Changes Of Elastic Parameters Research Articles

Study on magnetostriction of ferromagnetic particles–superconducting matrix based on multi-chain model

Based on the magnetic dipole theory and the elastic mechanical plane strain method, this paper establishes a multi-chain model of ferromagnetic particle inclusions–superconducting matrix and investigates the effects of the distribution form of ferromagnetic particle inclusions and elastic parameters on the effective magnetostriction of superconductors. A dimensionless parameter is introduced to describe the spatial distribution form of ferromagnetic particles in the matrix, and the calculation is carried out using the elastic mechanical plane strain method. The change of the effective magnetostriction following the elastic parameter is given for three kinds of distribution forms: single-chain, planar–laminar, and spatial three-dimensional multi-chain, respectively. The results show that the distribution of ferromagnetic particle inclusions and the change of elastic parameters have a notable influence on the displacement and magnetostrictive distribution of superconductors.

Elasticity of two-dimensional ferroelectrics across their paraelectric phase transformation

The mechanical behavior of two-dimensional (2D) materials across 2D phase changes is unknown, and the finite temperature ($T$) elasticity of paradigmatic SnSe monolayers -- ferroelectric 2D materials turning paraelectric as their unit cell (u.c.) turns from a rectangle onto a square -- is described here in a progressive manner. To begin with, their zero$-T$ {\em elastic energy landscape} gives way to (Boltzmann-like) averages from which the elastic behavior is determined. These estimates are complemented with results from the strain-fluctuation method, which employs the energy landscape or {\em ab initio} molecular dynamics (MD) data. Both approaches capture the coalescence of elastic moduli $\langle C_{11}(T)\rangle=\langle C_{22}(T)\rangle$ due to the structural transformation. The broad evolution and sudden changes of elastic parameters $\langle C_{11}(T)\rangle$, $\langle C_{22}(T)\rangle$, and $\langle C_{12}(T)\rangle$ of these atomically-thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.

High-frequency localized elastic full-waveform inversion for time-lapse seismic surveys

Seismic full-waveform inversion (FWI) is a powerful method used to estimate the elastic properties of the subsurface. To mitigate the nonlinearity and cycle-skipping problems, in a hierarchical manner, one first inverts the low-frequency content to determine long- and medium-wavelength structures and then increases the frequency content to obtain detailed information. However, the inversion of higher frequencies can be computationally very expensive, especially when the target of interest, such as oil/gas reservoirs and axial melt lens, is at a great depth, far away from source and receiver arrays. To address this problem, we have developed a localized FWI algorithm in which iterative modeling is performed locally, allowing us to extend inversions for higher frequencies with little computation effort. Our method is particularly useful for time-lapse seismic, where the changes in elastic parameters are local due to fluid extraction and injection in the subsurface. In our method, the sources and receivers are extrapolated to a region close to the target area, allowing forward modeling and inversion to be performed locally after low-frequency full-model inversion for the background model, which by nature only represents long- to medium-wavelength features. Numerical tests show that the inversion of low-frequency data for the overburden is sufficient to provide an accurate high-frequency estimation of elastic parameters of the target region.

Influence of Fine Grains on the Bending Fatigue Behavior of Two Implant Titanium Alloys.

By means of the ultrasonic surface impact (amplitude of 30 μm, strike number of 48,000 times/mm2), nanograins have been achieved in the surfaces of both Ti6Al4V(TC4) and Ti3Zr2Sn3Mo25Nb(TLM) titanium alloys, mainly because of the dislocation motion. Many mechanical properties are improved, such as hardness, residual stress, and roughness. The rotating–bending fatigue limits of TC4 and TLM subjected to ultrasonic impact are improved by 13.1% and 23.7%, separately. Because of the bending fatigue behavior, which is sensitive to the surface condition, cracks usually initiate from the surface defects under high stress amplitude. By means of an ultrasonic impact tip with the size of 8 mm, most of the inner cracks present at the zone with a depth range of 100~250 μm in the high life region. The inner crack core to TC4 usually appears as a deformed long and narrow α-phase, while the cracks in TLM specimens prefer to initiate at the triple grain boundary junctions. This zone crosses the grain refined layer and the deformed coarse grain layer. With the gradient change of elastic parameters, the model shows an increase of normal stress at this zone. Combined with the loss of plasticity and toughness, it is easy to understand these fatigue behaviors.

Influence of surface ultrasonic impact treatment on texture evolution and elastic properties in the volume of Zr1Nb alloy

The study is devoted to examination of the features of influence of ultrasonic impact treatment (UIT) on the evolution of texture and the changes of elastic parameters in the volume of specimens of Zr1Nb alloy with preliminary-formed strong crystallographic texture. In this case the bulk-wave ultrasonic velocities (vij) in the orthogonal directions in the different sections of the specimens were measured by the automatic US apparatus in initial state (after high-temperature rolling) and after UIT. The density (ρ) of the specimens was also measured in initial and deformed states. Based on the obtained results orientation distribution coefficients (Wij0) were calculated, complete pole figures were plotted, relative intensity of diffraction lines of the basal plane (ΔІ(0001)) and Kearns parameters (fi) were determined. The extreme values of Young (E) and shear (G) moduli, Poisson ratio (η) and their anisotropy were also calculated for different sections of the treated specimens. It is shown that UIT in applied regime changes the texture and elastic parameters in all specimen volume. Pole figures (0001) after UIT keep the view typical for rolled HCP alloys with ratio c/a < 1.633. The clear qualitative correlation between the texture and elastic parameters of the specimens in initial state and after UIT in their different sections is defined. The revealed features indicate that the evolution of crystallographic texture of Zr1Nb alloy specimens is a result of the depth nonuniformity of plastic deformation accumulated during the UIT process. The results are in agreement with available literature data. The effectiveness of applied US method and equipment for layer-by-layer analysis of the texture and elastic characteristics in the volume of spatially inhomogeneous materials subjected to directional surface thermomechanical treatment is shown.

Bayesian Time-lapse Difference Inversion Based on the exact Zoeppritz Equations with Blockiness Constraint

Accurately inverting changes in the reservoir elastic parameters that are caused by oil and gas exploitation is of great importance in accurately describing reservoir dynamics and enhancing recovery. Previously numerous time-lapse seismic inversion methods based on the approximate formulas of exact Zoeppritz equations or wave equations have been used to estimate these changes. However the low accuracy of calculations using approximate formulas and the significant calculation effort for the wave equations seriously limits the field application of these methods. However, these limitations can be overcome by using exact Zoeppritz equations. Therefore, we study the time-lapse seismic difference inversion method using the exact Zoeppritz equations. Firstly, the forward equation of time-lapse seismic difference data is derived based on the exact Zoeppritz equations. Secondly, the objective function based on Bayesian inversion theory is constructed using this equation, with the changes in elastic parameters assumed to obey a Gaussian distribution. In order to capture the sharp time-lapse changes of elastic parameters and further enhance the resolution of the inversion results, the blockiness constraint, which follows the differentiable Laplace distribution, is added to the prior Gaussian background model. All examples of its application show that the proposed method can obtain stable and reasonable P- and S-wave velocities and density changes from the difference data. The accuracy of estimation is higher than for existing methods, which verifies the effectiveness and feasibility of the new method. It can provide high-quality seismic inversion results for dynamic detailed reservoir description and well location during development.

Calibration of Circulating Tumor Cell’s Model in Narrow Flow

In this article our objective was to calibrate model of Circulating Tumor Cell (CTC). Different types of cancer produce different types of CTCs. For research purposes, we chose to set up the model according to MCF7 breast cancer cell lines, due to the availability of data from laboratory experiments. First, to obtain working model we used mechanics of our already existing RBC model, taking into consideration the differences between RBC and CTC. Next step was to find values for the elastic parameters of the cell model. We have chosen laboratory experiment where the deformability of breast cancer cell passing through narrow microfluidic channel was examined. The channel has similar dimensions as blood capillaries to mimic the in vivo environment. In order to achieve similar behavior of the cell’s model and the real cell in the experiment we needed to set fluid flow according to experimental data. This was achieved by adjusting the fluid force that is dependent on the volumetric flow rate. Due to the long computational time of the simulation we devised a function between the entry time and the volumetric flow rate. Afterwards we also found dependencies between the changes in elastic parameters and entry time, and we were able to set the elastic parameters so they mimic the behaviour from the laboratory experiment. Further work lies in validating these results.

AVO inversion on unconventional reservoirs: systematic estimation of uncertainty in the Vaca Muerta shale

Abstract Amplitude versus offset inversion is widely used in reservoir characterization, but its implementation on unconventional reservoirs represents a challenge owing to the subtle changes of elastic parameters that demarcate profitable areas. For this reason, it is important to have an estimation of the uncertainty expected from seismic inversion to improve the interpretation of inverted results. We have implemented a systematic estimation of uncertainty of relative elastic properties obtained by damped least squares inversion of Aki and Richards and Fatti et al. approximations of Zoeppritz’s equation. Well log data of the Vaca Muerta unconventional shale in Argentina was used to generate synthetic angle gathers, varying in terms of asignal-to-noise ratio, range of angle coverage and number of partial angle stacks. The inversion results provide a systematic estimation of the uncertainty of the inverted coefficients. Results show that signal-to-noise ratio and range of angle coverage of the seismic data are key parameters to assess the feasibility of the inversion. In case of characterization based on acoustic impedance, the inverted parameters show good correlation with the model, with these correlation values being predicted by the parameter resolution matrix values.

Time-lapse Seismic Analysis for Gao89 Area of CO2-EOR Project in SINOPEC Shengli Oilfield, China

Based on the time-lapse seismic data of CO2-EOR project in Gao89 area of Shengli Oilfield in China, this paper carries out the calibration of time-lapse seismic data and the analysis of amplitude differences before and during CO2 injection. From well-log based forward model, we applied Hertz-Mindlin formula and combined it with Gassmann's equation to predict the P-wave velocity, S-wave velocity and density logs at different effective pressure and CO2 fluid saturation. Then we made time-lapse synthetic seismogram to calibrate time lapse seismic data and analyzed amplitude differences from forward model. Our study shows that the effective pressure is the dominant factor for the changes of elastic parameters and seismic amplitudes at the early time of CO2 injection because the reservoir pressure was much lower than that of in-situ pressure. The deficit of reservoir pressure was caused by oil producing. In addition, CO2 saturation also affects the elastic parameters of reservoir and seismic amplitude. Finally, we calibrated the RMS amplitude of time-lapse seismic data at CO2 injection layers and caprocks in Gao89 CO2 injection area. The difference of time-lapse seismic amplitudes reflects low pressure zone of reservoir which is also the migration path and the distribution of CO2.

The time-lapse AVO difference inversion for changes in reservoir parameters

The result of conventional time-lapse seismic processing is the difference between the amplitude and the post-stack seismic data. Although stack processing can improve the signal-to-noise ratio (SNR) of seismic data, it also causes a considerable loss of important information about the amplitude changes and only gives the qualitative interpretation. To predict the changes in reservoir fluid more precisely and accurately, we also need the quantitative information of the reservoir. To achieve this aim, we develop the method of time-lapse AVO (amplitude versus offset) difference inversion. For the inversion of reservoir changes in elastic parameters, we apply the Gardner equation as the constraint and convert the three-parameter inversion of elastic parameter changes into a two-parameter inversion to make the inversion more stable. For the inversion of variations in the reservoir parameters, we infer the relation between the difference of the reflection coefficient and variations in the reservoir parameters, and then invert reservoir parameter changes directly. The results of the theoretical modeling computation and practical application show that our method can estimate the relative variations in reservoir density, P-wave and S-wave velocity, calculate reservoir changes in water saturation and effective pressure accurately, and then provide reference for the rational exploitation of the reservoir.

Stability of inhomogeneous micropolar cylindrical tube subject to combined loads

In the present paper, the stability of a nonlinear elastic cylindrical tube made of micropolar material is analyzed. It is assumed that the elastic properties of the tube vary through the wall thickness. The problem is studied for the case of axial compression of the tube under internal and external hydrostatic pressure. Applying linearization the neutral equilibrium equations have been derived, which describe the perturbed state of the tube. By solving these equations numerically the critical curves and corresponding buckling modes have been found, and the stability regions have been constructed in the planes of loading parameters (relative axial compression, relative internal or external pressure). Using these results, the influence of elastic properties, as well as the size of the tube, on the loss of stability is studied. Special attention has been paid to the analysis of how the pattern of change in elastic parameters affects the stability of a cylindrical tube made of micropolar material.

Joint PP and PS AVA seismic inversion using exact Zoeppritz equations

The Zoeppritz equations describe the relationship between seismic properties that are useful for the interpretation of lithology and fluid properties. Various approximations to the Zoeppritz equations are often used in linear amplitude variation with offset and amplitude variation with angle inversions, assuming low-contrast boundaries. These approximations restrict the inversion method to not-too-large-angle cases and reduce the inversion accuracy. Therefore, it is necessary to develop joint PP and PS prestack inversion methods using the exact Zoeppritz equations. We have developed a method for nonlinear joint prestack inversion using the exact Zoeppritz equations. We established an objective function to combine PP and PS information based on a least-squares approach, and we used the Taylor expansion method to derive a model updating formula for the inversion. We also used a mean shift method to improve the accuracy of inversion results. We validated our inversion using synthetic and field seismic data. The model for calculating synthetic data contained high-contrast interfaces to match the reservoir layers, which included, for example, coal seams and unconsolidated sandstone. The outputs of the inversion were the elastic parameters (P- and S-wave velocities, as well as density), rather than the changes in elastic parameters. We found that the nonlinear joint prestack inversion achieved more accurate results than the linear joint prestack inversion, regardless of incidence angle size. Furthermore, if the prestack data were of high enough quality, it was possible to identify thin layers from the inversion result.

4D propagated layer-based inversion

We developed a new model-based 4D inversion algorithm that propagated through a 4D data set from a well location, minimizing the traveltime and amplitude differences of the data. The model consisted of a finite number of layers in which the thickness and change in elastic parameters were solved in each layer. The inversion used a local optimization strategy at each trace, in which the solution of a previously inverted neighboring trace was used as the initial guess; it started from a 4D layer-based inversion solution found at a well location. Information from the well was, therefore, propagated into the data set whereas it remained consistent with the data. When several wells were used simultaneously, they propagated in a concurrent manner to determine each well’s area of influence. By using the time-shift and amplitude differences, it became possible to decouple density and P-wave velocity changes; however, even with this additional information, solutions were seldom consistent enough to provide coherent quantitative interpretation. We therefore introduced a new constraint based on production information and rock physics to guide the solution to realistic combinations of elastic parameters. We determined that this constraint was fairly independent of the geology. Examples of the prestack propagation inversion algorithm were shown on synthetic and real data examples. Comparisons were also made to standard 4D inversion highlighting the improvement in the coherency of the new results. We concluded that this type of model-based inversion was not designed to be used as a reconnaissance tool for 4D interpretation (this remains the job of data-driven inversion schemes) but was a powerful tool for either extracting as much information as possible from 4D seismic data or to test various hypothesis of different 4D scenarios.

Detection of a tall ridge at the core–mantle boundary from scattered PKP energy

The seismic wavefield mainly contains reflected, refracted and direct waves but energy related to elastic scattering can also be identified at frequencies of 1 Hz and higher. The scattered, high-frequency seismic wavefield contains information on the small-scale structure of the Earth's crust, mantle and core. Due to the high thermal conductivity of mantle materials causing rapid dissipation of thermal anomalies, the Earth's small-scale structure most likely reveals details of the composition of the interior, and, is therefore essential for our understanding of the dynamics and evolution of the Earth. Using specific ray configurations we can identify scattered energy originating in the lower mantle and under certain circumstances locate its point of origin in the Earth allowing further insight into the structure of the lowermost mantle. Here we present evidence, from scattered PKP waves, for a heterogeneous structure at the core–mantle boundary (CMB) beneath southern Africa. The structure rises approximately 80 km above the CMB and is located at the eastern edge of the African LLSVP. Mining-related and tectonic seismic events in South Africa, with mb from 3.2 to 6.0 recorded at epicentral distances of 119.3° to 138.8° from Yellowknife Array (YKA) (Canada), show large amplitude precursors to PKPdf arriving 3–15 s prior to the main phase. We use array processing to measure slowness and backazimuth of the scattered energy and determine the scatterer location in the deep Earth. To improve the resolution of the slowness vector at the medium aperture YKA we present a new application of the F-statistic. The high-resolution slowness and backazimuth measurements indicate scattering from a structure up to 80 km tall at the CMB with lateral dimensions of at least 1200 km by 300 km, at the edge of the African Large Low Shear Velocity Province. The forward scattering nature of the PKP probe indicates that this is velocity-type scattering resulting primarily from changes in elastic parameters. The PKP scattering data are in agreement with dynamically supported dense material related to the Large Low Shear Velocity Province.

Applications of Non-linear Elastic Wavefield Inversion for 4D Seismic Data to Characterize the Injected Carbon Dioxide

Elastic parameters are fundamental in estimating rock properties, fluid saturation and pore pressure in carbon dioxide injection and 4D seismic survey efficiently provides spatial changes of elastic parameters as well as baseline parameters. Conversely elastic parameters are governed by microstructures of material and dynamic conditions of measurement and thus depend on the temporal and spatial scale. Logging data were useful in estimating elastic properties at 10-50kHz time scale, and under partially saturation condition they could be taken into seismic time scale at saturation rate estimated by “partially Patchy saturation model” currently proposed and evidenced in good matching with logging data analysis, which took residual water saturation into account and adapted for building elastic wave velocities in 3D monitor seismic cube.4D seismic survey data, acquired by Japex in 2003 and 2005 on the area of onshore RITE/METI carbon dioxide injection test site, were analysed incorporated with repeated time-lapse logging data matched in scale by the currently proposed method. In this study, 1) I newly built the most probable full-scale baseline and monitor elastic wave velocity model of the 4D seismic survey in the depth domain using time scale adjusted and calibrated 4D AI cube in the time domain and 2) examined the feasibility of non-linear elastic wavefield inversion of synthetic 4D seismic data. Results of non-linear elastic wavefield inversion successfully showed estimates of 4D elastic wave velocity changes at excellent quality and accuracy.

4D seismic-to-well tying, a key step towards 4D inversion

Calibrating the 4D signal at the well with information obtained from production data is essential for it to be used quantitatively. We have developed a model-based inversion method to estimate the changes of elastic parameters in the reservoir due to production at the well. Our scheme is based on the observation that flow behavior is constrained by the dynamic properties of the layer (i.e., permeability), and, therefore, a layered model should be used to parameterize the inversion. The inversion scheme considers traveltime (inside and below the reservoir, but not in the overburden) and impedance effects implied by the change of elastic parameters (inside the reservoir). Therefore, even at zero offset, we can separate changes in density from changes in P-velocity. When using multiple offset data, we can use an exact formulation for the reflectivity if the base logs (density, P-velocity, and S-velocity) are available, otherwise, an approximation to the exact form can be used. Theoretical and practical analyses have shown that P-velocity is the best resolved parameter followed by density and, finally, S-velocity. Compared to classical data-driven inversion, our procedure introduces fewer artifacts and is less sensitive to tuning because the layered model parameterization introduces the missing low and high frequencies (although the seismic bandwidth plays an essential role in the resolution). This 4D inversion at the well is part of a larger scheme that uses the results obtained by this scheme to extend the inversion to the whole data set.

Elastic Parameters of Various Rafted Structures of Model Ni-Base Alloys

Two-phase microstructure of ordered cube-shaped precipitates in the disordered matrix is characteristic of Ni-base superalloys. This microstructure degrades under the applied stress: depending on the stress direction, lattice misfit and elastic parameters of both constituent phases, the precipitates coalesce and change their overall shape. Various atomic configurations were modeled in this work representing various morphologies of precipitates developed under applied stress. A model Ni-base alloy containing six alloying elements typical of advanced Ni-based superalloys was used. Generated configurations were further subject to study of elastic parameters by means of computer straining experiments. Relaxation of atomic positions in the strained crystal blocks was implemented using molecular dynamics calculations with phenomenological Lennard-Jones pair potentials and interactions involving three coordination spheres. Changes of elastic parameters due to varying precipitates morphology are discussed.

Permeability changes in coal: Analytical modeling

Abstract Permeability changes can be very large during depletion of coalbed methane wells: up to 100 times in the San Juan basin. Analytic models of permeability increase during depletion are accessible, easy to use, and practical. They are more transparent, and less complicated, than coupled numerical models. However, there are minor differences between the analytic models, and these are reviewed here. There are also discrepancies in attempting to match field data, which is the final test of a model, and these are discussed. Two different sets of San Juan data have been modeled, after suppressing the pressure-dependent permeability, with reasonably consistent reservoir parameters. The matching parameters appear to be justifiable, the small porosities do not seem to be ruled out by reservoir experts, and the changes of elastic parameters (including pore–volume compressibility) with depletion do not seem unreasonable. The analytic models are used in reservoir simulators to model and predict injection of greenhouse gases in coal seams. Only when we can match the permeability increase of coalbed methane wells during depletion, will we have the confidence to use the analytic models in reservoir simulators to match or predict sequestration of greenhouse gases such as CO2.

Effect of Ordering on the Elastic Parameters of Multicomponent Ni-Based Systems

Ordering in Ni-based superalloys is the crucial process controlling the development of the characteristic two-phase microstructure and subsequently the mechanical properties. Disordered systems containing up to six alloying elements typical of advanced Ni-based superalloys were modelled in this work. Their ordering at elevated temperatures was simulated using a Monte Carlo approach with phenomenological Lennard-Jones pair potentials. Selected atomic configurations differing in the degree of order were subject to further studies of elastic parameters. Hydrostatic deformation and uniaxial deformation along high symmetry directions of model crystals were simulated. Molecular dynamics was used to relax local atomic positions in deformed crystals. Changes of elastic parameters due to ordering in face centred cubic lattice are discussed.

Influence of Anisotropic Elastic Parameters on Seismic Imaging: Numerical and Physical Modelling Studies

The wavefront curvature in an anisotropic medium is significantly influenced by the elastic parameters ε(near-vertical P-wave anisotropy), δ*. (P-wave anisotropy) and γ(SH-wave anisotropy). The effects of changes in these elastic parameters on the size of the Fresnel-zone have been studied using numerical modelling techniques and measured anisotropy of real sedimentary rocks. Ray paths for a P-wave gather above horizontal reflectors with a tilted axis of symmetry and contrasting velocity characteristics were also studied in order to determine how changes in elastic parameters affect the reflection point dispersal, and hence the smearing effect in stacked seismic data. Anisotropic migration of synthetic and physical modelling data was also carried out to demonstrate the effect of using inaccurate elastic parameters, and hence, wrong velocity functions in migrating seismic data.Numerical modelling results strongly indicate that the anisotropic elastic parameters significantly affect the size of the Fresnel zone, which determines the spatial resolving power for unmigrated seismic data. The magnitude of ray path distortion and reflection point dispersal is found to vary with the value and sign of the elastic parameter δ*. Ignoring anisotropy or using incorrect elastic parameters in migration will lead to wrong depth estimation and spatial mispositioning of reflection events.Experimental seismic data obtained using physical modelling demonstrate that anisotropy can significantly affect the spatial resolving power of seismic waves. The extent of these effects depends on the wavefront curvature which is influenced by the elastic parameters and orientation of the symmetry axis. These observations indicate that the imaging of reflection events from the base of thick shale sediments will be affected by anisotropy.