Thermodynamic description of aqueous nonelectrolytes at infinite dilution over a wide range of state parameters

A new, virial-like equation of state (EoS) for describing the thermodynamic properties of aqueous nonelectrolytes at infinite dilution is proposed. It is based on the accurate EoS for a solvent (H₂O) given by Hill (1990) and requires only three empirical parameters to be fitted to experimental data, and these are independent of temperature and pressure. Knowledge of the thermodynamic properties of a pure gas, together with these three parameters, enables prediction of the whole set thermodynamic properties of the solute at infinite dilution (chemical potential, entropy, molar volume, and apparent molar heat capacity) over a wide range of temperatures (0 to 500°C) and pressures (1 to 2000 bars), including the near-critical region. In the cases in which experimental thermodynamic data are lacking, the empirical parameters can be estimated solely from the known standard-state properties of the solute. The new EoS is compatible with the Helgeson-Kirkham-Flowers model for aqueous electrolytes, and thus it can be applied to reactions involving minerals, gases, and aqueous ions, in addition to uncharged species.     

Molecular dynamics simulation of the CH4 and CH4-H2O systems up to 10 GPa and 2573 K

Based on our previous study of the intermolecular potential for pure H₂O and the strict evaluation of the competitive potential models for pure CH₄ and the ab initio fitting potential surface across CH₄-H₂O molecules in this study, we carried out more than two thousand molecular dynamics simulations for the PVTx properties of pure CH₄ and the CH₄-H₂O mixtures up to 2573 K and 10 GPa. Comparison of 1941 simulations with experimental PVT data for pure CH₄ shows an average deviation of 0.96% and a maximum deviation of 2.82%. The comparison of the results of 519 simulations of the mixtures with the experimental measurements reveals that the PVTx properties of the CH₄-H₂O mixtures generally agree with the extensive experimental data with an average deviation of 0.83% and 4% in maximum, which is equivalent to the experimental uncertainty. Moreover, the maximum deviation between the experimental data and the simulation results decreases to about 2% as temperature and pressure increase, indicating that the high accuracy of the simulation is well retained in the high temperature and pressure region.After the validation of the simulation method and the intermolecular potential models, we systematically simulated the PVTx properties of this binary system from 673 K and 0.05 GPa to 2573 K and 10 GPa. In order to integrate all the simulation results and the experimental data for the calculation of thermodynamic properties, an equation of state (EOS) is developed for the CH₄-H₂O system covering 673-2573 K and 0.01-10 GPa. Isochores for compositions <4 mol% CH₄ up to 773 K and 600 MPa are also determined in this paper. The program for the EOS can be downloaded from www.geochem-model.org/programs.htm.     

超临界流体热力学函数的理论计算

Ｄｕａｎ等（１９９２。１９９６）基于分子间相互作用势能模型,建立了一个适合于超临界流体的状态方程,此方程能反演出世界上几十个实验室测定的成千上万个纯组分及混合物的ＰＶＴ（压力、体积、温度）数据（温压范围：Ｐ〈２ＧＰａ,Ｔｃ〈Ｔ〈２０００Ｋ）。最近的研究发现,此方程能准确预测Ｈ２Ｏ、ＣＯ２、ＣＨ４、Ｎ２及它们的混合物在Ｔ＝１．３Ｔｃ,Ｐ＝０到Ｔ＝２０００Ｋ,Ｐ＝１０ＧＰａ这一温压范围内的压力、体积、     

宽广温压范围内纯流体pVT性质的预测

一个具有 1 9个参数的半经验状态方程 ,可以很容易地转化为关于体积的多项式方程 ,应用起来十分方便。对于气体和超临界流体 ,该方程可以在很宽的温压范围内保持较高的精度。用该方程计算 H2 O、CO2 、CH4、H2 、CO、O2 等流体的 p VT关系 ,结果令人满意。在从常温常压直到 4 0 0 0～ 50 0 0 K和 90～ 60 0 GPa的范围内 ,预测的体积误差为 :平均偏差小于 1 % ,最大偏差小于 6% ,标准偏差小于 1 .5%。     

Characterization of CO2CH4H2O fluid inclusions by microthermometry and laser Raman microprobe spectroscopy: Inferences for clathrate and fluid equilibria

Microthermometry (MT) and laser Raman microprobe (LRM) spectroscopy (at room temperature and at about 0°C) were done on 33 synthetically produced CO₂CH₄H₂O fluid inclusions in quartz (from R. Bodnar and M. Sterner). At room temperature, the inclusions consist of an aqueous liquid, a CO₂CH₄ supercritical carbonic fluid and (in most cases) graphite. In all these inclusions, the melting temperature for solid CO₂ is less than that for the homogenization of the vapor bubble in the carbonic fluid.A method is described whereby MT data for CO₂CH₄H₂O inclusions can be projected within the CO₂CH₄ binary phase diagram to infer CO₂:CH₄ ratios in the carbonic fluid (<2 to > 35 mole% CH₄ in the inclusions under study). This method takes into account the formation of CO₂CH₄ clathrate hydrate during MT analysis. Unless clathrate formation is properly considered, errors arise in the determination of the bulk CO₂CH₄ ratio. For the inclusions in our study, these errors are on the order of 5 to 8 mole% CH₄. Our interpretation of the MT data indicates that CH₄ is preferentially partitioned into the clathrate over the coexisting carbonic fluid, in contradiction to the prediction from Parrish and Prausnitz's (1972) model for clathrate equilibria. Comparison of LRM analyses on the bulk carbonic fluid (in the absence of clathrate) and the residual carbonic fluid (in the presence of clathrate) confirm the preferential partitioning of CH₄ into the clathrate. LRM analyses of the clathrate itself indicate that CH₄ occupies both types of cage sites in the clathrate structure, whereas CO₂ may only occupy one site. Two by-products of the combined LRM and MT analyses of the same inclusions are derivation of empirical ratios of Raman quantification factors for high-density CO₂CH₄ fluids and the ability to determine CO₂:CH₄ ratios of inclusions whose MT data lie near the critical region for CO₂CH₄. Thus, the joint use of LRM and MT techniques provides information that could not be obtained by either technique alone.     

Calcite solubility in supercritical CO2H2O fluids

An extraction-quench apparatus was used to measure calcite solubilities in supercritical CO₂H₂O mixtures. Experiments were conducted at 1 kbar and 2 kbar, between 240°C and 620°C and from X_CO2 = .02 toX_CO2 = .15 in order to determine the solubility behavior as a function of pressure, temperature and CO₂ content. The results indicate that calcite solubilities under these conditions behave similarly to previously investigated calcite solubilities at lower pressures and temperatures (SHARP and Kennedy, 1965). At constant X_CO2, the solubility increases with increasing pressure, but it decreases with increasing temperature. When the temperature and pressure are constant, the calcite solubility rises with increasing X_CO2 to a maximum value at X_CO2 between 0.02 and 0.05. For higher CO₂ contents, up to X_CO2 = .15, the calcite solubility decreases, probably due to the decrease of H₂O activities to values significantly below unity.The solubility behavior can be successfully modeled by making the assumption that Ca⁺⁺ is the dominant calcium species and that the carbon-bearing species are CO_2(aq) and HCO⁻₃. Since for these dilute H₂OCO₂ fluids, all activity coefficients can be assumed to not differ significantly from unity, ionization constants for the reaction H₂O + CO_2(aq) H⁺ + HCO⁻₃ can be calculated at 1 and 2 kbar between 250°C and 550°C. These calculated values are in good agreement with the low temperature determinations of the ionization constants for this reaction determined by Read (1975). Values of the molal Gibbs free energy of CO_2(aq) obtained in our study exhibit a much greater positive departure from ideality than those calculated with the modified Redlich-Kwong equations of either Flowers (1979) or Kerrick and Jacobs (1981) for dilute CO₂ aqueous solutions.     

Equation of state of the H2O, CO2, and H2O-CO2 systems up to 10 GPa and 2573.15 K: Molecular dynamics simulations with ab initio potential surface

Based on our previous development of the molecular interaction potential for pure H₂O and CO₂ [Zhang, Z.G., Duan, Z.H. 2005a. Isothermal-isobaric molecular dynamics simulations of the PVT properties of water over wide range of temperatures and pressures. Phys. Earth Planet Interiors149, 335-354; Zhang, Z.G., Duan, Z.H. 2005b. An optimized molecular potential for carbon dioxide. J. Chem. Phys.122, 214507] and the ab initio potential surface across CO₂-H₂O molecules constructed in this study, we carried out more than one thousand molecular dynamics simulations of the PVTx properties of the CO₂-H₂O mixtures in the temperature-pressure range from 673.15 to 2573.15 K up to 10.0 GPa. Comparison with extensive experimental PVTx data indicates that the simulated results generally agree with experimental data within 2% in density, equivalent to experimental uncertainty. Even the data under the highest experimental temperature-pressure conditions (up to 1673 K and 1.94 GPa) are well predicted with the agreement within 1.0% in density, indicating that the high accuracy of the simulation is well retained as the temperature and pressure increase. The consistent and stable predictability of the simulation from low to high temperature-pressure and the fact that the molecular dynamics simulation resort to no experimental data but to ab initio molecular potential makes us convinced that the simulation results should be reliable up to at least 2573 K and 10 GPa with errors less than 2% in density. In order to integrate all the simulation results of this study and previous studies [Zhang and Duan, 2005a, 2005b] and the experimental data for the calculation of volumetric properties (volume, density, and excess volume), heat properties, and chemical properties (fugacity, activity, and possibly supercritical phase separation), an equation of state (EOS) is laboriously developed for the CO₂, H₂O, and CO₂-H₂O systems. This EOS reproduces all the experimental and simulated data covering a wide temperature and pressure range from 673.15 to 2573.15 K and from 0 to 10.0 GPa within experimental or simulation uncertainty.     

Phase equilibria of the system methane-ethane from temperature scaling Gibbs Ensemble Monte Carlo simulation

A new technique of temperature scaling method combined with the conventional Gibbs Ensemble Monte Carlo simulation was used to study liquid-vapor phase equilibria of the methane-ethane (CH₄-C₂H₆) system. With this efficient method, a new set of united-atom Lennard-Jones potential parameters for pure C₂H₆ was found to be more accurate than those of previous models in the prediction of phase equilibria. Using the optimized potentials for liquid simulations (OPLS) potential for CH₄ and the potential of this study for C₂H₆, together with a simple mixing rule, we simulated the equilibrium compositions and densities of the CH₄-C₂H₆ mixtures with accuracy close to experiments. The simulated data are supplements to experiments, and may cover a larger temperature-pressure-composition space than experiments. Compared with some well-established equations of state such as Peng-Robinson equation of state (PR-EQS), the simulated results are found to be closer to experiments, at least in some temperature and pressure ranges.     

CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100°C and up to 600 bar

Evaluating the feasibility of CO₂ geologic sequestration requires the use of pressure-temperature-composition (P-T-X) data for mixtures of CO₂ and H₂O at moderate pressures and temperatures (typically below 500 bar and below 100°C). For this purpose, published experimental P-T-X data in this temperature and pressure range are reviewed. These data cover the two-phase region where a CO₂-rich phase (generally gas) and an H₂O-rich liquid coexist and are reported as the mutual solubilities of H₂O and CO₂ in the two coexisting phases. For the most part, mutual solubilities reported from various sources are in good agreement. In this paper, a noniterative procedure is presented to calculate the composition of the compressed CO₂ and liquid H₂O phases at equilibrium, based on equating chemical potentials and using the Redlich-Kwong equation of state to express departure from ideal behavior. The procedure is an extension of that used by King et al. (1992), covering a broader range of temperatures and experimental data than those authors, and is readily expandable to a nonideal liquid phase. The calculation method and formulation are kept as simple as possible to avoid degrading the performance of numerical models of water-CO₂ flows for which they are intended. The method is implemented in a computer routine, and inverse modeling is used to determine, simultaneously, (1) new Redlich-Kwong parameters for the CO₂-H₂O mixture, and (2) aqueous solubility constants for gaseous and liquid CO₂ as a function of temperature. In doing so, mutual solubilities of H₂O from 15 to 100°C and CO₂ from 12 to 110°C and up to 600 bar are generally reproduced within a few percent of experimental values. Fugacity coefficients of pure CO₂ are reproduced mostly within one percent of published reference data.     

Calcite solubility and speciation in supercritical NaCl-HCl aqueous fluids

The solubility of calcite in NaCl-H₂O and in HCl-H₂O fluids was measured using an extraction-quench hydrothermal apparatus. Experiments were conducted at 2 kbar, between 400° C and 600° C. Measurements in NaCl-H₂O were conducted in two ways: 1) at constant pressure and NaCl concentration, as a function of temperature; and 2) at constant pressure and temperature, as a function of NaCl concentration. In both the NaCl-H₂O and the HCl-H₂O systems, the solubility of calcite increases with increasing chlorine concentrations. For example, the log calcium molality in equilibrium with calcite increases from –3.75 at 2 kbar and 500° C, in pure H₂O to –3.10 at 2 kbar and 500° C at log NaCl molality=–1.67. At fixed pressure and NaCl molality, the solubility of calcite is almost constant from 400° C to 550° C, but increases somewhat at higher temperatures. The results can be used to determine the dominant calcium species in the experimental solutions as a function of NaCl concentration and to obtain values for the second dissociation constant of CaCl_2(aq). At 2 kbar, 400° C, 500° C, and 600° C, we calculate values for the log of the dissociation constant of CaCl⁺ of –2.1, –3.2, and –4.3, respectively. The 400° C and 500° C values are consistent with those obtained by Frantz and Marshall (1982) using electrical conductance techniques. However, our 600° C value is 0.8 log units higher than that reported by Frantz and Marshall. The calcite solubilities in the NaCl-H₂O and HCl-H₂O systems are inconsistent with the solubilities of calcite in pure H₂O reported by Walther and Long (1986). They are, however, consistent with the measurements of calcite solubilities in pure H₂O presented in this study. These results allow for the calculation of the solubilities of calcium silicates and carbonates in fluids that contain CO₂ and NaCl.     

A unified equation for calculating methane vapor pressures in the CH4-H2O system with measured Raman shifts

A unified equation has been derived by using all available data for calculating methane vapor pressures with measured Raman shifts of C-H symmetric stretching band (υ₁) in the vapor phase of sample fluids near room temperature. This equation eliminates discrepancies among the existing data sets and can be applied at any Raman laboratory. Raman shifts of C-H symmetric stretching band of methane in the vapor phase of CH₄-H₂O mixtures prepared in a high-pressure optical cell were also measured at temperatures between room temperature and 200 °C, and pressures up to 37 MPa. The results show that the CH₄υ₁ band position shifts to higher wavenumber as temperature increases. We also demonstrated that this Raman band shift is a simple function of methane vapor density, and, therefore, when combined with equation of state of methane, methane vapor pressures in the sample fluids at elevated temperatures can be calculated from measured Raman peak positions. This method can be applied to determine the pressure of CH₄-bearing systems, such as methane-rich fluid inclusions from sedimentary basins or experimental fluids in hydrothermal diamond-anvil cell or other types of optical cell.     

An experimental study of the solubility of molybdenum in H2O and KCl-H2O solutions from 500 °C to 800 °C, and 150 to 300 MPa

The solubility of molybdenum (Mo) was determined at temperatures from 500 °C to 800 °C and 150 to 300 MPa in KCl-H₂O and pure H₂O solutions in cold-seal experiments. The solutions were trapped as synthetic fluid inclusions in quartz at experimental conditions, and analyzed by laser ablation inductively coupled plasma mass spectrometry (LA ICPMS).Mo solubilities of 1.6 wt% in the case of KCl-bearing aqueous solutions and up to 0.8 wt% in pure H₂O were found. Mo solubility is temperature dependent, but not pressure dependent over the investigated range, and correlates positively with salinity (KCl concentration). Molar ratios of ∼1 for Mo/Cl and Mo/K are derived based on our data. In combination with results of synchrotron X-ray absorption spectroscopy of individual fluid inclusions, it is suggested that Mo-oxo-chloride complexes are present at high salinity (>20 wt% KCl) and ion pairs at moderate to low salinity (<11 wt% KCl) in KCl-H₂O aqueous solutions. Similarly, in the pure H₂O experiments molybdic acid is the dominant species in aqueous solution. The results of these hydrothermal Mo experiments fit with earlier studies conducted at lower temperatures and indicate that high Mo concentrations can be transported in aqueous solutions. Therefore, the Mo concentration in aqueous fluids seems not to be the limiting factor for ore formation, whereas precipitation processes and the availability of sulfur appear to be the main controlling factors in the formation of molybdenite (MoS₂).     

Experimental determination of the solubility of the assemblage paragonite,albite, and quartz in supercritical H2O

The concentrations of Na, Al, and Si in an aqueous fluid in equilibrium with natural albite, paragonite, and quartz have been measured between 350°C and 500°C and 1 to 2.5 kbar. Si is the dominant solute in solution and is near values reported for quartz solubility in pure H₂O. At 1 kbar the concentrations of Na and Al remain fairly constant from 350°C to 425°C but then decrease at 450°C. At 2 kbar, Na increases slightly with increasing temperature while Al remains nearly constant. Concentrations of Si, Na, and Al all increase with increasing pressure at constant temperature.The molality of Al is close to that of Na and is nearly a log unit greater than calculated molalities assuming Al(OH)⁰₃ is the dominant Al species. This indicates a Na-Al complex is the dominant Al species in solution as shown by Anderson and Burnham (1983) at higher temperature and pressure. The complex can be written as NaAl(OH)⁰₄ ± nSiO₂ where n is the number of Si atoms in the complex. The value of n is not well constrained but appears to be less than or equal to 3.The results indicate Al can be readily transported in pure H₂O solutions at temperatures and pressures as low as 350°C and 1 kbar.     

Carbonic metamorphism of charnockites in the southwestern Indian Shield: A fluid inclusion study

Forming the southwestern segment of the Precambrian granulite facies terrain of the Indian shield, the Kerala region largely comprises charnockites, khondalites and migmatitic gneisses. Fluid inclusions in quartz from the charnockites show distinct distribution patterns consistent with three generations of inclusions. The early monophase type records entrapment of high-density CO₂-rich fluid (0.95–1.0 g cm⁻³). A subsequent monophase type with lower-density CO₂-rich fluid (0.65–0.75 g cm⁻³) coexists with CO₂H₂O inclusions having an average degree of filling of 0.2 (H₂O = 20%; CO₂ = 80%). Late aqueous biphase inclusions show coexistence with a second category of CO₂H₂O inclusions showing a degree of filling of 0.6 (H₂O = 60%; CO₂ = 40%). The CO₂-isochores for early carbonic inclusions yield a pressure range of 4.6–6.1 kbar at granulite facies temperatures of 650–800°C, depicting the entrapment of fluids present during or close to the peak metamorphic stage. A definite sequence of fluid evolution is traceable for the subsequent stages. Thus, the coexisting CO₂ and CO₂H₂O inclusions were entrapped at 510°C and 2.2 kbar, marking the waning of carbonic regime and the beginning of aqueous regime. At 330°C and 0.4 kbar, fluid unmixing occurred, leading to the simultaneous entrapment of mixed CO₂H₂O and H₂O inclusions along rehealed microfractures. The data presented indicate that the metamorphic fluids evolved from early high-density carbonic through mixed carbonic-aqueous to late aqueous types. The dry granulite mineral assemblage of charnockites is a result of metamorphic equilibration under water-deficient and high-P_CO2 conditions.     

A high temperature equation of state for the H2O-CaCl2 and H2O-MgCl2 systems

An equation of state (EOS) is developed for salt-water systems in the high temperature range. As an example of the applications, this EOS is parameterized for the calculation of density, immiscibility, and the compositions of coexisting phases in the CaCl₂-H₂O and MgCl₂-H₂O systems from 523 to 973 K and from saturation pressure to 1500 bar. All available volumetric and phase equilibrium measurements of these binaries are well represented by this equation. This EOS is based on a Helmholtz free energy representation constructed from a reference system containing hard-sphere and polar contributions plus an empirical correction. For the temperature and pressure range in this study, the electrolyte solutes are assumed to be associated. The water molecules are modeled as hard spheres with point dipoles and the solute molecules, MgCl₂ and CaCl₂, as hard spheres with point quadrupoles. The free energy of the reference system is calculated from an analytical representation of the Helmholtz free energy of the hard-sphere contributions and perturbative estimates of the electrostatic contributions. The empirical correction used to account for deviations of the reference system predictions from measured data is based on a virial expansion. The formalism allows generalization to aqueous systems containing insoluble gases (CO₂, CH₄), alkali chlorides (NaCl, KCl), and alkaline earth chlorides (CaCl₂, MgCl₂). The program of this model is available as an electronic annex (see EA1 and EA2) and can also be downloaded at: http://www.geochem-model.org/programs.htm.     

Ternary system H<Subscript>2</Subscript>O-CO<Subscript>2</Subscript>-NaCl at high <Emphasis Type="Italic">T</Emphasis>-<Emphasis Type="Italic">P</Emphasis> parameters: An empirical mixing model

New experimental data on the solubility of NaCl in gaseous CO₂ were obtained at pressures (P) of 30–70 MPa and temperatures of 623 and 673 K on experimental equipment making possible to sample a portion of the gas in the course of the experiment. The new measures have demonstrated that the NaCl solubility increases with increasing temperature (T) and pressure and is approximately four to five orders of magnitude higher than the saturated vapor pressure of NaCl at the corresponding temperature. The paper also reports newly obtained experimental data on the equilibrium conditions of the reaction of talc decomposition into enstatite and quartz at a variable H₂O/NaCl ratio in the fluid. The results of the experiments validate the empirical equations previously suggested for H₂O and NaCl activities in concentrated aqueous salt solutions that can be used in describing silica-saturated fluids at high T-P parameters. A new empirical equation is suggested for the Gibbs free mixing energy in the H₂O-CO₂-NaCl ternary system, with the parameters of the equation calibrated against experimental data on phase equilibria in marginal binary systems and on the location of the boundary of the region of homogeneous three-component fluid according to data on synthetic fluid inclusions in quartz.     

Prediction of oxygen solubility in pure water and brines up to high temperatures and pressures

A thermodynamic model is presented to calculate the oxygen solubility in pure water (273-600 K, 0-200 bar) and natural brines containing Na⁺, K⁺, Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, over a wide range of temperature, pressure and ionic strength with or close to experimental accuracy. This model is based on an accurate equation of state to calculate vapor phase chemical potential and a specific particle interaction model for liquid phase chemical potential. With this approach, the model can not only reproduce the existing experimental data, but also extrapolate beyond the data range from simple aqueous salt system to complicated brine systems including seawater. Compared with previous models, this model covers much wider temperature and pressure space in variable composition brine systems. A program for this model can be downloaded from the website: http://www.geochem-model.org.     

A simple relationship between isothermal bulk modulus and thermal pressure for geophysical minerals

The variations in isothermal bulk modulus with an increase in temperature are found to be related linearly with the change in thermal pressure for geophysical minerals, such as MgO, CaO, Al₂O₃, MgAl₂O₄ and Mg₂SiO₄. Analysis of the relationship yields a value of the Anderson–Gruneisen parameter for each mineral in close agreement with known values. An important finding of the present study is the derivation of an isobaric equation of state representing the relationship between volume and temperature at ambient pressure. This equation for isobaric volume expansion looks like the Birch equation for isothermal compression. The calculated values of volume expansion for the minerals at high temperatures present close agreement with the available experimental data. The formulation developed in the present study has also been used to predict the volumes at simultaneously elevated temperatures and pressures for CaSiO₃ perovskite and NaCl minerals, in good agreement with the experimental values.     

Equations of state of CaSiO3 Perovskite: a molecular dynamics study

The molar volumes and bulk moduli of CaSiO₃ perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K ₀′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO₃ perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO₃ perovskite. Our results support the view that CaSiO₃ perovskite remains invisible in the Earth’s lower mantle.     

An improved model calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar

A thermodynamic model for the solubility of carbon dioxide (CO₂) in pure water and in aqueous NaCl solutions for temperatures from 273 to 533 K, for pressures from 0 to 2000 bar, and for ionic strength from 0 to 4.3 m is presented. The model is based on a specific particle interaction theory for the liquid phase and a highly accurate equation of state for the vapor phase. With this specific interaction approach, this model is able to predict CO₂ solubility in other systems, such as CO₂–H₂O–CaCl₂ and CO₂–seawater, without fitting experimental data from these systems. Comparison of the model predictions with experimental data indicates that the model is within or close to experimental uncertainty, which is about 7% in CO₂ solubility.