Equation Of State Calculations Research Articles

Equation of State Calculations by Fast Computing Machines

Equation of State Calculations by Fast Computing Machines

DISCREPANCY OF MCMP DERIVED FROM EXPERIMENTS AND PREDICTION MODELS OF SOME INDONESIAN OIL FIELDS

Most of oil fi elds in Indonesian have been categorized as mature fi elds, since the primary stages of theoil production nearly fi nished. Therefore EOR technology is the only option to rejuvenate those old oil fi eldsto increase the oil recovery. CO2 miscible fl ooding, one of the proven EOR technology, can be implementedin some Indonesia oil fi elds if they fulfi ll the screening criteria for CO2 injection. Laboratory works initiallyshould be carried out to determine some parameters for calibrating the reservoir simulation program. Themost important parameter is MCMP (multiple contact miscibility pressure), this pressure level can be usedto determine the displacement effi ciency of the CO2 injection. Above the MCMP will be more effi cientcompare to below MCMP injection pressure. MCMP is normally can be obtained in the lab by a Slim tubeapparatus. In case there are no oil and gas sample available, some correlations based on the empiricalfi eld data are also available in the literature as well as EOS (equation of state) for predicting MCMP. Somereservoir fl uids MCMP have been evaluated using those three methods. Then, discrepancies were calculatedto compare the results of Slim tube tests, correlations and EOS calculation. Four correlations such as NPC(National Petroleum Council), Cronquist et al, Yellig-Metcalfe, Holm-Yosendal and one EOS modeling ofPeng-Robinson (1978) have been proposed to predict the MCMP fourteen reservoirs. Moreover, those MCMPwere also run using Slim tube. Holm-Yosendal correlation has nine reservoirs and secondly Yellig-Metcalfemethod possesses six reservoirs with discrepancy below 10% compare to MCMP obtained from Slim Tubetests. While the other methods are not appropriate as well as Peng-Robinson EOS modeling without anylaboratory data for calibration.

The Highly Accurate Relation Between the Radius and Mass of the White Dwarf Star From Zero to Finite Temperature

In this research, first considering the electron–electron interaction in the high-density Fermi electron gas at T = 0 K, this interaction causes the pressure 2/137 time less than the original value. However, the pressure of the Fermi electron gas should have something to do with temperature. Then, we estimate the temperature effect using statistical mechanics and find that the complicated form of the pressure p depends on temperature at the given particle number N and volume V. According to this, the central density–mass (ρc-M), central density–radius (ρc-R), and mass–radius (M-R) relations of the white dwarf star are obtained by considering the equation of state (EOS). Traditional formula gives the problematic mass–radius relation R∝M−1/3 for the low-density white dwarf stars because it leads to R→∞ and p→0 when M→0. We correct this relation and obtain two reasonable relations in the relativistic and nonrelativistic regions. In our EOS calculations, the central density is divided into the high-, middle-, and low-density regions. All three relations are almost unchanged until 108 K in the high-density region. The temperature effect mainly affects the middle- and low-density regions, and it becomes explicitly above 107 K. Our calculations can explain Sloan Digital Sky Survey observations where some white dwarf stars with a radius of more than 8 × 103 km have larger mass than the predictions by the relativistic EOS at T = 0 K. This result tells us that the temperature effect is important for the low and middle central-density white dwarf star and also useful to estimate the inner temperature of a white dwarf star.

Application of BWRS equation of state for calculation of fluid density and viscosity

This study aimed to develop a viscosity model and improve the existing density function solving method by using the BWRS equation of state. The analysis revealed that the density function increased monotonically, so the improved dichotomy for solving density was developed. On the basis of the similarity between P-V-T and T-μ-P relationship, a viscosity model was developed. The new algorithm for solving density has a wider application scope, its calculation accuracy can satisfy the requirements. The new viscosity model could well predict the viscosity of pure propane and carbon dioxide (ADD%: 1.75 and 2.49), and that of methane–propane (ADD%: 1.5).

Thermodynamics of Helium-4 Dimerization and Trimerization.

A new equation of state (EOS) for helium-4 is used to obtain the equilibrium thermochemical properties of helium-4 dimerization (24He ⇌ 4He2) and trimerization (34He ⇌ 4He3) between 3.0 and 10.0 K. It is shown that at sufficiently low temperatures there are appreciable populations of dimer and trimer. The calculations account only for monomer, dimer, and trimer. At 3.0 K, the respective KPo values for dimerization and trimerization are 0.4832 and 0.4876, respectively. The standard enthalpy changes at 3.0 K are -54.53 and -110.0 J/mol, and standard entropy changes are -24.22 and -42.97 J/mol-K. Statistical thermodynamic calculations provide results that are qualitatively consistent with those obtained from the EOS calculations.

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, ({hbox {C}}_{10} {hbox {H}}_8 {hbox {O}}_4)_n, also called mylar) shock-compressed to (155 pm 20) GPa and (6000 pm 1000) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

Density and temperature dependence of the cross sections after excitation of Ar XVIII by electron impact

We propose a novel distorted wave approach within the fundamental framework of relativity theory to calculate the dynamics of magnetic sublevels excitations of highly charged ions by electron impact within a quantum plasma. These cross sections can be used to predict the alignment parameter and subsequent angular pattern of the photoemission. Two kinds of modified Shukla and Eliasson [Phys. Rev. Lett. 108, 165007 (2012)] models, based on the quantum hydrodynamic theory, are adopted to determine the effects of screened Coulomb interaction among charged particles. The bound and continuous state (radial) wave functions are addressed through the one-dimensional Dirac equations, where the numerical convergence is checked. As an application, the 1s1∕2 → 2p3∕2 transition in Ar XVIII is used as a probe for the assessment of the quantum plasma shielding effects and the exchange-correlation effects on the energies, excitation cross sections, alignment parameters, and angular patterns of x-ray emission vs electron densities, from 1019 to 1024 cm−3, and compared to existing data. Our results highlight that the inclusion of the effect of plasma density and temperature not only leads to a significant reduction in the magnetic sublevels cross section, but also produces a change in the alignment parameter and angular pattern of the photoemission. The exchange-correlation effect is found to be crucial to the atomic structure, yet it weakens in the scattering process. In addition to insights into collision dynamics, this study opens the door to a further understanding of the polarization and angular distribution properties of x-ray radiation under extreme conditions. The present study is of interest for the warm density matter physics and high-energy density physics applications. The obtained atomic structure, sublevel cross section, and angular pattern of the photoemission are essential fundamental properties for advanced diagnostics and equation of state calculations in planet interior, inertial confinement fusion, and Z pulsed power facility.

Water–Hydrocarbon Phase Equilibria with SAFT-VR Mie Equation of State

The study of water–hydrocarbon phase equilibria is very important for both scientific and industrial purposes. This work is a thorough investigation of the predictive capability of SAFT-VR Mie equation of state (EoS) for aqueous hydrocarbon phase equilibria, including n-alkanes, alkenes, cycloalkanes, branched alkanes, and aromatic hydrocarbons. For alkenes and alkyl benzenes, induced association (solvation) with water is considered. The model is able to capture the correct phase equilibrium topology for mixtures of n-alkanes and alkyl-benzenes with water as type III according to Van Konynenburg and Scott, but it is not able to predict the barometric shift for alkanes longer than n-hexacosane due to the overshoot of the critical temperature of water. Quantitative results for the solubility of water in light hydrocarbons such as methane, ethane, and ethylene, as well as the mutual solubility of hydrocarbons and water above the solubility minimum, are possible. The latter is not predicted with SAFT-VR Mie EoS similar to other EoSs in literature. Accurate predictions are also reported for the pressure of the three-phase equilibrium and the critical lines for the binary mixtures. Henry’s law constant is often used for the prediction of low-pressure vapor–liquid equilibrium due to the low mutual solubility of hydrocarbons and water. EoS calculations are in reasonable agreement with experimental data for Henry’s constant, especially at higher temperatures. Qualitatively, SAFT-VR Mie captures the maximum of Henry’s constant with temperature, as well as the shift with the carbon number at temperatures near critical to water. SAFT-VR Mie is shown to be overall capable of straightforward prediction of phase equilibria of aqueous hydrocarbon mixtures.

Theoretical determination of level delocalizations, plasma shifts and radiative properties of fusion relevant Ni XXII in finite temperature dense plasmas using a generalized analytical b-potential

We propose a novel relativistic method to explore the atomic structure of highly charged ions perturbed by a dense plasma. The calculations are performed within the general framework of the ion sphere theory and application of the generalized analytical b-potential combined with the multi-configuration Dirac-Fock approximation. In the method, the relativistic effects provided by the Dirac-Coulomb Hamiltonian, Breit interaction and two kinds of quantum electrodynamics corrections, self-energy and vacuum polarization, are accounted for systematically via perturbation theory. The level delocalizations, line shifts and radiative properties among the levels of the 2sx2py (x+y=5) configurations of Ni XXII under the finite temperature dense plasma conditions are demonstrated for illustrative purposes. Such ions can exist in inertial confinement devices or in laser-produced plasmas. Systematic changes are determined for the properties under study in respect of increased temperature and electron density. The obtained atomic structure, line shift, and level delocalization are essential fundamental properties for advanced diagnostics, equation of state calculations, line identifications, and benchmark data for ionization balance calculations ect.

Magnetism and magnetoresistance in the critical region of a dilute ferromagnet

We present detailed experimental measurements and simulations of the field-dependent magnetization and magnetoresistance in the vicinity of the Curie temperature in the highly disordered dilute ferromagnetic semiconductor (Ga,Mn)As. The observed dependence of the magnetization on external magnetic field and temperature is consistent with three-dimensional Heisenberg equation of state calculations including a narrow distribution of critical temperatures. The magnetoresistance shows a peak at the Curie temperature due to the suppression of magnetic scattering in an applied magnetic field, which is well-described by considering changes in the square of the magnetization induced by the magnetic field.

A Method and Apparatus for Direct Enthalpy Rise Measurement for Gas Compression

Gas property prediction is necessary for proper design of compressors. Equations of state are utilized to predict the thermo-physical gas properties needed for such calculations. These are semi-empirical models that allow the calculation of thermodynamic properties such as density, enthalpy, and speed of sound of gas mixtures for known pressures and temperature. Currently, there is limited or no data publically available to verify the results of these equation of state calculations for the range of pressures, temperatures, and gas compositions relevant to many oil and gas applications. Especially for isentropic enthalpy head (i.e., the enthalpy rise along constant entropy lines), which is a critical parameter required to accurately design and performance test compressors, limited public domain data are available for equation of state validation. In this paper, a method and test apparatus is described to measure compression enthalpy rise directly. In this apparatus, a test gas is compressed using a fast acting piston inside an adiabatic autoclave. Test results are then corrected using calibration efficiencies from a known reference gas compression process at a similar Reynolds number. The paper describes the test apparatus, calibration, measurement methodology, and test results for one complex hydrocarbon gas composition at elevated temperatures and pressures. An uncertainty analysis of the new measurement method is also presented and results are compared to several equations of state. The results show that commonly used equations of state significantly underpredicted the compression enthalpy rise for the test gas case by more than 6%.

A comprehensive comparison among four different approaches for predicting the solubility of pharmaceutical solid compounds in supercritical carbon dioxide

Supercritical technologies have been developed in the food, environmental, biochemical and pharmaceutical product processing during the recent decades. Obtaining accurate experimental solubilities of pharmaceutical compounds in supercritical carbon dioxide (SC-CO2) and their correlations are highly important and essential for the design of industrial operating units. In this study, the solubilities of six pharmaceutical compounds (Anti-HIV, Antiinflammatory and Anti-cancer) in SC-CO2 were correlated using four different models: cubic equation of state (EoS) model (SRK and modified-Pazuki EoSs), empirical and semi-empirical models (Chrastil, Mendez-Santiago-Teja, Spark et al. and Bian et al. models), regular solution model coupled with the Flory-Huggins equation, and an artificial neural network-based (ANN-based) model. In EoS calculations, twin-parametric van der Waals (vdW2) and Panagiotopoulos-Reid (mrPR) mixing rules were used for estimating the supercritical solution properties, with three different sets employed for obtaining critical and physicochemical properties of the solid compounds. To evaluate the capabilities of various approaches, a comprehensive comparison was carried out among the four models based on several statistical criteria, including AARD, Radj and F-value. Results of the analysis of variance (ANOVA) indicated that the ANN-based model provided the best results in terms of correlating the experimental solubility of the pharmaceutical compounds in SC-CO2.

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum MonteCarlo Simulations.

Understanding planetary interiors is directly linked to our ability of simulating exotic quantum mechanical systems such as hydrogen (H) and hydrogen-helium (H-He) mixtures at high pressures and temperatures. Equation of state (EOS) tables based on density functional theory are commonly used by planetary scientists, although this method allows only for a qualitative description of the phase diagram. Here we report quantum MonteCarlo (QMC) molecular dynamics simulations of pure H and H-He mixture. We calculate the first QMC EOS at 6000K for a H-He mixture of a protosolar composition, and show the crucial influence of He on the H metallization pressure. Our results can be used to calibrate other EOS calculations and are very timely given the accurate determination of Jupiter's gravitational field from the NASA Juno mission and the effort to determine its structure.

Equation of state and optical properties of warm dense helium

We used molecular dynamics simulations based on density functional theory to study the thermophysical properties of warm dense helium. The influence of different exchange-correlation (XC) functionals was analyzed. We calculated the equation of state at high pressures up to several Mbar and temperatures up to 100 000 K in order to reconstruct recent static, single shock, and quasi-isentropic compression experiments. Furthermore, we calculated the dynamic electrical conductivity and determined the reflectivity and DC conductivity. We compared our results with experimental data and found good agreement between our calculations and the high-pressure experiments. The different XC functionals give similar results in the equation of state calculations, but have a strong impact on the reflectivity and the DC conductivity.

A free energy study of the liquid-liquid phase transition of the Jagla two-scale potential

A fundamental understanding of pure-component liquid-liquid phase separation in network-forming fluids remains an open challenge. While considerable progress has been recently made in demonstrating the existence of such a phase transition in some models via rigorous free energy calculations, it remains unclear what aspects of a model are sufficient, necessary, and/or prohibited in order for it to exhibit a liquid-liquid phase transition (LLPT). Among the simplest models capable of producing water-like anomalies is the spherically-symmetry two-scale Jagla potential, for which an LLPT has been identified via equation of state calculations. In this work, we perform rigorous free energy calculations to demonstrate the existence of an LLPT in the Jagla model. We also utilize finite-size scaling analysis to calculate the surface tension associated with the LLPT. In addition to the thermodynamics of the model, we investigate the relaxation times for density and bond-orientational order in both liquid phases and show that, contrary to assertions in the literature, the characteristic relaxation time of bond-orientational order is not orders of magnitude slower than that of density. To the contrary, we actually identify conditions for which density is the slowly relaxing order parameter. In addition to the original parameterization of the Jagla model, we provide in the “Appendix” preliminary free energy surface calculations for select parameterizations of the generalized family of Jagla potentials spanning from the original (anomalous, water-like) Jagla model to the Lennard-Jones model. These calculations indicate that, as the parameterization moves towards the Lennard-Jones limit, the LLPT disappears within the range of parameters explored. Throughout the paper, we compare our results for the Jagla model with those found in the literature for the ST2 model of water in order to emphasize key similarities and differences between two models that exhibit pure-component liquid-liquid phase separation. Synopsis: We perform rigorous free energy calculations to demonstrate the existence of a liquid-liquid phase transition (LLPT) in the spherically-symmetry two-scale Jagla potential. We also calculate the surface tension associated with the LLPT and investigate the relaxation times of density and bond-orientational order to gain further insight into the LLPT phenomenon.

Electronic Structures of LNA Phosphorothioate Oligonucleotides.

Important oligonucleotides in anti-sense research have been investigated in silico and experimentally. This involves quantum mechanical (QM) calculations and chromatography experiments on locked nucleic acid (LNA) phosphorothioate (PS) oligonucleotides. iso-potential electrostatic surfaces are essential in this study and have been calculated from the wave functions derived from the QM calculations that provide binding information and other properties of these molecules. The QM calculations give details of the electronic structures in terms of e.g., energy and bonding, which make them distinguish or differentiate between the individual PS diastereoisomers determined by the position of sulfur atoms. Rules are derived from the electronic calculations of these molecules and include the effects of the phosphorothioate chirality and formation of electrostatic potential surfaces. Physical and electrochemical descriptors of the PS oligonucleotides are compared to the experiments in which chiral states on these molecules can be distinguished. The calculations demonstrate that electronic structure, electrostatic potential, and topology are highly sensitive to single PS configuration changes and can give a lead to understanding the activity of the molecules.

Structural, electronic and elastic properties of Zn 3 As 2

Abstract In this paper, we report ab initio studies of structural, electronic and elastic properties of a II-V group semiconductor compound, Zn3As2 along with its experimental Compton profile (CP). For experimental CP, 59.54 keV gamma ray (radiation source:5 Ci 241Am) spectrometer is used and to deal with the theoretical part, density functional theory, Hartree-Fock as well as the hybrid functional theory, implemented in CRYSTAL code, are used. A full structure optimization following an equation of state calculation is performed to get the structural parameters. Further directional CPs, band structure, density of states, Mulliken population analysis and elastic properties have also been computed. A concurrence-test with experimental CP proves hybrid scheme to provide the best results in the present case.

Unified low-parametrical equation used to calculate the viscosity coefficient of argon

Using the previously obtained dependence of excess viscosity on internal energy density and low-parametric unified equation of state for calculation of thermodynamic properties of liquid, gas, and fluid, the equation for the excess viscosity of argon in the range of the “mixed” mechanism of momentum transfer in the shear flow was derived. Different versions of approximation of excess viscosity dependence on the density of interaction energy were compared, and the optimal version of this dependence was determined. A simple unified low-parametric equation was obtained for describing the coefficient of argon viscosity in a wide range of state parameters. It is shown that the proposed low-parametric equation for calculating the viscosity coefficient of liquid and gas allows reliable extrapolation beyond the studied region.

Equation of state of dense plasmas with pseudoatom molecular dynamics.

We present an approximation for calculating the equation of state (EOS) of warm and hot dense matter that is built on the previously published pseudoatom molecular dynamics (PAMD) model of dense plasmas [Starrett et al., Phys. Rev. E 91, 013104 (2015)PLEEE81539-375510.1103/PhysRevE.91.013104]. While the EOS calculation with PAMD was previously limited to orbital-free density functional theory (DFT), the new approximation presented here allows a Kohn-Sham DFT treatment of the electrons. The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures. The method is validated by comparisons with pressures from ab initio simulations of Be, Al, Si, and Fe. The EOS in the Thomas-Fermi approximation shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum. We calculate the principal Hugoniots of aluminum and silicon up to 500 eV. We find that the ionic structure of the plasma has a modest effect that peaks at temperatures of a few eV and that the features arising from the electronic structure agree well with ab initio simulations.

Thermodynamic property prediction for high molecular weight molecules based on their constituent family

A method for predicting the critical temperature of high molecular weight molecules is proposed. The method is based on a modification of the functional form of the Joback method and the use of constituent functional group trends. To demonstrate the predictive capability of the method several pure fluids and their binary mixtures with CO2 are studied. In particular, diglyme, triglyme and tetraglyme whose molecular weights range from 134 to 222, are shown to reveal excellent predictions between 3 and 9% deviation for saturated liquid densities. Application to vapor–liquid phase equilibria for CO2-glyme systems exhibit 4–8% deviation in saturated liquid densities and 1% for vapor densities. For the system of oleic acid + CO2, pure component parameters from the method allow the correlation of the vapor pressure of oleic acid and the solubility of H2 in oleic acid with a BWR type of equation of state and temperature dependent interaction parameters. Solubility of CO2 in triolein is also well correlated. The critical temperature of a polyalkylene glycol with a molecular weight of 1100 is predicted to be 842 K, whereas the prediction by of the Joback method predicts 8541 K, and so cannot be used in equation of state calculations. The pure component properties predicted with the new functional form of the Joback method also allow reliable correlation of CO2-polyalkylene glycol vapor–liquid equilibria.