Prediction of Biot’s coefficient from rock-physical modeling of North Sea chalk

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. E89-E96 ◽  
Author(s):  
Casper Olsen ◽  
Kathrine Hedegaard ◽  
Ida L. Fabricius ◽  
Manika Prasad
Keyword(s):  
Aspect Ratio ◽  
North Sea ◽  
Free Parameter ◽  
The Self ◽  
P Wave ◽  
Biot’S Coefficient ◽  
Aspect Ratios ◽  
Consistent Model ◽  
Self Consistent ◽  
Water Saturated

We predict Biot’s coefficient for North Sea chalk based on density and P-wave velocity for water-saturated chalk. We compare three effective medium models: Berryman’s self-consistent model, the isoframe model, and the bounding-average method (BAM). The self-consistent model is used with two combinations of aspect ratios. In one combination, the aspect ratio is equal for pores and grains. In the other combination, the aspect ratio for grains is kept constant close to 1 and the aspect ratio for pores varies. All the models include one free parameter that determines the stiffness of the rock for a fixed porosity. This free parameter is compared with Biot’s coefficient to discuss whether the free parameter is related to pore-space compressibility for North Sea chalk. We also discuss how consistent the models are between P-wave modulus and shear modulus for dry and water-saturated chalk. The acoustic velocity and the density data for dry and water-saturated chalk are all laboratory data. The isoframe model and the BAM model predict Biot’s coefficient with a smaller error than the self-consistent model does. The free parameter in the isoframe model and the BAM model is related to Biot’s coefficient. The free parameter in the self-consistent model is related only to Biot’s coefficient for water-saturated chalk when the aspect ratios for pores and grains are equal. The isoframe and the BAM model are generally more consistent for chalk than the self-consistent model is.

scholarly journals Fracture Shape and Orientation Contributions to P-Wave Velocity and Anisotropy of Alpine Fault Mylonites

2021 ◽  
Vol 9 ◽  
Author(s):  
Jirapat Charoensawan ◽  
Ludmila Adam ◽  
Michael Ofman ◽  
Virginia Toy ◽  
Jonathan Simpson ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Shear Zone ◽  
Numerical Study ◽  
Numerical Models ◽  
Propagation Model ◽  
P Wave ◽  
Micro Ct ◽  
Alpine Fault ◽  
Aspect Ratios ◽  
Ct Data

P-wave anisotropy is significant in the mylonitic Alpine Fault shear zone. Mineral- and texture-induced anisotropy are dominant in these rocks but further complicated by the presence of fractures. Electron back-scattered diffraction and synchrotron X-ray microtomography (micro-CT) data are acquired on exhumed schist, protomylonite, mylonite, and ultramylonite samples to quantify mineral phases, crystal preferred orientations, microfractures, and porosity. The samples are composed of quartz, plagioclase, mica and accessory garnet, and contain 3–5% porosity. Based on the micro-CT data, the representative pore shape has an aspect ratio of 5:2:1. Two numerical models are compared to calculate the velocity of fractured rocks: a 2D wave propagation model, and a differential effective medium model (3D). The results from both models have comparable pore-free fast and slow velocities of 6.5 and 5.5 km/s, respectively. Introducing 5% fractures with 5:2:1 aspect ratio, oriented with the longest axes parallel to foliation decreases these velocities to 6.3 and 5.0 km/s, respectively. Adding both randomly oriented and foliation-parallel fractures hinders the anisotropy increase with fracture volume. The anisotropy becomes independent of porosity when 80% of fractures are randomly oriented. Modeled anisotropy in 2D and 3D are different for similar fracture aspect ratios, being 30 and 15%, respectively. This discrepancy is the result of the underlying assumptions and limitations. Our numerical results explain the effects that fracture orientations and shapes have on previously published field- and laboratory-based studies. Through this numerical study, we show how mica-dominated, pore-free P-wave anisotropy compares to that of fracture volume, shape and orientation for protolith and shear zone rocks of the Alpine Fault.

Using laboratory data to understand how pore aspect ratio influences elastic parameters and AVO

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
Kamal Moravej ◽  
Alison Malcolm
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Selective Laser Sintering ◽  
Laboratory Data ◽  
Physical Models ◽  
P Wave ◽  
S Wave ◽  
Water Saturated ◽  
The Impact

Pore geometry is an important parameter in reservoir characterization that affects the permeability of reservoirs and can also be a controlling factor on the impact of pressure and saturation on reservoirs elastic properties. We use SLS (Selective Laser Sintering) 3D printing technology to build physical models to experimentally investigate the impacts of pore aspect ratio on P-, and S- wave velocities and amplitude variation with offset (AVO). We printed six models to study the effects of the pore aspect ratio of prolate and oblate pore structures on elastic properties and AVO signatures. We find that the P-wave velocity is reduced by decreasing the pore aspect ratio (flatter pore structure), whereas the shear wave velocity is less sensitive to the pore aspect ratio. This effect is reduced when the samples are water saturated. We present new experimental and processing techniques to extract realistic AVO signatures from our experimental data and show that the pore aspect ratio has similar effects on AVO as fluid compressibility. This shows that not considering the pore aspect ratio in AVO analysis can lead to misleading interpretations. We further show that these effects are reduced in water-saturated samples.

Quantitative estimation of incompatibility stresses and elastic energy stored in ferritic steel

2008 ◽  
Vol 41 (5) ◽  
pp. 854-867 ◽  
Author(s):  
A. Baczmanski ◽  
P. Lipinski ◽  
A. Tidu ◽  
K. Wierzbanowski ◽  
B. Pathiraj
Keyword(s):  
Elastic Energy ◽  
Ferritic Steel ◽  
Quantitative Estimation ◽  
Second Order ◽  
The Self ◽  
X Ray Diffraction ◽  
Near Surface ◽  
Consistent Model ◽  
Self Consistent ◽  
Euler Space

Plastic incompatibility second-order stresses were determined for different orientations of a polycrystalline grain, using X-ray diffraction data and results of the self-consistent elasto-plastic model. The stresses in cold rolled ferritic steel were determined both in as-received and under tensile loaded conditions. It has been shown that the Reuss model and the self-consistent model applied to near surface volume provide the best approaches to determine diffraction elastic constants. For the first time, the elastic energy in an anisotropic material (arising from plastic incompatibilities between grains having various lattice orientations) has been determined. The second-order incompatibility stresses and stored elastic energy are presented in Euler space.

Estimating Brown-Korringa constants for fluid substitution in multimineralic rocks

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. L27-L35 ◽  
Author(s):  
Gary Mavko ◽  
Tapan Mukerji
Keyword(s):  
Solid Phase ◽  
The Self ◽  
Fluid Substitution ◽  
Gassmann’S Equation ◽  
Consistent Model ◽  
Additional Constant ◽  
Self Consistent ◽  
The Individual ◽  
Pore Lining ◽  
Consistent Formulation

Brown and Korringa extended Gassmann’s equations for fluid substitution in rocks to allow for arbitrarily mixed mineralogy. This extension was accomplished by adding just one additional constant—replacing the mineral bulk modulus with two less intuitive constants. Even though virtually all rocks have mixed mineralogy, the Brown and Korringa equations are seldom used because values for the constants are unknown. We estimate plausible values for the Brown-Korringa constants, based on effective medium models. The self-consistent formulation is used to describe a rock whose mineral and pore phases are randomly distributed ellipsoids—a plausible representation of randomly mixed mineral grains, as with dispersed clay in sandstone. Using the self-consistent model, the two constants are predicted to be nearly identical, justifying the use of an average mineral modulus in Gassmann’s equations. For small contrasts in mineral stiffness, the Brown-Korringa constants are approximately equal to the Voigt-Reuss-Hill average of the individual mineral bulk moduli. In a second approach, a multilayered spherical shell model is used to describe a rock where a particular solid phase preferentially coats grains or lines pores. In this case, the constants can differ substantially from each other, demonstrating the need for the Brown-Korringa equation. A third model represents weak pore-lining or pore-filling clay within an arbitrary pore geometry. The clay-fluid mix can be replaced exactly with an average fluid or “mud.” When the nonclay minerals have similar moduli, then the replacement of the clay-fluid mix causes the Brown-Korringa equation to revert to Gassmann’s equation.

Self-Organized High Aspect Ratios Titanium Oxide Nanotube Arrays Prepared by Anodization

2008 ◽  
Vol 368-372 ◽  
pp. 529-531
Author(s):  
Jin Liang Tao ◽  
Jian Ling Zhao ◽  
Rong Qing Xu ◽  
Ying Juan Mi ◽  
Ying Ru Kang ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Deionized Water ◽  
The Self ◽  
Ion Concentration ◽  
Nanotube Arrays ◽  
Self Organized ◽  
Aspect Ratios ◽  
Titania Nanotube Arrays ◽  
Anodic Voltage ◽  
Size And Morphology

The self-organized nanotube arrays were fabricated in glycerol electrolyte containing different additives, such as deionized water or ethylene glycol. The effects of anodization conditions, including anodic voltage, electrolyte viscosity, additives and ion concentration on the pores size and morphology were studied. Combined with preoxidation process, high aspect ratio titania nanotube arrays were formed rapidly in glycerol and saturated NaF solutions at 60 V for 1 h. SEM observation showed that a film with the thickness of about 10μm was obtained. A possible mechanism of the nanotubes growth was presented.

A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions

1995 ◽  
Vol 62 (3) ◽  
pp. 566-572 ◽  
Author(s):  
Y. Huang ◽  
K. X. Hu
Keyword(s):  
Aspect Ratio ◽  
Current Approach ◽  
Effective Moduli ◽  
Shear Moduli ◽  
Aspect Ratios ◽  
Isotropic Distribution ◽  
Energy Equivalence ◽  
Self Consistent ◽  
Consistent Method

The determination of the effective moduli for a material containing elliptical inclusions is the objective of this paper. This is done by incorporating an inclusion/matrix/composite model into a general energy equivalence framework. Through the evaluation of the average strain in each individual inclusion, the current approach can handle the inclusion’s orientation dependency in a straightforward manner. The case of an in-plane isotropic distribution of elliptical inclusions is addressed in detail. For the case of reinforcements, or hard inclusions, the effect of the inclusion aspect ratio on in-plane effective moduli is small if the aspect ratio is larger than 0.5. For aspect ratios less than 0.3, the effective moduli increase dramatically, which implies that flat reinforcements are much more effective than traditional cylindrical reinforcements. It is also established that the generalized self-consistent method predicts a stronger dependence of effective moduli on the inclusion aspect ratio than does the Mori-Tanaka method, especially for shear moduli.

scholarly journals Modelling Secular Variation in the Southwest Pacific for the last 400 years

2021 ◽  
Author(s):  
◽  
Maha Ali Alfheid
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Geomagnetic Field ◽  
Dipole Model ◽  
The Self ◽  
Pacific Region ◽  
Spherical Cap ◽  
Southwest Pacific ◽  
Consistent Model ◽  
Self Consistent

<p>A spherical cap harmonic analysis (SCHA) model has been used to derive a high-resolution regional model of the geomagnetic field in the southwest Pacific region over the past 400 years. Two different methods, a self-consistent and the gufm1 dipole method, have been used to fill in gaps in the available data.  The data used in the analysis were largely measurements of the magnetic field recorded in ships logs on voyages of exploration in the region. The method chosen for the investigation used a spherical cap of radius 𝜃₀ = 50° centered at co-latitude and longitude of (115°, 160°). The results of each method used for SCHA are presented as contour plots of magnetic field declination, inclination and intensity and are compared with similar plots for a global model, gufm1. The root mean square misfit of the self- consistent and gufm1 dipole model to the actual data were around 2900 nT and 23000 nT respectively.  Overall, the results suggest that the self-consistent model produces a more reliable model of the geomagnetic field within the area of interest than does the gufm1 dipole model. With more data included the self-consistent model could be further improved and used to develop a high-resolution mathematical model of the geomagnetic field in the southwest Pacific region.</p>

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