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An activity-fugacity model is presented to calculate the N2, O2 and Ar solubility in pure water and aqueous electrolyte solutions. It is based on the Pitzer electrolyte theory for activity coefficient and an accurate equation of state for the fugacity of vapor phase. The model can accurately calculate the N2 solubility in pure water (273–636 K and 1–600 bar), aqueous NaCl solution (278–398 K, 1–616 bar and 0–6 mol/kg) and aqueous KCl, CaCl2, Na2SO4 and MgSO4 solutions, the O2 solubility in pure water (273–616 K and 0.2–202 bar) and aqueous NaCl, KCl, MgCl2, CaCl2, Na2SO4, K2SO4 and MgSO4 solutions, and the Ar solubility in pure water (273–568 K and 1–127 bar) and aqueous NaCl, KCl, MgCl2 and CaCl2 solutions. The model can not only reproduce the reliable experimental data available, but also can be extended to predict the N2, O2 and Ar solubility in aqueous mixed-salt solution like seawater. The solubility of air in pure water or aqueous NaCl solution can be predicted from this model by the sum of solubility of N2, O2 and Ar in pure water or aqueous NaCl solution, covering a wide range of temperature, pressure and ionic strength. The program for this model can be obtained from the corresponding author ( maoshide@163.com ).

A simple and general relation between the solubility of quartz and the density of solution is derived rigorously. Based on this relation and the pressure-volume-temperature-composition model of Mao et al. (2010), an accurate density-based model is developed for the solubility of quartz in aqueous NaCl and/or CO2 solution up to 1273 K and 20,000 bar. The model parameters are regressed with carefully assessed experimental data. Compared to a large number of experimental data, the average absolute deviations of calculated quartz solubilities in water, aqueous NaCl solution and aqueous CO2 solution are 5.50%, 5.24% and 7.55%, respectively, which are within experimental uncertainties, and are much better than the most competitive models in literature. Particularly, this model can predict the experimental solubility of quartz in aqueous NaCl and CO2 solution without using any additional parameter. This model can be incorporated in software for accurate geochemical modeling. The strategy of this model should be promising for the solubilities of other minerals in water or multicomponent aqueous solutions.

An equation of state (EOS) explicit in Helmholtz free energy has been developed to calculate the vapor-liquid equilibrium (VLE) and pressure-volume-temperature-composition (PVTx) properties of the H2S H2O fluid mixture. This EOS, where five mixing parameters are used, is based on the highly accurate EOSs of pure H2S and H2O fluids, and contains a simple departure function. Compared to reliable experimental data available, the average absolute deviations of H2S solubility in liquid phase, water content in vapor phase, and liquid density of the H2S H2O system are 3.88%, 5.03% and 0.20%, respectively. The EOS of the H2S H2O fluid mixture, together with the Pitzer activity coefficient of H2S in aqueous NaCl solution from previous study, can be used to predict the H2S solubility in aqueous NaCl solution with an average absolute deviation of 7.52%. The water content of vapor phase in the H2S H2O NaCl system can be reproduced with the fluid EOS of H2S H2O system by a fugacity-activity method within experimental uncertainties. The fluid EOS of H2S H2O system, combined with the Helmholtz free energy EOS of H2O NaCl fluid mixture, can predict the PVTx properties of the H2S H2O NaCl mixture without using additional mixing parameters. The developed EOS can be safely used under the conditions of CO2 capture and sequestration (273–473 K, 0–400 bar and 0–6 mol kg−1), beyond which the EOS also has some extrapolated ability. The computer codes are in the supplemental data and can be downloaded from Applied Geochemistry or obtained from the corresponding author.

A general equation of state (EOS) explicit in Helmholtz free energy has been developed to predict the pressure–volume-temperature-composition ( PVTx ) and vapor-liquid equilibrium (VLE) properties of the CH 4 –C 2 H 6 –C 3 H 8 –CO 2 –N 2 fluid mixtures (main components of natural gases). This EOS, which is a function of temperature, density and composition, with four mixing parameters used, is based on the improved EOS of Sun and Ely (2004) for the pure components (CH 4 , C 2 H 6 , C 3 H 8 , CO 2 and N 2 ) and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Comparison with the experimental data available indicates that the EOS can calculate the PVTx and VLE properties of the CH 4 –C 2 H 6 –C 3 H 8 –CO 2 –N 2 fluid mixtures within or close to experimental uncertainties up to 623 K and 1000 bar within full range of composition. Isochores of the CH 4 –C 2 H 6 –C 3 H 8 –CO 2 –N 2 system can be directly calculated from this EOS to interpret the corresponding microthermometric and Raman analysis data of fluid inclusions. The general EOS can calculate other thermodynamic properties if the ideal Helmholtz free energy of fluids is combined, and can also be extended to the multi-component natural gases including the secondary alkanes (carbon number above three) and none-alkane components such as H 2 S, SO 2 , O 2 , CO, Ar and H 2 O. This part of work will be finished in the near future.

Based on the Pitzer electrolyte theory, an accurate density model of binary sulfate-water systems (Li2SO4-H2O, Na2SO4-H2O, K2SO4-H2O and MgSO4-H2O) has been established. Corresponding model parameters are obtained by the least square method. Compared with reliable experimental data of the Li2SO4-H2O, Na2SO4-H2O, K2SO4-H2O and MgSO4-H2O systems, the average density deviations are 0.046%, 0.036%, 0.051%, 0.038%, respectively, which are within or close to experimental uncertainties. Combined a simple mixing rule with the density models of binary sulfate-water systems and previous chloride-water systems (LiCl-H2O, NaCl-H2O, KCl-H2O, MgCl2-H2O and CaCl2-H2O), a predictive density model is proposed for aqueous mixed electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl− and SO42− under conditions of CO2 capture and sequestration (CCS) (generally less than 473 K and 300 bar). Compared to experimental density data of multi-component water-salt systems, the average density deviation of each system is usually less than 0.1%. The model can be used to calculate the apparent molar volume at infinite dilution and the volumetric properties of CO2-bearing multi-component electrolyte solutions under the CCS conditions. A computer code for the volumetric properties of multi-component aqueous electrolyte solutions can be obtained from the corresponding author.

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.

Based on the Pitzer electrolyte theory for activity coefficient and an accurate equation of state for vapor fugacity, an improved activity-fugacity model is developed to calculate CO2 solubility in aqueous KCl, MgCl2, CaCl2, Na2SO4, K2SO4 and MgSO4 solutions, respectively. The valid range of temperature, pressure and ion strength is up to 450 K, 500 bar and 5 mol kg− 1. Average absolute deviation of CO2 solubility is about 5% compared to a large number of experimental data available, within or close to experimental uncertainties. By combining the interaction parameters of CO2 and ions developed here with those of CO2 and Na+ and Cl− from an earlier study of Mao et al. (2013), this model can be used to accurately predict CO2 solubility in aqueous mixed-salt solution containing Na+, K+, Mg2 +, Ca2 +, Cl− and SO2–4under conditions of CO2 capture and sequestration (generally less than 423 K and 500 bar). Computer code of the application program can be obtained from the corresponding author ( maoshide@163.com ).

An equation of state (EOS) explicit in Helmholtz free energy has been improved to calculate the PVTx and vapor–liquid phase equilibrium properties of CH4–CO2 fluid mixture. This EOS, where four mixing parameters are used, is based on highly accurate EOSs recommended by NIST for pure components (CH4 and CO2) and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Comparison with experimental data available indicates that the EOS can calculate both vapor–liquid phase equilibrium and volumetric properties of this binary fluid system with accuracy close to that of experimental data up to high temperature and pressure within full range of composition. The EOS of CH4–CO2 fluid, together with the updated Gibbs free energy model of solid CO2 (dry ice), is applied to calculate the CH4 content (xCH4) and molar volume (Vm) of the CH4–CO2 fluid inclusion based on the assumption that the volume of an inclusion keeps constant during heating and cooling. Vm−xCH4 diagrams are presented, which describe phase transitions involving vapor, liquid and CO2 solid phases of CH4–CO2 fluid inclusions. Isochores of CH4–CO2 inclusions at given xCH4 and Vm can be easily calculated from the improved EOS.

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.

Since 1990, many groups of pressure–volume–temperature (PVT) data from experiments and molecular dynamics (MD) or Monte Carlo (MC) simulations have been reported for supercritical and subcritical water. In this work, fifteen groups of PVT data (253.15–4356 K and 0–90.5 GPa) are evaluated in detail with the aid of the highly accurate IAPWS-95 formulation. The evaluation gives the following results: (1) Six datasets are found to be of good accuracy. They include the simulated results based on SPCE potential above 100 MPa and those derived from sound velocity measurements, but the simulated results below 100 MPa have large uncertainties. (2) The data from measurements with a piston cylinder apparatus and simulations with an exp-6 potential contain large uncertainties and systematic deviations. (3) The other seven datasets show obvious systematic deviations. They include those from experiments with synthesized fluid inclusion techniques (three groups), measured velocities of sound (one group), and automated high-pressure dilatometer (one group) and simulations with TIP4P potential (two groups), where the simulated data based on TIP4P potential below 200 MPa have large uncertainties. (4) The simulated data but those below 1 GPa agree with each other within 2–3%, and mostly within 2%. The data from fluid inclusions show similar systematic deviations, which are less than 2–5%. The data obtained with automated high-pressure dilatometer and those derived from sound velocity measurements agree with each other within 0.3–0.6% in most cases, except for those above 10 GPa. In principle, the systematic deviations mentioned above, except for those of the simulated data below 1 GPa, can be largely eliminated or significantly reduced by appropriate corrections, and then the accuracy of the relevant data can be improved significantly. These are very important for the improvement of experiments or simulations and the refinement and correct use of the PVT data in developing thermodynamic models of water or water-bearing fluids.

A predictive thermodynamic model is constructed to calculate the pressure–volume–temperature–composition (PVTx) properties of CO2–H2O–NaCl fluid mixtures by the Helmholtz free energy model of CO2–H2O fluid mixtures. The new model uses no other mixing parameters but those of the CO2–H2O system, because the Helmholtz free energy of H2O–NaCl fluid at a given composition is equivalently converted into that of pure H2O by a scaled temperature redefined at the same pressure. In addition, the parameters developed by Driesner (2007) in the PVTx model of H2O–NaCl fluid system are refitted by the IAPWS-95 formulation. Comparisons with experimental data available show that the model can reproduce the single-phase PVTx properties of H2O–NaCl and CO2–H2O–NaCl fluid mixtures of all compositions from 273 to 1273 K and from 0 to 5000 bar, within or close to experimental uncertainty in most cases (with slightly lower accuracy at 5000–10,000 bar). The isochores of CO2–H2O–NaCl fluid can be obtained from this model by a bisection algorithm, and an application example is given to analyze some natural CO2–H2O–NaCl fluid inclusions in quartz from a wolframite deposit. Computer program code for calculation of molar volume of the CO2–H2O–NaCl fluid as a function of temperature, pressure and composition can be obtained from the corresponding author ( maoshide@163.com ).

article i nfo Article history: To determine compositions, homogenization pressures and isopleths of CO2-H2O-NaCl fluid inclusions, an im- proved activity-fugacity model is developed to calculate CO2 solubility in aqueous NaCl solutions. The model can predict the CO2 solubility in aqueous NaCl solutions from 273.15 K to 723.15 K, from 1 bar to 1500 bar and from 0 to 4.5 mol kg −1 of NaCl, within or close to experimental uncertainties. Compared to a large number of reliable experimental solubility data available, the average absolute deviation is 4.62% for the CO2 solubility in aqueous NaCl solutions. In the near-critical region, the calculated CO2 solubility deviations increase to over 10%. The CO2 solubility model, together with the updated volumetric model of CO2-H2O-NaCl fluid mixtures, is applied to calculate the CO2 contents, homogenization pressures, molar volumes and volume fractions of the CO2-H2O-NaCl fluid inclusions by an iterative method based on the assumption that the volume of an inclusion keeps constant during heating and cooling. Calculation program code of the CO2 solubility in aqueous NaCl solu- tions can be obtained from Chemical Geology or the correspondence author (maoshide@163.com).

This paper reports the application of thermodynamic models, including equations of state, to ternary CH4 H2O NaCl fluid inclusions. A simple equation describing pressure–temperature–salinity relations on the CH4 hydrate-liquid-vapor surface has been developed to calculate the NaCl contents (salinities) of inclusions, where the dissociation pressure of CH4 hydrate coexisting with vapor and liquid at a given temperature is calculated with a pressure equation of pure CH4. The pressure equation is a function of temperature and CH4 Raman peak position shift corrected by Ne lamp. With these relations and the latest CH4 solubility and PVTx models, a new iterative approach is presented to calculate the CH4 contents of CH4 H2O NaCl inclusions on the assumption that the bulk molar volume of an inclusion at the melting temperature of CH4 hydrate and at the vapor bubble disappearance (homogenization) temperature are identical. A prominent merit of this method is that the compositions, molar volumes and homogenization pressures of CH4 H2O NaCl inclusions can be simultaneously obtained without having to use volume fractions of vapor bubbles at the dissociation temperatures of CH4 hydrates determined based on optical observations or measurements. The homogenization pressures and isochores of CH4 H2O NaCl fluid inclusions from updated models are briefly discussed. The code to estimate PVTx properties of inclusions in the ternary system CH4 H2O NaCl, based on microthermometric and Raman data, can be obtained from Chemical Geology or the corresponding author ( maoshide@163.com ).

The IAPWS-95 formulation explicit in Helmholtz free energy proposed by Wagner and Prus (The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, Journal of Physical and Chemical Reference Data 2002 31(2), 387–535) is extended to calculate the volumetric property of the fluid water from 1 GPa and 273 K to 20 GPa and 4273 K. Comparison with large experimental and molecular dynamic simulation data above 1 GPa shows that the equation of state can reproduce the volume of the fluid water with an average absolute deviation of 0.52%. Thus the original IAPWS-95 formulation together with the extended part can be used in a much larger temperature–pressure region: 273–4273 K and 0–20 GPa. In addition, this paper also reports a reliable and highly efficient method to calculate the saturated properties of water so that the equation of state can be conveniently applied in the study of fluid inclusion: calculating homogenization pressures, homogenization densities (or molar volumes) and isochores. Computer code of the model can be obtained from the first author.

article i nfo A thermodynamic model explicit in Helmholtz free energy is constructed to calculate the single-phase PVTx properties of the CO2-CH4-C2H6-N2-H2O fluid mixtures. Parameters of the binary CO2-H2O, CH4-H2O, C2H6- H2O and N2-H2O mixtures are regressed from assessed experimental data. On the basis of the binary mixture parameters, the model can be used to predict the single-phase volumes of the CO2-CH4-C2H6-N2-H2O-NaCl fluid mixtures with a simple approach. Comparison with a large number of experimental data shows that the model can reproduce the single-phase PVTx properties of the CO2-CH4-C2H6-N2-H2O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar, with or close to experimental accuracy. Online calculations can be made on the website: www.geochem-model.org/.

Accurate prediction of both volumetric and vapor–liquid phase equilibria of binary CO2–H2O and CH4–H2O mixtures with a single equation of state proves to be difficult. In this study we use an activity–fugacity model to predict the vapor–liquid phase equilibria above 523 K and adapt a Helmoholtz model to calculate volumetric properties of these two binary systems. The average deviations of water content in the vapor phase from experimental data are 3.25% and 3.19% for the CO2–H2O and CH4–H2O mixtures, respectively, and the average deviations of gas solubility in liquid phase from experimental data are 4.29% and 3.50%, respectively. The model can find wide applications, and an example is given for the analysis of fluid inclusions in geochemistry.

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.

A thermodynamic model is presented to calculate methane solubility, liquid phase density and gas phase composition of the H2O–CH4 and H2O–CH4–NaCl systems from 273 to 523 K (possibly up to 573 K), from 1 to 2000 bar and from 0 to 6 mol kg−1 of NaCl with experimental accuracy. By a more strict theoretical approach and using updated experimental data, this model made substantial improvements over previous models: (1) the accuracy of methane solubility in pure water in the temperature range between 273 and 283 K is increased from about 10% to about 5%, but confirms the accuracy of the Duan model [Duan Z., Moller N., Weare J.H., 1992a. Prediction of methane solubilities in natural waters to high ionic strength from 0 to 250 °C and from 0 to 1600 bar. Geochim. Cosmochim. Acta 56, 1451–1460] above 283 K up to 2000 bar; (2) the accuracy of methane solubility in the NaCl aqueous solutions is increased from >12% to about 6% on average from 273 K and 1 bar to 523 K and 2000 bar; (3) this model is able to calculate water content in the gas phase and liquid phase density, which cannot be calculated by previous models; and (4) it covers a wider range of temperature and pressure space. With a simple approach, this model is extended to predict CH4 solubility in other aqueous salt solutions containing Na+, K+, Mg2+, Ca2+, Cl− and SO 4 2 − , such as seawater and geothermal brines, with excellent accuracy. This model is also able to calculate homogenization pressure of fluid inclusions (CH4–H2O–NaCl) and CH4 solubility in water at gas–liquid–hydrate phase equilibrium. A computer code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm .

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 .