An equation of state for carbon dioxide valid from zero to extreme pressures

High-temperature and high-pressure equations of state (EOSs) of Pt have been developed using measured shock compression data up to 290 GPa and volume thermal expansion data between 100 and nearly 2000 K and 0 GPa. The lattice thermal pressures at high temperatures have been estimated based on the Mie–Grüneisen relation with the Debye thermal model and the Vinet isothermal EOS. The contribution of electronic thermal pressure at high temperatures has also been included here. The optimized EOS parameters of Pt are K0T=273 GPa, K0T′=5.20, γ0=2.70, and q=1.10 with Θ0=230 K, where the subscript 0 refers to the ambient conditions. The temperature-pressure-volume (T-P-V) data of Pt have also been measured up to 1600 K and 42 GPa, using synchrotron powder x-ray diffraction experiments combined with a Kawai-type multianvil high pressure apparatus and sintered diamond anvils. We find that the newly developed T-P-V EOS of Pt is fully consistent with not only the shock compression data up to 290 GPa and volume thermal expansion data up to near 2000 K, but also the present measured synchrotron T-P-V data and recently measured T-P-V data of Pt up to 1900 K and 80 GPa. Thus we find that there is no need to include a volume dependence of q over a wide pressure range up to more than 300 GPa. The present EOS has been developed without any pressure scale. Such excellent consistency between the EOS and experimental values over wide temperature and pressure ranges shows that the present EOS can be used as a reliable primary pressure standard for static experiments up to 300 GPa and 3000 K.

Two- and three-phase equilibria in systems containing benzene derivatives, carbon dioxide, and water at 373.15 K and 10–30 MPa

Phase equilibria in systems containing o-cresol, p-cresol, carbon dioxide, and ethanol at 323.15–473.15 K and 10–35 MPa

Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state (EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume (or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently: (1) the room pressure EOS for iron- and titanium-bearing silicate melts needs to be improved; (2) the partial molar properties of the H2O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS; (3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of double-bob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data, and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.

A new technique for simultaneous measurement of PVT and phase equilibria properties of fluids at high temperatures and pressures

In the present survey some important trends in the high pressure thermodynamics of fluid mixtures of non-electrolytes are reviewed. First the pressure dependence of excess functions such as the excess Gibbs energy G E , the excess enthalpy H E , the excess entropy S E and the excess heat capacity C P E is discussed. It can be obtained from the knowledge of the excess volume V E as a function of pressure, temperature and composition. Experimental results demonstrate that the variations of V E as a function of pressure and temperature can be important and comparable to those of the molar volumes themselves. A detailed discussion shows that further progress in this field depends on the development of an accurate equation of state for mixtures. Since furthermore direct calorimetric measurements are practically completely lacking at high pressures most thermodynamic informations have to be deduced up to now from high pressure phase equilibria and critical phenomena where our knowledge is much better. The pressure dependence and critical phenomena of liquid-gas, liquid-liquid and gas-gas equilibria will be shortly reviewed. Mainly binary systems will be treated but phase separation phenomena in some ternary and multicomponent systems will be equally considered. Recent results concerning the rate of phase separation will be additionally presented. New developments during recent years have shown that the limits between liquid-gas, liquid-liquid and gas-gas equilibria are not well defined and that continuous transitions occur. This continuity will be demonstrated for binary mixtures of hydrocarbons with carbon dioxide and methane and for some inert gas systems. The significance of high pressure phase equilibria in fluid mixtures for practical applications is shortly discussed, e.g. for high pressure extractions, supercritical fluid chromatography and for some other high pressure techniques and processes. Methods for the calculation of fluid phase equilibria in mixtures under high pressure are reviewed. They start from equations of state or from theories of mixtures using sometimes sophisticated mixing rules for the parameters. Some results are presented and compared with experimental data. Finally a characteristic example for the pressure dependence of chemical equilibria in liquid solutions is considered and the standard value of the reaction volume Δ V θ is determined from measurements of the equilibrium constant K as a function of pressure at constant temperature. It is shown how standard values of the reaction enthalpy Δ H θ can be obtained from temperature jump experiments in such solutions at high pressure.

The accurate equation of state (EOS) of MgO can be used as a pressure scale, but the EOS currently used has too much uncertainty to serve as a pressure scale, especially at high-pressure and high-temperature conditions. Here we present a complete EOS of solid MgO up to 345 GPa, 8500 K, and its derived pressure-volume-temperature (P-V-T) EOS form, which can be used as a pressure scale. In this EOS, the free energy is expressed as a three-parameter function based on a quasi-Debye thermodynamic model, which establishes a relatively accurate phonon thermodynamic description by determining the phonon dispersion relation and phonon density of states from the volume-dependent sound velocity. The three parameters are determined by a global optimization method, which minimizes the sum of the weighted variances between the physical quantities calculated by the thermodynamic model and the relevant experimental values within the unified EOS framework. To improve the accuracy of the EOS, the parameters are constrained by room-temperature sound velocities and shock compression data, including P-V-T data and sound velocities up to 265 GPa along the principal Hugoniot of MgO measured by us, the P-V-T data at 174--203 GPa, and partial P-V-T data of MgO preheated to 1850 K by others. The derived EOS of MgO can well reproduce not only the above data used to define the parameters, but also the shock compression data and the measured isobaric specific heat not used in the parameter optimization.

Thermodynamics of carbon dioxide mixtures at cryogenic conditions

Binary mixture phase equilibria for the vinyl laurate, vinyl methacrylate and vinyl propionate under high pressure carbon dioxide

High-pressure phase equilibrium for the binary systems of {carbon dioxide (1) + dimethyl carbonate (2)} and {carbon dioxide (1) + diethyl carbonate (2)} at temperatures of 273 K, 283 K, and 293 K

The solubility and the phase equilibria of essential oil with carbon dioxide calculated using a cubic equation of state

The experimental determination of temperatures in the high-pressure shocked state of condensed matter provides a useful supplement to equation-of-state models derived from Hugoniot measurements. An optical pyrometry technique has been developed to obtain temperature measurements during impact-driven shock wave experiments with solid and liquid samples at pressures near 100 GPa. Experimental results confirm that throughout moderate ranges of shock pressure amplitude, transparent dielectrics emit thermal radiation from the region of the shock front, with a spectrum which is characteristic of the Hugoniot state temperature. Shock temperatures in sodium chloride crystals have been measured in the pressure range 70-105 GPa. The observed temperatures, between 4000 and 8000 K, are in agreement with the results of earlier determinations and with calculations assuming the occurrence of shock-induced melting. Results of experiments to measure shock temperatures in metallic silver include a successful measurement of 5950 K at a pressure of 185 GPa. This result is consistent with the melting of silver under shock, with a melting pressure dependence described by the Lindemann criterion. Shock temperature measurements in silica (SiO2) have produced anomalous results suggestive of melting occurring in the stishovite phase near 100 GPa pressure and 4700 K temperature. Experimental measurements with [alpha]-quartz and fused silica samples extend from pressures of approximately 60 GPa to 140 GPa, with shock temperatures between approximately 4500 K and 7000 K. The experimental data allow quantification of the thermodynamic relations among silica phases, including heats of transition and the Gruneisen parameter. Shock temperatures in single crystal forsterite (Mg2SiO4) between pressures of 150 GPa and 175 GPa range from 4500 K to 4950 K, a result which is consistent with occurrence of a polymorphic solid state transition accompanied by a substantial heat of transition (~1.5 MJ/kg). These results have potentially important implications for solid earth geophysics, and knowledge of the melting curves of candidate minerals of the earth's mantle provides some constraints on the geotherm. Hugoniot temperatures have been measured in liquid water between approximately 50 GPa and 80 GPa, with results ranging from 3500 K to 5400 K. The observed temperatures are well reproduced by theoretical calculations assuming a constant specific heat model, but further work is required to characterize fully the thermal variation of H2O properties at high temperature. Compression measurements in pressure-volume states other than Hugoniot shock states and, in particular, in states of compression at constant entropy can provide both independent thermal equation-of-state information and the properties of high-density condensed phases inaccessible to shock wave experiments. Numerical calculations have been carried out for hypothetical experiments on water as well as carbon dioxide and liquid molecular hydrogen. The results of these calculations indicate that various experimental impact configurations may be employed to convert shock compression into isentropic compression, with pressures on the order of 100 GPa attained via impact velocities of a few kilometers per second. In the case of water, a net entropy production of a few percent of the Hugoniot entropy at the same pressure is predicted on the basis of these calculations.

This paper presents an evaluation of the performance of cubic equations of state in the prediction of the phase behavior of hyperbaric mixtures. It points out a number of problems that should be resolved in a cooperative way. Items related to EoS parameter definitions such as interaction coefficients, critical properties of hydrocarbon compounds and volume translation are investigated. VLE experimental data, isothermal flash compositional and volumetric data up to 4000 bar as well as PVT data up to 2000 bar for binary mixtures and synthetic multicomponent systems have been considered in this study. Correlation and prediction results are presented with the translated and modified Peng-Robinson (t-mPR) EoS. It is shown that serious problems are encountered at high pressure, when extrapolated interaction coefficients are used. Prediction of saturation pressures of gas condensates is more satisfactory when binary interaction parameters are obtained from high pressure dew point correlations. Compositional and volumetric predictions are remarkable under the assumption that definition of the EoS parameters is based on high pressure VLE binary data. Contradictory results are obtained with different methods for estimating the critical properties of high molecular weight hydrocarbons. Generalized expressions for the volume translation appear to be very efficient even at very high temperatures and pressures (up to 2000 bar).

Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Standard partial molal properties of inorganic neutral species

Phase behavior of polypropylene + n-pentane and polypropylene + n-pentane + carbon dioxide: modeling with cubic and non-cubic equations of state