservoirs. The use of amplitude offsets, S‐wave seismic data, and full‐waveform sonic data will help in the discrimination of lithology. The effect of in situ temperatures and pressures must be taken into account, especially in fractured and unconsolidated reservoirs. Fluids have a strong effect on seismic velocities, through their compressibility, density, and chemical effects on grain and clay surfaces. S‐wave measurements should help in bright spot analysis for gas reservoirs, but theoretical considerations still show that a deep, consolidated reservoir will not have any appreciable impedance contrast due to gas. The attenuation of seismic waves has received a great deal of attention recently. The idea that Q is independent of frequency has been challenged by experimental and theoretical findings of large peaks in attenuation in the low kHz and hundreds of kHz regions. The attenuation is thought to be due to fluid‐flow mechanisms and theories suggest that there may be large attenuation due to small amounts of gas in the pore space even at seismic frequencies. Models of the effect of pores, cracks, and fractures on seismic velocity have also been studied. The thin‐crack velocity models appear to be better suited for representing fractures than pores. The anisotropy of seismic waves, especially the splitting of polarized S‐waves, may be diagnostic of sets of oriented fractures in the crust. The electrical properties of rocks are strongly dependent upon the frequency of the energy and logging is presently being done at various frequencies. The effects of frequency, fluid salinity, clays, and pore‐grain geometry on electrical properties have been studied. Models of porous media have been used extensively to study the electrical and elastic properties of rocks. There has been great interest in extracting geometrical parameters about the rock and pore space directly from microscopic observation. Other models have focused on modeling several different properties to find relationships between rock properties.

scholarly journals Mathematical Modeling of Electrical Conductivity of Anisotropic Nanocomposite with Periodic Structure

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2948
Author(s):  
Sergey Korchagin ◽  
Ekaterina Pleshakova ◽  
Irina Alexandrova ◽  
Vitaliy Dolgov ◽  
Elena Dogadina ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Composite Materials ◽  
Optical Anisotropy ◽  
Nanocomposite Material ◽  
The Matrix ◽  
Self Similar ◽  
Anisotropic Form ◽  
Shape And Size

Composite materials consisting of a dielectric matrix with conductive inclusions are promising in the field of micro- and optoelectronics. The properties of a nanocomposite material are strongly influenced by the characteristics of the substances included in its composition, as well as the shape and size of inclusions and the orientation of particles in the matrix. The use of nanocomposite material has significantly expanded and covers various systems. The anisotropic form of inclusions is the main reason for the appearance of optical anisotropy. In this article, models and methods describing the electrical conductivity of a layered nanocomposite of a self-similar structure are proposed. The method of modeling the electrical conductivity of individual blocks, layers, and composite as a whole is carried out similarly to the method of determining the dielectric constant. The advantage of the method proposed in this paper is the removal of restrictions imposed on the theory of generalized conductivity associated with the need to set the dielectric constant.

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