Self-adapting extraction of matrix mineral bulk modulus and verification of fluid substitution

Gassmann＇s equations are commonly used for predicting seismic wave velocity in rock physics research.However the input matrix mineral bulk modulus parameters are not accurate,which greatly influences the prediction reliability.In this paper,combining the Russell fluid factor with the Gassman-Biot-Geertsma equation and introducing the dry-rock Poisson＇s ratio,we propose an effective matrix mineral bulk modulus extraction method.This method can adaptively invert the equivalent matrix mineral bulk modulus to apply the Gassmann equation to fluid substitution of complex carbonate reservoirs and increase the fluid prediction reliability.The verification of the actual material fluid substitution also shows that this method is reliable,efficient,and adaptable.

Theoretical Model of Dynamic Bulk Modulus for Aerated Hydraulic Fluid

Existing models of bulk modulus for aerated hydraulic fluids primarily focus on the effects of pressure and air fraction,whereas the effect of temperature on bulk modulus is disregarded.Based on the lumped parameter method and the full cavitation model,combined with the improved Henry’s law and the air polytropic course equation,a theoretical model of dynamic bulk modulus for an aerated hydraulic fluid is derived.The effects of system pressure,air fraction,and temperature on bulk modulus are investigated using the controlled variable method.The results show that the dynamic bulk modulus of the aerated hydraulic fluid is inconsistent during the compression process.At the same pressure point,the dynamic bulk modulus during expansion is higher than that during compression.Under the same initial air faction and pressure changing period,a higher temperature results in a lower dynamic bulk modulus.When the pressure is lower,the dynamic bulk modulus of each temperature point is more similar to each other.By comparing the theoretical results with the actual dynamic bulk modulus of the Shell Tellus S ISO32 standard air-containing oil,the goodness-of-fit between the theoretical model and experimental value at three temperatures is 0.9726,0.9732,and 0.9675,which validates the theoretical model.In this study,a calculation model of dynamic bulk modulus that considers temperature factors is proposed.It predicts the dynamic bulk modulus of aerated hydraulic fluids at different temperatures and provides a theoretical basis for improving the analytical model of bulk modulus.

First principles study on the charge density and the bulk modulus of the transition metals and their carbides and nitrides

A first principles study of the electronic properties and bulk modulus （B0） of the fcc and bcc transition metals, transition metal carbides and nitrides is presented. The calculations were performed by plane-wave pseudopotential method in the framework of the density functional theory with local density approximation. The density of states and the valence charge densities of these solids are plotted. The results show that B0 does not vary monotonically when the number of the valence d electrons increases. B0 reaches a maximum and then decreases for each of the four sorts of solids. It is related to the occupation of the bonding and anti-bonding states in the solid. The value of the valence charge density at the midpoint between the two nearest metal atoms tends to be proportional to B0.

INTERFACE EFFECT ON THE EFFECTIVE BULK MODULUS OF A PARTICLE-REINFORCED COMPOSITE

Classical micromechanical methods for calculating the effective moduli of a heteroge- neous material are generalized to include the interface(surface)effect.By using Hashin's Composite Sphere Assemblage(CSA)model,a new expression of the bulk modulus for a particle-reinforced com- posite is derived.It is emphasized that the present study is within the finite-deformation framework such that the effective properties are not influenced by the interface stress itself solely,but influenced by the change of the interface stress due to changes of the shape and size of the interface.Hence some inadequacies in previous papers are pointed out.

Higher Order Multipole Potentials and Electrostatic Screening Effects on Cohesive Energy and Bulk Modulus of Metallic Nanoparticles

Higher order rnultipole potentials and electrostatic screening effects are introduced to incorporate the dan gling bonds on the surface of a metallic nanopaticle and to modify the coulornb like potential energy terms, respectively. The total interaction energy function for any rnetallic nanoparticle is represented in terms of two- and three-body potentials. The two-body part is described by dipole-dipole interaction potential, and in the three-body part, triple-dipole （DDD） and dipole-dipole-quadrupole （DDQ） terrns are included. The size-dependent cohesive energy and bulk modulus are observed to decrease with decreasing sizes, a result which is in good agreement with the experimental values of Mo and W nanoparticles.

Isothermal bulk modulus and its first pressure derivative of NaCl at high pressure and high temperature

The isothermal bulk modulus and its first pressure derivative of NaCl are investigated using the classical molecular dynamics method and the quasi-harmonic Debye model. To ensure faithful molecular dynamics simulations, two types of potentials, the shell-model （SM） potential and the two-body rigid-ion Born-Mayer-Huggins-FumiqTosi （BMHFT） potential, are fully tested. Compared with the SM potential based simulation, the molecular dynamics simulation with the BMHFT potential is very successful in reproducing accurately the measured bulk modulus of NaCl. Particular attention is paid to the prediction of the isothermal bulk modulus and its first pressure derivative using the reliable potential and to the comparison of the SM and the BMHFT potentials based molecular dynamics simulations with the quasi-harmonic Debye model. The properties of NaCl in the pressure range of 0-30 GPa at temperatures up to the melting temperature of 1050 K are investigated.

Practical Performance of High Bulk Modulus Oil

Although hydraulic drives have an advantage of high power density, volumetric shrinkage of hydraulic fluids due to pressure causes various disadvantages such as delay of hydraulic response and compression energy loss. Hydraulic fluids of new concept, high bulk modulus oils, have been developed as a new approach to improve the performance of a hydraulic servo system and verified. In this paper, practical performances of high bulk modulus oil, such as oil temperature rise during pump test, air bubbles generation by ultrasonic wave vibration, oxidation stability and anti-wear property, were studied. And the new oil was confirmed to have excellent practical performances besides advantages in pressure response and volumetric efficiency of pumps. Various new applications of the new oil are promising.

Improved material descriptors for bulk modulus in intermetallic compounds via machine learning

Bulk modulus is an important mechanical property in the optimal design and selection of intermetallic compounds.In this study,bulk modulus datasets of intermetallic compounds were collected,and the features affecting the bulk modulus of intermetallics were screened via feature engineering.Three features B_(cal),dB_(avg),and TIE(corresponding to calculated bulk modulus,mean bulk modulus,and third ionization energy,respectively)were found to be the dominant factors influencing bulk modulus and can be extended to other multi-component alloys.Particularly,we predicted the bulk modulus with an accuracy of 95%using surrogate machine learning models with the selected features,and these features were also demonstrated to be effective for high-entropy alloys.Moreover,symbolic regression provided an expression for the relationship between bulk modulus and the screened features.The machine learning models provide a new approach for optimizing and predicting the bulk moduli of intermetallic compounds.

A novel relationship between elastic modulus and void ratio associated with principal stress for coral calcareous sand

Elastic moduli,e.g.shear modulus G and bulk modulus K,are important parameters of geotechnical materials,which are not only the indices for the evaluation of the deformation ability of soils but also the important basic parameters for the development of the constitutive models of geotechnical materials.In this study,a series of triaxial loading-unloading-reloading shear tests and isotropic loading-unloadingreloading tests are conducted to study several typical mechanical properties of coral calcareous sand(CCS),and the void ratio evolution during loading,unloading and reloading.The test results show that the stress-strain curves during multiple unloading processes are almost parallel,and their slopes are much greater than the deformation modulus at the initial stage of loading.The relationship between the confining pressure and the volumetric strain can be defined approximately by a hyperbolic equation under the condition of monotonic loading of confining pressure.Under the condition of confining pressure unloading,the evolution of void ratio is linear in the e-lnp0 plane,and these lines are a series of almost parallel lines if there are multiple processes of unloading.Based on the experimental results,it is found that the modified Hardin formulae for the elastic modulus estimation have a significant deviation from the tested values for CCS.Based on the experimental results,it is proposed that the elastic modulus of soils should be determined by the intersection line of two spatial surfaces in the G/K-e-p’/pa space(pa:atmosphere pressure).“Ye formulation”is further proposed for the estimation of the elastic modulus of CCS.This new estimation formulation for soil elastic modulus would provide a new method to accurately describe the mechanical behavior of granular soils.

Bulk moduli of two-dimensional Yukawa solids and liquids obtained from periodic compressions

Langevin dynamical simulations are performed to determine the bulk modulus in twodimensional(2D) dusty plasmas from uniform periodic radial compressions. The bulk modulus is calculated directly from its physical definition of the ratio of the internal pressure/stress to the volume strain. Under various conditions, the bulk moduli obtained agree with the previous theoretical derivations from completely different approaches. It is found that the bulk moduli of2D Yukawa solids and liquids are almost independent of the system temperature and the external compressional frequency.

Calculations of rock matrix modulus based on a linear regression relation

The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accurately estimate the bulk modulus by using conventional methods. In this paper, we present a new linear regression equation for calculating the parameter. In order to get this equation, we first derive a simplified Gassmann equation by using a reasonable assumption in which the compressive coefficient of the saturated pore fluid is much greater than the rock matrix, and, second, we use the Eshelby- Walsh relation to replace the equivalent modulus of a dry rock in the Gassmann equation. Results from the rock physics analysis of rock sample from a carbonate area show that rock matrix compressive coefficients calculated with water-saturated and dry rock samples using the linear regression method are very close （their error is less than 1%）. This means the new method is accurate and reliable.

AVO forwarding modeling in two-phase media: multiconstrained matrix mineral modulus inversion

AVO forward modeling is based on two-phase medium theory and is considered an effective method for describing reservoir rocks and fluids. However, the method depends on the input matrix mineral bulk modulus and the rationality of the two-phase medium model. We used the matrix mineral bulk modulus inversion method and multiple constraints to obtain a two-phase medium model with physical meaning. The proposed method guarantees the reliability of the obtained AVO characteristicsin two-phase media. By the comparative analysis of different lithology of the core sample, the advantages and accuracy of the inversion method can be illustrated. Also, the inversion method can be applied in LH area, and the AVO characteristics can be obtained when the porosity, fluid saturation, and other important lithology parameters are changed. In particular, the reflection coefficient amplitude difference between the fast P wave and S wave as a function of porosity at the same incidence angle, and the difference in the incidence angle threshold can be used to decipher porosity.

Trends in the band-gap pressure coefficients and bulk moduli in different structures of ZnGa_2S_4,ZnGa-2Se_4 and ZnGa-2Te_4

We have performed a first-principles investigation for the family of compounds ZnGa2X4 （X = S, Se, Te）. The properties of two possible structures, defect chalcopyrite and defect famatinite are both calculated. We reveal that ZnGa2S4 and ZnGa2Se4 have direct band gaps, while ZnGa2Te4 has an indirect band gap. The local density approximation band gaps are found to be very different in two structures, while the lattice parameters and bulk moduli are similar. We extend Cohen＇s empirical formula for zinc-blende compounds to this family of compounds. The pressure coefficients are calculated and metallization pressures are discussed. We find that agi remains fairly constant when thegroup-V/element X is varied in ZnGa2X4（Ⅱ-Ⅲ2-Ⅵ4）.

Prediction of a superhard material of ReN_4 with a high shear modulus

Using first-principles calculations, this paper systematically investigates the structural, elastic, and electronic properties of ReN4. The calculated positive eigenvalues of the elastic constant matrix show that the orthorhombic Pbca structure of ReN4 is elastically stable. The calculated band structure indicates that ReN4 is metallic. Compared with the synthesized superhard material WB4, it finds that ReN4 exhibits larger bulk and shear moduli as well as a smaller Poisson＇s ratio. In addition, the elastic constant c44 of ReN4 is larger than all the known 5d transition metal nitrides and borides. This combination of properties makes it an ideal candidate for a superhard material.

Calculation of Bulk Moduli of Carbon Nitride/metal Nitride Composites

ased on Marvin L. Cohen′s empirical approach, a simple model of calculation of bulk moduli of carbon nitride/metal nitride composites is shown. The calculated bulk modulus of the crystalline carbon nitride/TiN composite coating is comparable with that of cBN and diamond. This model predicts that the modulus of the composite is between the moduli of the two components.

Rock physics model for velocity–pressure relations and its application to shale pore pressure estimation

Acoustic wave velocity has been commonly utilized to predict subsurface geopressure using empirical relations.Acoustic wave velocity is, however, affected by many factors. To estimate pore pressure accurately, we here propose to use elastic rock physics models to understand and analyze quantitatively the various contributions from these different factors affecting wave velocity. We report a closed-form relationship between the frame flexibility factor(γ) in a rock physics model and differential pressure, which presents the major control of pressure on elastic properties such as bulk modulus and compressional wave velocity. For a gas-bearing shale with abundant micro-cracks and fractures, its bulk modulus is much lower at abnormally high pore pressure(high γ values) where thin cracks and flat pores are open than that at normal hydrostatic pressure(low γ values) where pores are more rounded on average. The developed relations between bulk modulus and differential pressure have been successfully applied to the Upper Ordovician Wufeng and Lower Silurian Longmaxi formations in the Dingshan area of the Sichuan Basin to map the three-dimensional spatial distribution of pore pressure in the shale, integrating core, log and seismic data. The estimated results agree well with field measurements. Pressure coefficient is positively correlated to gas content. The relations and methods reported here could be useful for hydrocarbon exploration, production, and drilling safety in both unconventional and conventional fields.

Shear wave velocity prediction during CO_2-EOR and sequestration in the Gao89 well block of the Shengli Oilfield

Shear-wave velocity is a key parameter for calibrating monitoring time-lapse 4D seismic data during CO2-EOR （Enhanced Oil Recovery） and CO2 sequestration. However, actual S-wave velocity data are lacking, especially in 4D data for CO2 sequestration because wells are closed after the CO2 injection and seismic monitoring is continued but no well log data are acquired. When CO2 is injected into a reservoir, the pressure and saturation of the reservoirs change as well as the elastic parameters of the reservoir rocks. We propose a method to predict the S-wave velocity in reservoirs at different pressures and porosities based on the Hertz-Mindlin and Gassmann equations. Because the coordination number is unknown in the Hertz Mindlin equation, we propose a new method to predict it. Thus, we use data at different CO2 injection stages in the Gao89 well block, Shengli Oilfield. First, the sand and mud beds are separated based on the structural characteristics of the thin sand beds and then the S-wave velocity as a function of reservoir pressure and porosity is calculated. Finally, synthetic seismic seismograms are generated based on the predicted P- and S-wave velocities at different stages of CO2 injection.

Insights into Elastic and Thermodynamics Properties of Binary Intermetallics in Ni-AI Alloys under Extreme Condition： Full-Electronic Quasi-Harmonic Study

Atomistic modeling based on the accurate first-principles method is used to investigate the lattice parameter, elastic constant, elastic modulus including bulk modulus （B） and shear modulus （G）, Poisson＇s ratio, and elastic anisotropy of Al, NiAl and NiaAl under extreme condition. The elastic constants obtained from calculations meet their mechanical stability criteria. Both NiAl and Ni3Al exhibit ductile behavior due to their high bulk mudulus to shear modulus ratios of B/G ratios. Through the full-electronic quasi-harmonic approximation, in which the mobile electrons are considered, we successfully obtain the thermo-physical properties including the thermal expansion coefficient, bulk modulus, heat capacity and entropy at simultaneously high temperatures and high pressures. The calculated quantities agree well with the available results. Some silent results are also interpreted. Several interesting features in the thermodynamic properties can also be observed.

First principle study on the elastic and thermodynamic properties of TiB_2 crystal under high temperature

This paper predicts the elastic and thermodynamic characteristics of TiB2 crystal through the method of density functional theory within the generalized gradient approximation （GGA）. The five independent elastic constants （Cij）, the bulk modulus （B0）, the dependence of bulk modulus （B0） on temperature T and pressure P and the coefficient of thermal expansion （αL） at various temperatures have been evaluated and discussed. According to calculation, the bulk modulus will increase with increasing pressure while decrease with the increasing temperature. The coefficient of thermal expansion is consistent with the famous Griineisen＇s law when the temperature is not too high. The obtained results agree well with the experimental and other theoretical results.

Pressure-induced phase transition in silicon nitride material

The equilibrium crystal structures,lattice parameters,elastic constants,and elastic moduli of the polymorphs α-,β-,and γ-Si3N4,have been calculated by first-principles method.β-Si3N4 is ductile in nature and has an ionic bonding.γSi3N4 is found to be a brittle material and has covalent chemical bonds,especially at high pressures.The phase boundary of the β→γ transition is obtained and a positive slope is found.This indicates that at higher temperatures it requires higher pressures to synthesize γ-Si3N4.On the other hand,the α→γ phase boundary can be described as P = 14.37198＋ 3.27 × 10？3T-7.83911 × 10？7T2-3.13552 × 10？10T3.The phase transition from α-to γ-Si3N4 occurs at 16.1 GPa and 1700 K.Then,the dependencies of bulk modulus,heat capacity,and thermal expansion on the pressure P are obtained in the ranges of 0 GPa-30 GPa and 0 K-2000 K.Significant features in these properties are observed at high temperatures.It turns out that the thermal expansion of γ-Si3N4 is larger than that of α-Si3N4 over wide pressure and temperature ranges.The evolutions of the heat capacity with temperature for the Si3N4 polymorphs are close to each other,which are important for possible applications of Si3N4.