Available Equations Of State Research Articles

Thermophysical Properties and Phase Behavior of CO2 with Impurities: Insight from Molecular Simulations.

Experimentally determining thermophysical properties for various compositions commonly found in CO2 transportation systems is extremely challenging. To overcome this challenge, we performed Monte Carlo (MC) and Molecular Dynamics (MD) simulations of CO2 rich mixtures to compute thermophysical properties such as densities, thermal expansion coefficients, isothermal compressibilities, heat capacities, Joule-Thomson coefficients, speed of sound, and viscosities at temperatures of (235-313) K and pressures of (20-200) bar. We computed thermophysical properties of pure CO2 and CO2 rich mixtures with N2, Ar, H2, and CH4 as impurities of (1-10) mol % and showed good agreement with available Equations of State (EoS). We showed that impurities decrease the values of thermal expansion coefficients, isothermal compressibilities, heat capacities, and Joule-Thomson coefficients in the gas phase, while these values increase in the liquid and supercritical phases. In contrast, impurities increase the value of speed of sound in the gas phase and decrease it in the liquid and supercritical phases. We present an extensive data set of thermophysical properties for CO2 rich mixtures with various impurities, which will help to design the safe and efficient operation of CO2 transportation systems.

Compactness in the thermal evolution of twin stars

In this work, we study the thermal evolution of twin star pairs, i.e., stars that present the same mass but different radius and compactness. We collect available equations of state that give origin to a second branch of stable compact stars with quarks in their core. For each equation of state, we investigate the particle composition inside stars and how differently each twin evolves over time, which depends on the central density/pressure and consequent crossing of the threshold for the Urca cooling process. We find that, although the general stellar thermal evolution depends on mass and particle composition, within one equation of state, only twin pairs that differ considerably on compactness can be clearly distinguished by how they cool down.

Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. We compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

Dependence on beam energy and nuclear equation of state of anisotropic flow and particle production in low-energy heavy-ion collisions

We analyze various flow coefficients of anisotropic momentum distribution of final state particles in mid-central ($b=5\text{--}9\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$) $\mathrm{Au}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}\mathrm{Au}$ collisions in the beam energy range ${E}_{\mathrm{Lab}}=1A\text{--}158A$ GeV. Different variants of the ultrarelativistic quantum molecular dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode, are employed for this investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is integrated with the pure transport calculation for description of the evolution of the fireball. We opt for the different available equations of state (EoS) replicating the hadronic as well as partonic degrees of freedom together with possible phase transitions, viz., hadron gas, chiral $+$ deconfinement EoS, and bag model EoS, to investigate their effect on the properties of the final state particles. We also attempt to gain insights about the dynamics of the medium by studying different features of particle production such as particle ratios and net-proton rapidity distribution. The results and conclusions drawn here would be useful to understand the response of various observables to the underlying physics of the model as well as to make comparisons with the upcoming measurements of the future experiments at the Facility for Antiproton and Ion Research (FAIR) and the Nuclotron-based Ion Collider fAcility (NICA).

A carbonaceous chondrite and cometary origin for icy moons of Jupiter and Saturn

The inner structure of icy moons comprises ices, liquid water, a silicate rocky core and sometimes an inner metallic core depending on thermal evolution and differentiation. Mineralogy and density models for the silicate part of the icy satellites cores were assessed assuming a carbonaceous chondritic (CI) bulk composition and using a free-energy minimization code and experiments. Densities of other components, solid and liquid sulfides, carbonaceous matter, were evaluated from available equations of state. Model densities for silicates are larger than assessed from magnesian terrestrial minerals, by 200 to 600 kg.m−3 for the hydrated silicates, and 300 to 500 kg.m−3 for the dry silicates, due to the high iron bulk concentration in CI. The stability of Na-phlogopite in the silicate fraction up to 1300 K favors the trapping of most 40K in the rocky/carbonaceous cores with important consequences for modeling of the thermal evolution of icy satellites. We find that CI density models of icy satellite cores taking into account only the silicate and metal/sulfide fraction cannot account for the observed densities and reduced moment of inertia of Titan and Ganymede without adding a lower density component. We propose that this low-density component is carbonaceous matter derived from insoluble organic matter, in proportion of ∼30-40% in volume and 15-20% in mass. This proportion is compatible with contributions from CI and comets, making these primitive bodies including their carbonaceous matter component likely precursors of icy moons, and potentially of most of the objects formed behind the snow line of the solar system.

Behavior of Isobaric Heat Capacity of Pentafluoroethane in the Gas Phase

The isobaric specific heat capacity cp of gaseous pentafluoroethane was measured and the behavior was presented. With a flow calorimeter, 29 cp data of pentafluoroethane were measured at temperatures T from (303 to 343) K and at pressures p from (0.5 to 2.4) MPa. Some of them were measured in the immediate vicinity of the saturation curve. The expanded uncertainties (k = 2) of the temperature measurements U(T) and the pressure measurements U(p) are estimated to be below 50 mK and 11 kPa, respectively. That for cp measurements Uc(cp) is assessed to extend from (14 to 60) J·kg–1·K–1. Then, the cp measurements including the previous 12 measurements were compared with some available equations of state. Using these confirmed data, the cp behaviors of gaseous pentafluoroethane were presented in a cp–p diagram.

Modelling the thermodynamics of air-component mixtures (N2, O2 and Ar): Comparison and performance analysis of available models

With a view to finding which of the available equations of state is the most suitable for the representation of the thermodynamics of mixtures containing nitrogen, oxygen and argon, this paper mainly intends to address the comparison of the performance of the - already optimized - GERG-2008, Bender and Peng-Robinson (PR) Equations of State (EoS) in the calculation of Vapour-Liquid Equilibrium (VLE) and volumetric properties of N2-O2-Ar mixtures. The comparison between experimental measurements collected in the literature and model calculations has led to conclude about the overall superiority of GERG-2008. It is also shown that the Peng-Robinson EoS leads to comparable results in VLE calculations and that the use of Bender EoS should be avoided as it leads, despite its complex multiparameter formulation, to very inaccurate results in the calculation of VLE properties of the binary Ar-O2 and of volumetric properties. For completeness, the paper also shows the poor accuracy of the PR EoS in calculating VLE properties when zero-kij are selected. Moreover, the paper evaluates the impact of deviations on densities, calculated with the different equations of state, on the computation of transport properties (thermal conductivity, viscosity), in turns determined by means of correlations which are typically applied. Liquid thermal conductivity is highly affected by errors on liquid density calculations while the liquid viscosity is independent of density. Differently, errors on vapour thermal conductivity and dynamic viscosity are lower than those observed on vapour density.

Density of Methylcyclohexane at Temperatures up to 600 K and Pressures up to 200 MPa

Using a bellows variable volumometer, precise density data were measured for methylcyclohexane, which is expected to be a chemical hydride for transportation and storage of hydrogen. For further development of an accurate equation of state, measurements were taken in the temperature and pressure ranges 410 K to 600 K and 10 MPa to 200 MPa, respectively. The uncertainties (\(k=2\)) were less than 3.5 mK for the temperature measurements, 0.080 MPa for the pressure measurements, and 0.11% for the density measurements. In the region above 100 MPa and 450 K, the uncertainty for the density measurement increased from 0.11% to 0.22%. The data obtained in this study were systematically compared with available experimental data and theoretical values derived from the available equation of state. This comparison indicated that the model needs to be improved.

Gaussian and non-Gaussian fluctuations in pure classical fluids

The particle number, energy, and volume probability distributions in the canonical, isothermal-isobaric, grand canonical, and isobaric-isenthalpic ensembles are investigated. In particular, we consider Gaussian and non-Gaussian behavior and formulate the results in terms of a single expression valid for all the ensembles employing common, experimentally accessible, thermodynamic derivatives. This is achieved using Fluctuation Solution Theory to help manipulate derivatives of the entropy. The properties of the distributions are then investigated using available equations of state for fluid water and argon. Purely Gaussian behavior is not observed for any of the state points considered here. A set of simple measures, involving thermodynamic derivatives, indicating non-Gaussian behavior is proposed. A general expression, valid in the high temperature limit, for small energy fluctuations in the canonical ensemble is provided.

Solid molecular nitrogen (δ-N2) inclusions in Juina diamonds: Exsolution at the base of the transition zone

Diamonds originating from the transition zone or lower mantle were previously identified based on the chemistry of their silicate or oxide mineral inclusions. Here we present data for such a super-deep origin based on the internal pressure of nitrogen in sub-micrometer inclusions in diamonds from Juina, Brazil. Infrared spectroscopy of four diamonds, rich in such inclusions revealed high concentrations of fully aggregated nitrogen (average of 900 ppm, all in B centers) and almost no platelets. Raman spectroscopy indicated the presence of solid, cubic δ-N2 at 10.9±0.2 GPa (corresponding to a density of 1900 kg/m3). Transmission electron microscopy of two diamonds found two generations of octahedral inclusions: microinclusions (average size: 150 nm, average concentration: 100 ppm) and nanoinclusions (20–30 nm, 350 ppm). EELS detected nitrogen and a diffraction pattern of one nanoinclusion yielded a tetragonal phase, which resembles γ-N2 with a density of 1400 kg/m3 (internal pressure = 2.7 GPa). We also observed up-warping of small areas (∼150 nm in size) on the polished surface of one diamond. The ∼2 nm rise can be explained by a shallow subsurface microinclusion, pressurized internally to more than 10 GPa.Using available equations of state for nitrogen and diamond, we calculated the pressures and temperatures of mechanical equilibrium of the inclusions and their diamond host at the mantle geotherm. The inclusions originated at the deepest part of the transition zone at pressures of ∼22 GPa (630 km) and temperatures of ∼1640 °C. We suggest that both generations are the result of exsolution of nitrogen from B centers and that growth took a few million years in a subducting mantle current. The microinclusions nucleated first, followed by the nanoinclusions. Shortly after the exsolution events, the diamonds were trapped in a plume or an ascending melt and were transported to the base of the lithosphere and later to the surface.

PρT and saturation properties of isopentane at T = (280–440) K and up to 200 MPa

We measured the PρT and saturation properties of isopentane within the temperature range of 280–440K at pressures up to 200MPa using a metal-bellows variable volumometer. The mass fraction purity of the isopentane sample was 0.998. The expanded uncertainties (k=2) in the temperature, pressure, and density measurements were estimated to be less than 3mK, 1.43kPa − 0.2% (P≦200MPa), and 0.11%, respectively. In the region above 100MPa at T=280K and 440K, the uncertainty in the density measurement increased from 0.11% to 0.14% and 0.22%, respectively. Eleven PρT measurements were carried out at temperatures and pressures reported in the literature for comparison. Additionally, the results of the present measurements were compared with those of the available equation of state.

Silicate impact-vapor condensate on the Moon: Theoretical estimates versus geochemical data

We numerically simulated the impacts of asteroids and comets on the Moon in order to calculate the amount of condensate that can be formed after the impacts and compare the results with data for lunar samples. Using available equations of state for quartz and dunite, we have determined pressure and density behind shock waves in these materials for particle velocities from 4 to 20km/s and obtained release adiabats from various points on the Hugoniot curves to very low pressures. For shock waves with particle velocities behind the front below 8km/s the release adiabats intersect the liquid branch of the two-phase curve and, during the following expansion, the liquid material vaporizes and does not condense, forming a two-phase mixture of melt and vapor. The condensate can appear during expansion of material compressed by a shock with higher (>8km/s) velocities. Using our hydrocode SOVA, we have conducted numerical simulations of the impacts of spherical quartz, dunite, and water–ice projectiles into targets of the same materials. Impact velocities were 15–25km/s for stony projectiles and 20–70km/s for icy impactors, and impact angles were 45°and 90° to the target surface. Along with the masses of condensates we calculated the masses of vaporized and melted material. Upon the impact of a projectile consisting of dunite into a target of quartz at a speed of 20km/s at an angle of 45°, vaporized and melted masses of the target are equal to 1.6 and 11 in units of projectile mass, respectively, and the mass of condensate is 0.19. Vaporized and condensed masses of the projectile are 0.16 and 0.02, more than 80% of the projectile mass is melted. The calculated ratio of vaporized to melted mass proved to be on the order of 0.1. However, we calculated that, at impact velocities below 20km/s, the condensate mass is only a small fraction of the vaporized and melted masses and, consequently, the major part of vapor disperses in vacuum in the form of separate molecules or molecular clusters. At an impact velocity of 15km/s, the abundance of silicate condensates relative to melt is 0.001–0.0001, in agreement with data from lunar samples. Should the observed condensate abundances be representative, the velocities of major asteroid impacts on the Moon could not substantially exceed 20km/s. Comet impacts at the same velocities produce much smaller amounts of vapor condensate because the low densities of cometary material induce lower shock pressures in the target.

Reference correlations for the viscosity and thermal conductivity of fluids over an extended range of conditions: hexane in the vapor, liquid, and supercritical regions (IUPAC Technical Report)

Abstract This article summarizes the correlation procedures developed for IUPAC Project 2012-040-1-100 [Reference correlations for the thermal conductivity and viscosity of fluids over extended range of conditions (vapor, liquid and supercritical regions)]. This project is focused on the development of wide-range reference correlations for the thermal conductivity and viscosity of fluids that incorporate as much theoretical knowledge of these properties as possible. The thermal conductivity and viscosity correlations developed here for pure fluids are functions of temperature and density. The best available equations of state for a given fluid are used to calculate the thermodynamic properties required for these correlations, often from measured temperatures and pressures. The correlation methodology developed during this project has been applied to hexane in this report but can be applied to any pure fluid with a reliable equation of state and reliable data for the thermal conductivity and viscosity over a significant range of temperatures and densities.

CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS

Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabular form, covering a wide range in density, temperature and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 15 and 40 solar mass progenitors. We do not find any simple correlations between individual nuclear matter properties at saturation and the outcome of these simulations. However, the new equations of state lead to the most compact neutron stars among the relativistic mean-field models which we considered. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s=4 neutron star.

Behavior of isobaric heat capacity of R32 in the gas phase

The specific isobaric heat capacity was measured for R 32 (difluoromethane) in the gas phase. Twenty-one measurements for R 32 were obtained at temperatures from 282 to 319 K and at pressures from 1.0 to 2.4 MPa, which are very close to the saturation curve. The expanded uncertainty (k = 2) of the temperature measurements is estimated to be less than 23 mK, and that of the pressure measurements is less than 15 kPa. The expanded uncertainty for cp is estimated to range from 15 to 47 J kg−1 K−1. The measurements were compared with available equations of state. Based on the measurements, heat capacity curves of the ideal gas and saturated vapor of R 32 were specified. These data will be very useful for improving available models, especially for correcting behavior in the gas phase, so as to represent reliable thermodynamic properties of R 32 and refrigerant mixtures with R32 that are used for refrigeration and air conditioning systems.

Measurement of the (p, $$\rho $$ , T) Properties for Pure Hydrocarbons at Temperatures up to 600 K and Pressures up to 200 MPa

The data available for the thermodynamic properties of propane, \(n\)-butane, and isobutane at temperatures above 440 K are outdated and show significant discrepancies with each other. The ambiguity associated with these data could be limiting to the development of any understanding related to the effects of mixing of these substances with other materials such as \(\text{ CO}_{2}\), ammonia, and non-flammable or lower-flammable HFC refrigerants. In this study, the (p, \(\rho \), T) properties of propane, \(n\)-butane, and isobutane were measured at temperatures ranging from (360 to 600) K and pressures ranging from (50 to 200) MPa. Precise measurements were carried out using a metal-bellows variable volumometer with a thermostatted air bath. The expanded uncertainties \((k = 2)\) in the temperature, pressure, and density measurements were estimated to be \( 423\) K, \(p 423\) K, \(p \ge 100\) MPa), respectively. The data obtained throughout this study were systematically compared with the calculated values derived from the available equations of state. These models agree well with the measured data at higher temperatures up to 600 K, demonstrating their suitability for an effective and precise examination of the mixing effects of potential alternative mixtures.

( $${p, \rho , T, x}$$ ) Properties of $$\text{ CO}_{2}$$ /Propane Binary Mixtures at 280 K to 440 K and 3 MPa to 200 MPa

The (p, $$\rho $$ , T, x) properties of binary mixtures of CO $$_{2}$$ (volume fraction purity 0.99999) and propane (mole fraction purity 0.9999) ( $$x_{1}$$ CO $$_{2}+x_{2}$$ propane; $$x_{1} = 0.1744$$ , 0.3863, 0.5837, and 0.7732) were measured in the compressed liquid phase using a metal-bellows variable volumometer. Measurements were conducted from 280 K to 440 K and 3 MPa to 200 MPa. The expanded uncertainties ( $$k = 2$$ ) were estimated to be temperature, $$<$$ 3 mK; pressure, 1.5 kPa ( $$p\le 7$$ MPa), 0.06 % (7 MPa $$< p\le 50$$ MPa), 0.1 % (50 MPa $$< p\le 150$$ MPa), 0.2 % ( $$p> 150$$ MPa); density, 0.10 %; and composition, $$4.4\times 10^{-4}$$ . At $$p >100$$ MPa and 280 K or 440 K, the uncertainties in density measurements increase to 0.14 % and 0.22 %, respectively. The data were compared with available equations of state. The excess molar volumes, $$v_\mathrm{m}^\mathrm{E}$$ , of the mixtures were calculated and plotted as a function of temperature and pressure.

Observations of multimode perturbation decay at non-accelerating, soft x-ray driven ablation fronts

Minimizing the growth of hydrodynamic instabilities is a fundamental design issue facing the achievement of thermonuclear ignition and burn with Inertial Confinement Fusion (ICF). The thin capsules and extreme accelerations found in ICF make it an inherently unstable system primarily to Rayleigh-Taylor (RT) occurring at the ablation front. A potential mechanism by which perturbations at the outer capsule surface can be reduced lies in the already present ablative Richtmyer-Meshkov (RM) effect, which operates during the first shock transit of the ablator. At present, the available Equation of State (EOS) models predict a wide range of behavior for the ablative RM oscillations of multimode isolated defects on plastic (CH) capsules. To resolve these differences, we conducted experiments at the OMEGA Laser Facility [T. R. Boehly et al., Optics Comm. 133 (1997)] that measured the evolution of gaussian-shaped bumps driven by soft x-ray ablation from a halfraum. Shock speeds in the CH target were measured to reach 15 μm/ns for halfraum radiation temperatures of 70 eV lasting for up to 7 ns. The evolution of gaussian-shaped bumps of different widths and heights were measured using on-axis x-ray radiography at up to 37× magnification. Bumps with initial widths of 34 and 44 μm FWHM were found to grow by 3× their initial areal density and then saturate out to 6 ns due to lateral compression of the bump characteristic of the formation of a rippled shock front propagating into the solid target. Narrower 17 μm FWHM bumps, on the other hand, grew by roughly 2× followed immediately by a decrease back to initial values of areal density out to 7 ns, which largely agrees with both LEOS 5310 and SESAME 7592 EOS predictions. The difference in observed behavior suggests that high spatial frequency modes found in narrower bumps are needed to significantly affect the ablation front profile on shorter time scales.

Genetic algorithm application for matching ordinary black oil PVT data

In the study of reservoirs, it is vital that we have a realistic physical model of the reservoir fluid that accurately describes the hydrocarbon system and its properties. The available equations of state (EOS) to model the fluid phase behavior have some inherent deficiencies that may cause erroneous predictions for real reservoir fluids, so these models should be tuned against experimental data by adjusting some parameters. Since there are many matching parameters, tuning the EOS against experimental data is a tedious and difficult work. In this study, a genetic algorithm as an optimization technique is used to solve this regression problem. This study presents a new method that uses a specially designed genetic algorithm to search for suitable regression parameters to match the EOS against measured data. The proposed method has been tested on three real black oil samples. The results show the surprising performance of the developed genetic algorithm to match the experimental data of the selected fluid samples. The main advantage of the used method is its high speed in finding a solution. Also, finding more than one solution, working automatically, confining the role of experts to the last stage, reducing costs and having the possibility of evaluating the different situations are the other advantages of this method to match ordinary black oil PVT data and makes it an ideal method to implement as an automatic EOS tuning algorithm for black oils.

Measurements of isobaric heat capacity of R32

The specific isobaric heat capacity (cp) was measured for R32 (difluoromethane) in the gas phase. Thirty-two measurements for R32 were obtained at temperatures from 274 to 353 K and at pressures from 0.65 to 2.4 MPa. Some of them are close to the saturation curve. The expanded uncertainty (k = 2) of the temperature measurements is estimated to be less than 26 mK, and that of the pressure measurements is less than 23 kPa. The expanded uncertainty for cp is estimated to range from 13 to 27 J kg−1 K−1. The experimental data were compared with available equations of state. These data will be essential for improving available models so as to represent more reliable thermodynamic properties of R32 and refrigerant mixtures with R32 that are used for refrigeration and air conditioning systems.