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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.

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 .