PbMoO4 elastic moduli, bulk modulus, compressibility, elastooptic constants

2005 ◽  
pp. 1-2
Author(s):  
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

Elastic Moduli of Thickly Coated Particle and Fiber-Reinforced Composites

1991 ◽  
Vol 58 (2) ◽  
pp. 388-398 ◽  
Author(s):  
Y. P. Qiu ◽  
G. J. Weng
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Elastic Moduli ◽  
Poisson Ratio ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Two Phase ◽  
Coated Particle ◽  
Replacement Method

Based on the models of Hashin (1962) and Hashin and Rosen (1964), the effective elastic moduli of thickly coated particle and fiber-reinforced composites are derived. The microgeometry of the composite is that of a progressively filled composite sphere or cylinder element model. The exact solutions of the effective bulk modulus κ of the particle-reinforced composite and those of the plain-strain bulk modulus κ23, axial shear modulus μ12, longitudinal Young’s modulus E11, major Poisson ratio ν12, of the fiber-reinforced one are derived by the replacement method. The bounds for the effective shear modulus μ and the effective transverse shear modulus μ23 of these two kinds of composite, respectively, are solved with the aid of Christensen and Lo’s (1979) formulations. By considering the six possible geometrical arrangements of the three constituent phases, the values of κ, and of κ23, μ12, E11, and ν12 are found to always lie within the Hashin-Shtrikman (1963) bounds, and the Hashin (1965), Hill (1964), and Walpole (1969) bounds, respectively, but unlike the two-phase composites, none coincides with their bounds. The bounds of μ and μ23 derived here are consistently tighter than their bounds but, as for the two-phase composites, one of the bounds sometimes may fall slightly below or above theirs and therefore it is suggested that these two sets of bounds be used in combination, always choosing the higher for the lower bound and the lower for the upper one.

Differences between static and dynamic elastic moduli: Importance of experimental methods

2020 ◽  
Author(s):  
Elisabeth Bemer ◽  
Noalwenn Dubos-Sallée ◽  
Patrick N. J. Rasolofosaon
Keyword(s):  
Bulk Modulus ◽  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Local Strain ◽  
Experimental Methods ◽  
Triaxial Tests ◽  
Strain Gauges ◽  
Strain Measurements ◽  
Dynamic Elastic Moduli

<p>The differences between static and dynamic elastic moduli remain a controversial issue in rock physics. Various empirical correlations can be found in the literature. However, the experimental methods used to derive the static and dynamic elastic moduli differ and may entail substantial part of the discrepancies observed at the laboratory scale. The representativeness and bias of these methods should be fully assessed before applying big data analytics to the numerous datasets available in the literature.</p><p>We will illustrate, discuss and analyze the differences inherent to static and dynamic measurements through a series of triaxial and petroacoustic tests performed on an outcrop carbonate. The studied rock formation is Euville limestone, which is a crinoidal grainstone composed of roughly 99% calcite and coming from Meuse department located in Paris Basin. Sister plugs have been cored from the same quarry block and observed under CT-scanner to check their homogeneity levels.</p><p>The triaxial device is equipped with an internal stress sensor and provides axial strain measurements both from strain gauges glued to the samples and LVDTs placed inside the confinement chamber. Two measures of the static Young's modulus can thus be derived: the first one from the local strain measurements provided by the strain gauges and the second one from the semi-local strain measurements provided by the LVDTs. The P- and S-wave velocities are measured both through first break picking and the phase spectral ratio method, providing also two different measures of the dynamic Young's modulus.</p><p>The triaxial tests have been performed in drained conditions and the measured static elastic moduli correspond to drained elastic moduli. The petroacoustic tests have been performed using the fluid substitution method, which consists in measuring the acoustic velocities for various saturating fluids of different bulk modulus. No weakening or dispersion effects have been observed. Gassmann's equation can then be used to derive the dynamic drained elastic moduli and the solid matrix bulk modulus, which is otherwise either taken from the literature for pure calcite or dolomite samples, or computed using Voigt-Reuss-Hill or Hashin-Shtrikman averaging of the mineral constituents.</p><p>For the studied carbonate formation, we obtain similar values for static and dynamic elastic moduli when derived from careful lab experiments. Based on the obtained results, we will finally make recommendations, emphasizing the necessity of using relevant experimental techniques for a consistent characterization of the relation between static and dynamic elastic moduli.</p>

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

2010 ◽  
Vol 74 (2) ◽  
pp. 341-350 ◽  
Author(s):  
E. K. H. Salje ◽  
J. Koppensteiner ◽  
W. Schranz ◽  
E. Fritsch
Keyword(s):  
Bulk Modulus ◽  
Porous Materials ◽  
Power Law ◽  
Master Curve ◽  
Elastic Moduli ◽  
External Stress ◽  
Effective Elastic Moduli ◽  
Critical Porosity ◽  
Elastic Instabilities ◽  
Linear Decay

AbstractThe collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity ϕc at which small stresses will lead to the collapse of the sample. For several samples we find ϕc ~0.5 with an almost linear decay of the bulk moduli with porosity at ϕc <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law κ ~ (1–ϕm, m>2, between ϕ = 0.5 and ϕ = 1.

Elasticity and Stability of Fe-P Ordered Systems from First Principles

2005 ◽  
Vol 482 ◽  
pp. 135-138 ◽  
Author(s):  
Miroslav Černý ◽  
Jaroslav Pokluda
Keyword(s):  
Bulk Modulus ◽  
Spin Polarization ◽  
First Principles ◽  
Elastic Moduli ◽  
Magnetic Ordering ◽  
Relative Content ◽  
Atomic Concentration ◽  
Program Code ◽  
Computational Program ◽  
Crystal Cells

Elastic properties of Fe-P ordered system (the bulk modulus and the theoretical strength under isotropic tension) are computed by means of ab initio computational program code VASP. Different configurations and relative amounts of constituent atoms are considered in the crystal cells of known stable phases as well as of some hypothetical structures. The influence of a relative content of P in the alloy on computed properties is studied. Magnetic ordering is taken into account by means of collinear spin-polarization. The results of calculations reveal that, somewhat surprisingly, no dramatic changes of elastic moduli are to be expected up to the 67% atomic concentration of P.

scholarly journals Towards more realistic values of elastic moduli for volcano modelling

2020 ◽  
Author(s):  
Michael Heap ◽  
Marlène Villeneuve ◽  
Fabien Albino ◽  
Jamie Farquharson ◽  
Elodie Brothelande ◽  
...  
Keyword(s):  
Rock Mass ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Volcanic Rock ◽  
Elastic Moduli ◽  
Numerical Models ◽  
Laboratory Data ◽  
Volcanic Rocks ◽  
Published Data ◽  
Selection Of

&lt;p&gt;The accuracy of elastic analytical solutions and numerical models, widely used in volcanology to interpret surface ground deformation, depends heavily on the Young&amp;#8217;s modulus chosen to represent the medium. The paucity of laboratory studies that provide Young&amp;#8217;s moduli for volcanic rocks, and studies that tackle the topic of upscaling these values to the relevant lengthscale, has left volcano modellers ill-equipped to select appropriate Young&amp;#8217;s moduli for their models. Here we present a wealth of laboratory data and suggest tools, widely used in geotechnics but adapted here to better suit volcanic rocks, to upscale these values to the scale of a volcanic rock mass. We provide the means to estimate upscaled values of Young&amp;#8217;s modulus, Poisson&amp;#8217;s ratio, shear modulus, and bulk modulus for a volcanic rock mass that can be improved with laboratory measurements and/or structural assessments of the studied area, but do not rely on them. In the absence of information, we estimate upscaled values of Young&amp;#8217;s modulus, Poisson&amp;#8217;s ratio, shear modulus, and bulk modulus for volcanic rock with an average porosity and an average fracture density/quality to be 5.4 GPa, 0.3, 2.1 GPa, and 4.5 GPa, respectively. The proposed Young&amp;#8217;s modulus for a typical volcanic rock mass of 5.4 GPa is much lower than the values typically used in volcano modelling. We also offer two methods to estimate depth-dependent rock mass Young&amp;#8217;s moduli, and provide two examples, using published data from boreholes within K&amp;#299;lauea volcano (USA) and Mt. Unzen (Japan), to demonstrate how to apply our approach to real datasets. It is our hope that our data and analysis will assist in the selection of elastic moduli for volcano modelling. To this end, our new publication (Heap et al., 2019), which outlines our approach in detail, also provides a Microsoft Excel&amp;#169; spreadsheet containing the data and necessary equations to calculate rock mass elastic moduli that can be updated when new data become available. The selection of the most appropriate elastic moduli will provide the most accurate model predictions and therefore the most reliable information regarding the unrest of a particular volcano or volcanic terrain.&lt;/p&gt;&lt;p&gt;Heap, M.J., Villeneuve, M., Albino, F., Farquharson, J.I., Brothelande, E., Amelung, F., Got, J.L. and Baud, P., 2019. Towards more realistic values of elastic moduli for volcano modelling. Journal of Volcanology and Geothermal Research, https://doi.org/10.1016/j.jvolgeores.2019.106684.&lt;/p&gt;

Elastic Moduli of H2O: Liquid, Ice VI and Ice VII

1983 ◽  
Vol 22 ◽  
Author(s):  
M. Grimsditch ◽  
A. Rahman ◽  
A. Poliant
Keyword(s):  
Molecular Dynamics ◽  
Bulk Modulus ◽  
Room Temperature ◽  
Elastic Moduli ◽  
Brillouin Scattering ◽  
Density Measurements ◽  
Molecular Dynamics Calculations ◽  
Pressure Region ◽  
Scattering Study ◽  
High Pressure Region

ABSTRACTThe results of a Brillouin scattering study of the room temperature phases of H2;O (liquid, ice VI and ice VII) up to 30 GPa are presented. Longitudinal elastic moduli thus obtained are compared with values of the bulk modulus obtained from density measurements [1] and with both static and molecular dynamics calculations of the bulk modulus using potentials which have been proposed in studies of the liquid state. The calculations indicate that the potentials are not capable of describing the high pressure region of ice VII.

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