Critical porosity and elastic properties of microporous mixed carbonate-siliciclastic rocks

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. E93-E109 ◽  
Author(s):  
F. Fournier ◽  
J. Borgomano
Keyword(s):  
Elastic Property ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Critical Porosity ◽  
Cretaceous Rock ◽  
Petrographic Analyses ◽  
Siliciclastic Rocks ◽  
Property Changes ◽  
Steep Slopes ◽  
Mixed Carbonate

By integrating elastic-property measurements and quantitative mineralogic and petrographic analyses of 45 mixed carbonate-siliciclastic samples from two wells drilled in Late Cretaceous rock of the South Provence Basin (southeast France), we can (1) identify and quantify the parameters controlling elastic properties; (2) demonstrate that micrite can be considered as a porous medium with a low critical porosity, averaging 18%; and (3) relate diagenetic transformations, pore-structure modifications, and elastic-property changes. Microporous carbonates with compact anhedral and euhedral microrhombic micrites display a steeper decrease in compressional and shear velocities with increasing porosity than do carbonate rocks with moldic, intergranular, or intercrystalline macroporosity. The low value of critical porosity estimated in micrites (18%), as well as the steep slopes of velocity-porosity relationships at low porosity, is believed to result from a pore-network geometry characterized by very flat, thin pores bounded by planar faces of micrite crystals. Cementation of microrhombic micrite steeply increases elastic moduli, whereas dissolution processes significantly increase porosity with low variations of elastic moduli. Thus, critical-porosity concepts can help describe and model elastic properties of micritic microporous carbonate.

Novel approach for simulating the elastic properties of porous rocks including the critical porosity phenomena

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. L37-L44 ◽  
Author(s):  
Mikhail Markov ◽  
Elena Kazatchenko ◽  
Aleksandr Mousatov ◽  
Evgeny Pervago
Keyword(s):  
Elastic Properties ◽  
Elastic Moduli ◽  
Phase 1 ◽  
Elastic Solid ◽  
Critical Value ◽  
Porous Rocks ◽  
Rock Falls ◽  
Critical Porosity ◽  
Type Phase ◽  
Wide Range

We tested an approach for calculating the effective elastic properties of rocks taking into account their critical porosity (the percolation threshold). The concept of critical porosity considers that when the porosity of a rock exceeds the critical value, the shear modulus of the rock tends to zero, making it lose its rigidity and the rock falls apart. The classical homogenization schemes do not describe the mechanical properties of a rock near the critical porosity. The approach proposed here is based on the generalized differential effective medium (GDEM) method. We introduce a model of porous elastic media composed of an elastic solid host containing ellipsoidal inclusions of two types. Inclusions of the first type (phase 1) represent pores, and inclusions of the second type (phase 2) contain elastic solid material described by the same elastic properties as the host (phase 0). In this model, with an increase in porosity, the concentration of the host decreased, and it tended to zero near the critical porosity. The model was used for simulation of rock elastic moduli. We compared the modeling results for elastic moduli and acoustic velocities with the experimental data and empirical petrophysical equations. The comparison showed that the GDEM model describes the elastic properties behavior in a wide range of porosity up to the critical value.

scholarly journals Ultrasound velocities and elastic properties of LICL doped zinc –borate glasses

2018 ◽  
Vol 7 (4.5) ◽  
pp. 580
Author(s):  
D. Vijayatha ◽  
G. Chandrashekaraiah ◽  
R. Viswanatha ◽  
C. Narayana Reddy
Keyword(s):  
Shear Modulus ◽  
Elastic Property ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Zinc Borate ◽  
Ultra Sound ◽  
Borate Glasses ◽  
Zinc Ions ◽  
Moduli Of Elasticity ◽  
Sound Velocities

Sound velocities and elastic property measurements have been employed to study the strength and rigidity of the structure of ZnO-B2O3 glasses doped with LiCl. Moduli of elasticity such as longitudinal, Young`s , bulk and shear modulus have been calculated using ultra sound velocities such as longitudinal and transverse velocities are measured at a frequency of 10 MHz as function of LiCl concentration. Both sound velocities and elastic moduli decrease with increase of LiCl concentration. The results are discussed in the view of borate network and dual structural role played by the divalent zinc ions present in the network. The results indicate that the Zn+2 ions are likely to occupy network forming positions in this glass system. While LiCl is a typically dissolved in the borate network and Cl- occupy the interstitial positions. 

Measurement and Calculation of Elastic Properties in Low Carbon Steel Sheet

2005 ◽  
Vol 495-497 ◽  
pp. 1591-1596 ◽  
Author(s):  
Vladimir Luzin ◽  
S. Banovic ◽  
Thomas Gnäupel-Herold ◽  
Henry Prask ◽  
R.E. Ricker
Keyword(s):  
Carbon Steel ◽  
Elastic Property ◽  
Elastic Properties ◽  
Steel Sheet ◽  
Low Carbon Steel ◽  
Low Carbon ◽  
Forming Process ◽  
Element Analysis ◽  
Wide Range ◽  
Carbon Steel Sheet

Low carbon steel (usually in sheet form) has found a wide range of applications in industry due to its high formability. The inner and outer panels of a car body are good examples of such an implementation. While low carbon steel has been used in this application for many decades, a reliable predictive capability of the forming process and “springback” has still not been achieved. NIST has been involved in addressing this and other formability problems for several years. In this paper, texture produced by the in-plane straining and its relationship to springback is reported. Low carbon steel sheet was examined in the as-received condition and after balanced biaxial straining to 25%. This was performed using the Marciniak in-plane stretching test. Both experimental measurements and numerical calculations have been utilized to evaluate anisotropy and evolution of the elastic properties during forming. We employ several techniques for elastic property measurements (dynamic mechanical analysis, static four point bending, mechanical resonance frequency measurements), and several calculation schemes (orientation distribution function averaging, finite element analysis) which are based on texture measurements (neutron diffraction, electron back scattering diffraction). The following objectives are pursued: a) To test a range of different experimental techniques for elastic property measurements in sheet metals; b) To validate numerical calculation methods of the elastic properties by experiments; c) To evaluate elastic property changes (and texture development) during biaxial straining. On the basis of the investigation, recommendations are made for the evaluation of elastic properties in textured sheet metal.

scholarly journals Noncontacting Torquemeters Utilizing Magneto-Elastic Properties of Steel Shafts

1969 ◽  
Author(s):  
Egil Angeid
Keyword(s):  
Elastic Property ◽  
Gas Turbine ◽  
Elastic Properties ◽  
Industrial Applications ◽  
Low Speed

The magneto-elastic property of steel shafts makes noncontacting torquementers possible. Early magneto-elastic torquemeters suffered from excessive sensitivity to variations in airgap and shaft temperature. These drawbacks have been eliminated in the Torductor® torquemeter, which has been very successful in low-speed industrial applications. In gas turbine applications, some special problems are encountered. These problems, and ways to minimize them, are discussed.

Stress sensitivity of sandstones

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 444-455 ◽  
Author(s):  
Jack Dvorkin ◽  
Amos Nur ◽  
Caren Chaika
Keyword(s):  
Elastic Modulus ◽  
Effective Stress ◽  
Elastic Moduli ◽  
Hydrostatic Stress ◽  
Clay Content ◽  
Stress Sensitivity ◽  
High Porosity ◽  
Effective Pressure ◽  
Critical Porosity ◽  
Difference Formula

Our observations made on dry‐sandstone ultrasonic velocity data relate to the variation in velocity (or modulus) with effective stress, and the ability to predict a velocity for a rock under one effective pressure when it is known only under a different effective pressure. We find that the sensitivity of elastic moduli, and velocities, to effective hydrostatic stress increases with decreasing porosity. Specifically, we calculate the difference between an elastic modulus, [Formula: see text], of a sample of porosity ϕ at effective pressure [Formula: see text] and the same modulus, [Formula: see text], at effective pressure [Formula: see text]. If this difference, [Formula: see text], is plotted versus porosity for a suite of samples, then the scatter of ΔM is close to zero as porosity approaches the critical porosity value, and reaches its maximum as porosity approaches zero. The dependence of this scatter on porosity is close to linear. Critical porosity here is the porosity above which rock can exist only as a suspension—between 36% and 40% for sandstones. This stress‐sensitivity pattern of grain‐supported sandstones (clay content below 0.35) practically does not depend on clay content. In practical terms, the uncertainty of determining elastic moduli at a higher effective stress from the measurements at a lower effective stress is small at high porosity and increases with decreasing porosity. We explain this effect by using a combination of two heuristic models—the critical porosity model and the modified solid model. The former is based on the observation that the elastic‐modulus‐versus‐porosity relation can be approximated by a straight line that connects two points in the modulus‐porosity plane: the modulus of the solid phase at zero porosity and zero at critical porosity. The second one reflects the fact that at constant effective stress, low‐porosity sandstones (even with small amounts of clay) exhibit large variability in elastic moduli. We attribute this variability to compliant cracks that hardly affect porosity but strongly affect the stiffness. The above qualitative observation helps to quantitatively constrain P‐ and S‐wave velocities at varying stresses from a single measurement at a fixed stress. We also show that there are distinctive linear relations between Poisson’s ratios (ν) of sandstone measured at two different stresses. For example, in consolidated medium‐porosity sandstones [Formula: see text], where the subscripts indicate hydrostatic stress in MPa. Linear functions can also be used to relate the changes (with hydrostatic stress) in shear moduli to those in compressional moduli. For example, [Formula: see text], where [Formula: see text] is shear modulus and [Formula: see text] is compressional modulus, both in GPa, and the subscripts indicate stress in MPa.

Elastic properties and phonon conductivities of Ti3Al(C0.5,N0.5)2 and Ti2Al(C0.5,N0.5) solid solutions

2008 ◽  
Vol 23 (6) ◽  
pp. 1517-1521 ◽  
Author(s):  
M. Radovic ◽  
A. Ganguly ◽  
M.W. Barsoum
Keyword(s):  
Elastic Properties ◽  
Solid Solutions ◽  
Room Temperature ◽  
Elastic Moduli ◽  
Unit Cell ◽  
Young’S Moduli ◽  
Temperature Shear ◽  
End Members ◽  
Cell Volumes ◽  
Thermal Conductivities

Herein we compare the lattice parameters, room temperature shear and Young’s moduli, and phonon thermal conductivities of Ti2AlC0.5N0.5 and Ti3Al(C0.5, N0.5)2 solid solutions with those of their end members, namely Ti2AlC, Ti2AlN, Ti3AlC2, and Ti4AlN2.9. In general, the replacement of C by N decreases the unit cell volumes and increases the elastic moduli and phonon thermal conductivities. The increase in the latter two properties, however, is sensitive to the concentrations of defects, most likely vacancies on one or more of the sublattices.

Elastic reflectivity vectors and the geometry of intercept-gradient crossplots

2019 ◽  
Vol 38 (10) ◽  
pp. 762-769
Author(s):  
Patrick Connolly
Keyword(s):  
Elastic Property ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Seismic Data ◽  
Measurement Errors ◽  
Rock Physics ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Well Log Analysis

Reflectivities of elastic properties can be expressed as a sum of the reflectivities of P-wave velocity, S-wave velocity, and density, as can the amplitude-variation-with-offset (AVO) parameters, intercept, gradient, and curvature. This common format allows elastic property reflectivities to be expressed as a sum of AVO parameters. Most AVO studies are conducted using a two-term approximation, so it is helpful to reduce the three-term expressions for elastic reflectivities to two by assuming a relationship between P-wave velocity and density. Reduced to two AVO components, elastic property reflectivities can be represented as vectors on intercept-gradient crossplots. Normalizing the lengths of the vectors allows them to serve as basis vectors such that the position of any point in intercept-gradient space can be inferred directly from changes in elastic properties. This provides a direct link between properties commonly used in rock physics and attributes that can be measured from seismic data. The theory is best exploited by constructing new seismic data sets from combinations of intercept and gradient data at various projection angles. Elastic property reflectivity theory can be transferred to the impedance domain to aid in the analysis of well data to help inform the choice of projection angles. Because of the effects of gradient measurement errors, seismic projection angles are unlikely to be the same as theoretical angles or angles derived from well-log analysis, so seismic data will need to be scanned through a range of angles to find the optimum.

Elastic Properties of Artificially Layered Thin Films

1987 ◽  
Vol 103 ◽  
Author(s):  
Robert C. Cammarata
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Composite Materials ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Metallic Thin Films ◽  
Theoretical Understanding ◽  
Composition Modulation

ABSTRACTEnhancements in the elastic moduli by factors of two or more in compositionally modulated metallic thin films have been observed for a certain range of composition modulation wavelengths. The experimental and theoretical understanding of this phenomenon, known as the supermodulus effect, is reviewed. Also, the mechanical properties of other artificially layered and composite materials are discussed and compared with the behavior of metallic superlattice thin films.

On the analysis and prediction of elastic properties in alkali Na2O–B2O3–V2O5 glasses under the substitution of V2O5 by Na2O

2019 ◽  
Vol 60 (6) ◽  
pp. 213-221
Author(s):  
Amin Abd El-Moneim ◽  
Hassan Y. Alfifi
Keyword(s):  
Elastic Properties ◽  
Dissociation Energy ◽  
Packing Density ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Unit Volume ◽  
Dominant Role ◽  
Glass Network ◽  
Poisson's Ratio ◽  
Structural Units

In this article, we have continued our recent work(30,42) on the prediction of elastic properties in alkali borovanadate glasses. Changes in the elastic moduli and Poisson’s ratio due to the substitution of V2O5 by Na2O in the ternary alkali Na2O–B2O3–V2O5 glasses have been analysed and predicted on the basis of the theories and approaches that existing in the field. Both the packing density and dissociation energy per unit volume of the glass were evaluated in terms of the basic structural units that constitute the glass network. In addition to this, the theoretical values of elastic moduli and Poisson’s ratio were calculated from the Makishima–Mackenzie’s model and compared with the corresponding experimental values. The results revealed that the concentrations of the basic structural units BO3, BO4, VO5 and VO4 play a dominant role in correcting the anomalous behaviour between experimental elastic moduli and calculated dissociation energy per unit volume. An excellent agreement between the theoretical and experimental elastic moduli was achieved for majority of the samples. The correlation between bulk modulus and the ratio between packing density and mean atomic volume has also been achieved on the basis of Abd El-Moneim and Alfifi’s approaches.

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