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The SW96 formulation explicit in Helmholtz free energy proposed by Span and Wagner (1996) is the most accurate multifunction equation of state of CO2 fluid, from which all thermodynamic properties can be obtained over a wide temperature-pressure range from 216.592 to 1100 K and from 0 to 8000 bar with or close to experimental accuracy. This paper reports the applications of the SW96 formulation in fluid inclusions and mineral-fluid equilibria. A reliable and highly efficient algorithm is presented for the saturated properties of CO2 so that the formulation can be conveniently applied in the study of fluid inclusions, such as calculation of homogenization pressures, homogenization densities (or molar volumes), volume fractions of vapor phase and isochores. Meanwhile, the univariant curves of some typical decarbonation reactions of minerals are calculated with the SW96 formulation and relevant thermodynamic models of minerals. The computer code of the SW96 formulation can be obtained from the corresponding author.

An equation of state (EOS) in the form of Helmholtz free energy for fluid mixtures was improved by using four mixing parameters. It can calculate the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of the CO2–N2 fluid mixture. This EOS is based on highly accurate EOSs of pure CO2 and N2 fluids and contains a simple generalized departure function of Lemmon and Jacobsen (1999). This EOS can reproduce experimental PVTx and VLE data available up to 673 K and 1000 bar, with an accuracy within or close to experimental uncertainties. The EOS of CO2–N2 fluid mixture and an updated Gibbs free energy model of solid CO2, can be combined to determine the compositions and molar volumes of CO2–N2 fluid inclusions with the melting temperature of solid CO2 and the vapor-liquid homogenization temperature which can be directly obtained from experimental microthermometric analysis. Isochores of CO2–N2 inclusions can be easily calculated from this EOS.

Some errors and metastable phase relations are found in a recently reported oxygen fugacity–silica activity [log f O2-log a (SiO2)] diagram of the fayalite-kirschsteinite-hedenbergite-magnetite-wollastonite (Fa-Kst-Hd-Mt-Wo) system at 400 °C and 1 kbar (Markl et al. 2001). Systematic thermodynamic analysis reveals that the composite exsolution lamellae of Mt and Hd in the olivine from the Ilimaussaq Intrusion, Greenland, should form when the reaction 3Fa+3Kst+O2 = 3Hd+2Mt is overstepped on rapid cooling. This process is also accompanied by favorable f O2 and a (SiO2) conditions. It is also found that the reaction mechanisms from Ca-Fe-rich olivine (Fa+Kst) to Mt+Hd are very different above and below the equilibrium temperature of the Mt-absent reaction Hd+Kst = Fa+2Wo. The mechanisms above the equilibrium temperature are obviously simpler than those below the equilibrium temperature. Despite this difference, the two types of mechanisms have many features in common: (1) Mt and Hd can form in Ca-Fe-rich olivine on continuous cooling; (2) If a (SiO2) is not buffered, an increase in f O2 alone is enough to transform Ca-Fe-rich olivine into Mt and Hd; (3) At a fixed f O2 or a (SiO2), the formation of Mt and/or Hd on cooling requires appropriate a (SiO2) or f O2; and (4) The increase in a (SiO2) is favorable to the formation of Hd, but it is not essential for the intergrown exsolution of Mt and Hd. These common features are closely related to the fact that the process from Fa+Kst to Mt+Hd is an entropy decreasing oxidation reaction.

A highly accurate P, V, T,x model is developed for aqueous chloride solutions of the binary systems, viz. (LiCl + H2O), (NaCl + H2O), (KCl + H2O), (MgCl2 +H 2O), (CaCl2 +H 2O), (SrCl2 +H 2O), and (BaCl2 +H 2O). The applied ranges of temperature, pressure, and concentrations for the systems (LiCl + H2O), (NaCl + H2O), (KCl + H2O), (MgCl2 +H 2O), (CaCl2 +H 2O), (SrCl2 +H 2O), and (BaCl2 +H 2O) are (273 K to 564 K, 0.1 MPa to 40 MPa, and 0 to 10 molal), (273 K to 573 K, 0.1 MPa to 100 MPa, and 0 to 6.0 molal), (273 K to 543 K, 0.1 MPa to 50 MPa, and 0 to 4.5 molal), (273 K to 543 K, 0.1 MPa to 40 MPa, and 0 to 3.0 molal), (273 K to 523 K, 0.1 MPa to 60 MPa, and 0 to 6.0 molal), (298 K to 473 K, 0.1 MPa to 2 MPa, and 0 to 2.0 molal) and (273 K to 473 K, 0.1 MPa to 20 MPa, and 0 to 1.6 molal), respectively. Comparison of the model with thousands of experimental data points concludes that the average deviation over the above T, P, m range is 0.020% to 0.066% in density (or volume) for these systems, which indicates high accuracy. From this model, various volumetric properties, such as the apparent molar volume at infinite dilution and isochores of fluid inclusions, can be calculated, thus having a wide range of geological applications, such as reservoir fluid flow simulation and fluid-inclusion study. A computer code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm and online calculations is made available on: www.geochem-model.org/models.htm

It is proved that the fugacity coefficient (ϕ) of a mixture and the fugacity coefficient of component i ( ϕ ˆ i ) follow the relation ln ϕ ˆ i = ∂ ( n ln ϕ ) / ∂ n i T , P , n j ( j ≠ i ) , = ∂ ( n ln ϕ ) / ∂ n i T , P , V t , n j ( j ≠ i ) , where ni is the amount-of-substance of component i, and T, P, Vt and n are the temperature, pressure, total volume and total amount-of-substance of the system, respectively. This relation is very useful for the derivation of ϕ ˆ i . It allows the ϕ function to contain both P and V, so ϕ can be expressed with various equations of state (either volume-explicit or pressure-explicit). This approach can also use the similarity of the ϕ expressions of pure fluids and mixtures to simplify the derivation of ϕ ˆ i . Besides, ϕ ˆ i can also be directly derived from equation of state through a variation of the approach above. These approaches are much easier than the commonly used ones when the equation of state for fluids is complex.

An accurate model is presented to calculate the solubilities of C2H6 in pure water (273–444 K and 0–1000 bar) and in aqueous NaCl solutions (273–348 K, 0–16 bar and 0–6.3 mol kg−1). This model is based on a specific particle interaction theory for liquid phase and a new accurate equation of state developed in this study for vapor phase. Precision of the model is within or close to the uncertainty of experimental solubilities (about 7%). A FORTRAN code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm .

The IAPWS-95 formulation explicit in Helmholtz free energy proposed by Wagner and Pruβ (2002) is the best equation of state of water, from which all thermodynamic properties can be obtained over a wide T – p range from 273.16 to 1273 K and from 0 to 1000 MPa with experimental accuracy. This paper reports the applications of the IAPWS-95 formulation in fluid inclusion and mineral-water phase equilibria. A reliable and highly efficient calculation method is presented for the saturated properties of water so that the formulation can be conveniently applied in the study of fluid inclusion, such as calculating homogenization pressures, homogenization densities (or molar volumes), volume fractions and isochores. Meanwhile, the univariant curves of some mineral-dehydration reactions are calculated based on the IAPWS-95 formulation. The computer code of the IAPWS-95 formulation can be obtained from the corresponding author.