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Thermodynamic description of equilibria in mixed fluids (H2O-nonpolar gas) in a wide range of temperatures (25–700°C) and pressures (1–5000 bar)

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Abstract

A new method is proposed for calculating equilibria in mixed multicomponent systems H2O-nonpolar gas at high temperatures and pressures. The method is based on calculation of electrostatic interactions between a solute component and surrounding molecules of a solvent (H2O). The SUPCRT98 database and the Helgeson-Kirkham-Flowers equation of state for components of an aqueous solution were used for computer realization of the method. The thermodynamic properties of solute gases at elevated temperatures and pressures are calculated by the Redlich-Kwong equation. The dielectric properties of a mixed solvent are determined using the modified Kirkwood equation. The proposed method was approved in description of the available set of experimental data on constants of H2O and NaCl dissociation, as well as data on solubility of both covalent and ionic crystals [SiO2, AgCl, Ag2SO4, Ca(OH)2, CaCO3] in mixed solvents H2O-nonpolar component [1,4-dioxane (C4H4O2), Ar, CO2]. The calculation and experimental data agree in a wide range of PTx conditions (temperatures up to 500°C, pressures up to 5000 bar, and mole fractions (x) of a nonpolar component in fluid up to 0.3). The proposed approach can be used for assessing the Born parameters of solute components. The calculation algorithm developed allows us not only to consider separate reactions but also to study equilibria in hydrothermal systems as a whole. Hence, the proposed approach can be used for constructing thermodynamic models of evolution of fluids rich in volatile components and vital to natural processes of mineral formation.

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References

  1. Ya. Yu. Akhadov, Dielectric Properties of Binary Solutions. Handbook (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  2. N. N. Akinfiev, “Algorithm of Calculation of Heterogeneous Equilibria for Electronic Microcomputers,” Geokhimiya, No. 6, 882–890 (1986).

  3. N. N. Akinfiev, “Program BALANS for Calculating Equilibria in Multisystems,” in Abstract of Papers for MGRI Conference “Progress in Earth Sciences” (Moscow, 1993), p. 70 [in Russian].

  4. N. N. Akinfiev, “Calculation Model for Ore Deposition from Boiling Fluid with Regard for Dielectric Permeability,” Geokhimiya, No. 10, 1465–1478 (1994).

  5. N. N. Akinfiev, “Thermodynamic Description of H2O-Gas Binary Systems Using the Redlich-Kwong Equation in a Wide Range of Parameters of State,” Geokhimiya, No. 2, 226–234 (1997) [Geochem. Int., 1997, No. 2, pp. 188–196].

  6. N. N. Akinfiev, “Method for Calculating Equilibria in H2O-Nonpolar Gas Mixed Fluids with Regard for Dielectric Permeability,” Geokhimiya, No. 3, 1–9 (1998) [Geochem. Int., 1998, No. 3, pp. 250–257].

  7. N. N. Akinfiev and A. V. Zotov, “Thermodynamic Description of Chloride, Hydrosulfide, and Hydroxyl Complexes of Ag(I), Cu(I), and Au(I) at Temperatures of 25–500°C and Pressures of 1–2000 Bars,” Geokhimiya, No. 10, 1–17 (2001).

  8. N. N. Akinfiev, A. V. Zotov, Zh. Shott, et al., “The Study of Chlorargyrite Solubility in H2O-CO2 Fluid at 400°C: Experiment and Thermodynamic Description,” Geokhimiya, No. 11, 1133–1142 (1998) [Geochem. Int., 1998, No. 11, pp. 1023–1037].

  9. J. Alvarez, R. Crovetto, and R. Fernandez-Prini, “The Dissolution of N2 and H2 in Water from Room Temperature to 640 K,” Ber. Bunsenges. Phys. Chem. 92, 935–940 (1988).

    Google Scholar 

  10. D. G. Archer and P. Wang, “The Dielectric Constant of Water and Debye-Hückel Limiting Law Slopes,” J. Phys. Chem. Ref. Data 19, 371–411 (1990).

    Google Scholar 

  11. M. Born, Von, “Volumen und Hydratationswarme der Ionen,” Zeitschr. Physik 1, 45–48 (1920).

    Google Scholar 

  12. T. S. Bowers, “The Deposition of Gold and Other Metals: Pressure-Induced Fluid Immiscibility and Associated Stable Isotope Signatures,” Geochim. Cosmochim. Acta 55, 2417–2434 (1991).

    Article  Google Scholar 

  13. T. S. Bowers and H. C. Helgeson, “Calculation of the Thermodynamic and Geochemical Consequences of Nonideal Mixing in the System H2O-CO2-NaCl on Phase Relations in Geologic Systems: Equation of State for H2O-CO2-NaCl Fluids at High Pressures and Temperatures,” Geochim. Cosmochim. Acta 47, 1247–1275 (1983).

    Article  Google Scholar 

  14. S. A. Clongh, Y. Beers, and G. P. Klein, “Dipole Moments of Water From Stark Measurements of H2O, HDO, and D2O,” J. Chem. Phys. 59, 2254–2259 (1973).

    Google Scholar 

  15. R. Crovetto and R. H. Wood, “Solubility in Water and Density of Aqueous CO2 Near the Solvent Critical Temperature,” Fluid Phase Equilib. 74, 271–288 (1992).

    Article  Google Scholar 

  16. J.-L. Dandurand and J. Schott, “Prediction of Ion Association in Mixed-Crustal Fluids,” J. Phys. Chem. 96, 7770–7777 (1992).

    Article  Google Scholar 

  17. T. W. Davis, E. J. Ricci, C. G. Sauter, “Solubilities of Salts in Dioxane-Water Solvents,” J. Am. Chem. Soc. 61, 3274–3284 (1939).

    Google Scholar 

  18. R. Deul and E. U. Frank, “Dielectric Constant of Water-Benzene Mixture System to 400°C and 2800 bar,” Ber. Bunsen-Ges. Phys. Chem. 95(8), 847–853 (1991).

    Google Scholar 

  19. S. E. Drummond and H. Ohmoto, “Chemical Evolution and Mineral Deposition in Boiling Hydrothermal Systems,” Econ. Geol. 80, 126–147 (1985).

    Google Scholar 

  20. J. Dubessi, C. Ramboz, C. Ngueyen-Trung, et al., “Physical and Chemical Controls (\(f_{O_2 } \), T, pH) of the Opposite Behaviour of U and Sn-W as Examplified by Hydrothermal Deposits in France and Great Britain, and Solubility Data,” Bull. Mineral 110, 261–281 (1987).

    Google Scholar 

  21. J. Dubessy, B. Poty, and C. Ranboz, “Advances in C-O-H-N-S Fluid Geochemistry Based on MICROGRAM Spectrometric Analysis of Fluid Inclusions,” Eur. J. Mineral, No. 1, 517–534 (1989).

  22. L. A. Dunn and W. L. Marshall, “Electrical Conductances and Ionization Behavior of Sodium Chloride in Dioxane-Water Mixtures at 100°C,” J. Phys. Chem. 73, 2619–2622 (1969).

    Google Scholar 

  23. A. J. Ellis and R. M. Golding, “The Solubility of Carbon Dioxide Above 100°C in Water and in Sodium Chloride Solutions,” Am. J. Sci. 261, 47–60 (1963).

    Google Scholar 

  24. J. B. Fein and J. V. Walther, “Calcite Solubility in Supercritical CO2-H2O Fluids,” Geochim. Cosmochim. Acta 51, 1665–1673 (1987).

    Article  Google Scholar 

  25. J. B. Fein and J. V. Walther, “Portlandite Solubilities in Supercritial Ar-H2O Mixtures: Implications for Quantifying Solvent Effects,” Am. J. Sci. 289, 975–993 (1989).

    Google Scholar 

  26. J. M. Ferri and L. K. Baumgartner, “Thermodynamic Models of Molecular Fluids at Elevated Temperatures and Pressures of Metamorphism,” in Thermodynamic Modeling in Geology: Minerals, Fluids, and Melts (Mir, Moscow, 1992), pp. 354–389 [in Russian].

    Google Scholar 

  27. R. M. Fuoss, “Ionic Association. III. The Equilibrium Between Ion Pairs and Free Ions,” J. Am. Chem. Soc. 80, 5059–5061 (1958).

    Google Scholar 

  28. F. Gibert, B. Moine, J. Schott, and J.-L. Dandurand, “Modeling of the Transport and Deposition of Tungsten in the Sheelite-bearing Calc-Silicate Gneisses of Montagne Noire, France,” Contrib. Mineral. Petrol. 112, 371–384 (1992).

    Article  Google Scholar 

  29. Handbook for Chemists (Khimiya, Leningrad, 1966), Vol. 1 [in Russian].

  30. H. S. Harned and L. D. Fallon, “The Properties of Electrolytes in Mixtures of Water and Organic Solvents. II. Ionization Constant of Water in 20, 45, and 70% Dioxane-Water Mixtures,” J. Am. Chem. Soc. 61, 2374–2377 (1939).

    Google Scholar 

  31. H. C. Helgeson and D. H. Kirkham, “Theoretical Predication of the Thermodynamic Properties of Aqueous Electrolytes at High Pressures and Temperatures. III. Equation of State for Aqueous Species at Infinite Dilution,” Am. J. Sci. 276, 97–240 (1976).

    Google Scholar 

  32. H. C. Helgeson, D. H. Kirkham, and G. C. Flowers, “Theoretical Prediction of the Thermodynamic Behavior of Electrolytes at High Pressures and Temperatures. IV. Calculation of Activity Coefficients, Osmotic Coefficients, and Apparent Molal and Standard and Relative Partial Molal Properties to 600°C and 5 kbar,” Am. J. Sci. 281, 1249–1516 (1981).

    Google Scholar 

  33. P. G. Hill, “A Unified Fundamental Equation for the Thermodynamic Properties of H2O,” J. Phys. Chem. Ref. Data 19, 1233–1274 (1990).

    Google Scholar 

  34. E. Högfeldt, Stability Constants of Metal-Ion Complexes. Part A: Inorganic Ligands (Pergamon Press, IUPAC. Chemical Data Series, London, 1982), Vol. 21.

    Google Scholar 

  35. H. D. Holland and S. D. Malinin, “The Solubility and Occurrence of Non-Ore Minerals,” in Geochemistry of Hydrothermal Ore Deposits (J. Wiley and Sons, New York, 1979), pp. 461–508.

    Google Scholar 

  36. J. R. Holloway, “Compositions and Volumes of Supercritical Fluids in the Earth’s Crust,” in Fluid Inclusions: Application to Petrology (Mineral. Assoc. Canada, Toronto, 1981), pp. 13–38.

    Google Scholar 

  37. J. W. Johnson, E. H. Oelkers, and H. C. Helgeson, “SUPCRT92: A Software Package for Calculating the Standard Molal Thermodynamic Properties of Minerals, Gases, Aqueous Species, and Reactions from 1 to 5000 Bars and 0 to 1000°C,” Comp. Geosci. 18, 899–947 (1992).

    Google Scholar 

  38. J. G. Kirkwood, “The Dielectric Polarization of Polar Liquids,” J. Phys. Chem. 7, 911–919 (1939).

    Google Scholar 

  39. N. Kishima and H. Sakai, “Fugacity-Concentration Relationship of Dilute Hydrogen in Water at Elevated Temperature and Pressure,” Earth Planet. Sci. Lett. 67, 79–86 (1984).

    Article  Google Scholar 

  40. G. R. Kolonin, G. A. Pal’yanova, G. P. Shironosova, and K. G. Morgunov, “Thermodynamic Model of Possible Gold Potential in High-Temperature Chloride H2O-CO2 Fluid,” Geokhimiya, No. 12, 1725–1734 (1994).

  41. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).

    Google Scholar 

  42. K. A. Levin, “Experimental and Thermodynamic Studies of Stability of Chloride Silver Complexes in KCl and NaCl Solutions (to 7 m) at 300–500°C,” Geokhimiya, No. 10, 1463–1468 (1992).

  43. H. Looyenga, “Dielectric Constant of Heterogeneous Mixtures,” Physica 31, 401–406 (1965).

    Article  Google Scholar 

  44. S. D. Malinin, Physical Chemistry of Hydrothermal Systems with Carbon Dioxide (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  45. W. L. Marshall and E. U. Frank, “Ion Product of Water Substance, 0–1000°C, 1–10000 Bars. New International Formulation and Its Background,” J. Phys. Chem. Ref. Data 10, 295–304 (1981).

    Google Scholar 

  46. S. K. Matthäi, R. W. Henley, and C. A. Heinrich, “Gold Precipitation by Fluid Mixing in Bedding Parallel Fractures Near Carbonaceous Slates at the Cosmopolitan Howley Gold Deposit, Northern Australia,” Econ. Geol. 90(8), 2123–2142 (1995).

    Google Scholar 

  47. W. F. Murphy, “The Rayleigh Depolarization Ratio and Rotation Raman Spectrum of Water Vapour and the Polarization Complex for Water Molecule,” J. Chem. Phys. 67, 5877–5882 (1977).

    Google Scholar 

  48. J. Naden and T. J. Shepherd, “Role of Methane and Carbon Dioxide in Gold Deposition,” Nature 342, 793–795 (1989).

    Article  Google Scholar 

  49. A. Yu. Namiot, Gas Solubility in Water: Handbook (Nedra, Moscow, 1991) [in Russian].

    Google Scholar 

  50. P. G. Novgorodov, “Quartz Solubility in H2O-CO2 Mixtures at 700°C and 3–5 kbar,” Geokhimiya, No. 12, 1484–1489 (1975).

  51. A. G. Orlov and S. N. Smirnov, “Calculations of Parameters of Phase Equilibria in Binary Systems with Polar Components Based on Their Dielectric Permeability,” Teploenergetika, No. 8, 66–69 (1994).

  52. Physical Quantities: Handbook, Ed. by I. S. Grigor’ev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991) [in Russian].

    Google Scholar 

  53. L. N. Plummer and E. Busenberg, “The Solubilities of Calcite, Aragonite, and Vaterite in CO2-H2O Solutions between 0 and 90°C, and an Evaluation of the Aqueous Model for the System CaCO3-CO2-H2O,” Geochim. Cosmochim. Acta 46, 1011–1040 (1982).

    Google Scholar 

  54. A. V. Plyasunov and I. V. Zakirov, “Assessment of Thermodynamic Properties of H2O-CO2 Homogeneous Mixtures at High Temperatures and Pressures,” in Outlines of Physicochemical Petrology (Nauka, Moscow, 1991), No. 17, pp. 71–88 [in Russian].

    Google Scholar 

  55. V. A. Pokrovskii and H. C. Helgeson, “Unified Description of Incongruent Reactions and Mineral Solubilities As Function of Bulk Composition and Solution pH in Hydrothermal Systems,” Can. Mineral. 29, 909–942 (1991).

    Google Scholar 

  56. V. Yu. Prokof’ev, Geochemical Peculiar Features of Ore-forming Fluids in Gold Hydrothermal Deposits of Different Genetic Types (Nauka, Novosibirsk, 2000) [in Russian].

    Google Scholar 

  57. R. P. Rafal’skii, Hydrothermal Equilibria and Processes of Mineral Formation (Atomizdat, Moscow, 1973) [in Russian].

    Google Scholar 

  58. F. Robert and W. C. Kelly, “Ore-forming Fluids in Archean Gold-bearing Quartz Veins at the Sigma Mine, Abitibi Greenstone Belt, Quebec, Canada,” Econ. Geol. 82, 1464–1482 (1987).

    Google Scholar 

  59. B. N. Ryzhenko, Thermodynamics of Equilibria in Hydrothermal Solutions (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  60. J. Schott and J.-L. Dandurand, “Prediction of Thermodynamic Behavior of Aqueous Silica in Aqueous Complex Solutions at Various Temperatures,” in Chemical Transport in Metasomatic Processes (1987), pp. 733–754.

  61. J. S. Seewald and W. E. Seyfried, Jr., “Experimental Determination of Portlandite Solubility in H2O and Acetate Solutions at 100–350°C and 500 Bars: Constraints on Calcium Hydroxide and Calcium Acetate Complex Stability,” Geochim. Cosmochim. Acta 55, 659–669 (1991).

    Article  Google Scholar 

  62. T. M. Seward, “The Stability of Chloride Complexes of Silver in Hydrothermal Solutions up to 350°C,” Geochim. Cosmochim. Acta 40, 1329–1337 (1976).

    Article  Google Scholar 

  63. E. L. Shock and H. C. Helgeson, “Calculation of the Thermodynamic and Transport Properties of Aqueous Species at High Pressures and Temperatures: Correlation Algorithms for Ionic Species and Equation of State Predictions to 5 kbar and 1000°C,” Geochim. Cosmochim. Acta 52, 2009–2036 (1988).

    Article  Google Scholar 

  64. E. L. Shock, H. C. Helgeson, and D. A. Sverjensky, “Calculation of the Thermodynamic and Transport Properties of Aqueous Species at High Pressures and Temperatures: Standard Partial Molal Properties of Inorganic Neutral Species,” Geochim. Cosmochim. Acta 53, 2157–2183 (1989).

    Google Scholar 

  65. E. L. Shock, D. C. Sassani, M. Willis, and D. A. Sverjensky, “Inorganic Species in Geologic Fluids: Correlations Among Standard Molal Thermodynamic Properties of Aqueous Ions and Hydroxide Complexes,” Geochim. Cosmochim. Acta 61, 907–950 (1997).

    Google Scholar 

  66. E. L. Shock, E. H. Oelkers, J. W. Johnson, et al., “Calculation of the Thermodynamic and Transport Properties of Aqueous Species at High Pressures and Temperatures: Effective Electrostatic Radii, Dissociation Constants and Standard Partial Molal Properties to 1000°C and 5 kbar,” J. Chem. Soc. Faraday Trans. 88(6), 803–826 (1992).

    Article  Google Scholar 

  67. R. A. Sommerfeld, “Quartz Solution Reaction: 400–500°C, 1000 Bars,” J. Geophys. Res. 72, 4253–4257 (1967).

    Google Scholar 

  68. D. A. Sverjensky, E. L. Shock, and H. C. Helgeson, “Prediction of Thermodynamic Properties of Aqueous Metal Complexes to 1000°C and 5 kbar,” Geochim. Cosmochim. Acta 61, 1359–1412 (1997).

    Article  Google Scholar 

  69. B. R. Tagirov, A. V. Zotov, and N. N. Akinfiev, “Experimental Study of Dissociation of HCl from 350 to 500°C and from 500 to 2500 Bars: Thermodynamic Properties of HCl(aq),” Geochim. Cosmochim. Acta 61, 4267–4280 (1997).

    Article  Google Scholar 

  70. J. C. Tanger IV and H. C. Helgeson, “Calculation of the Thermodynamic and Transport Properties of Aqueous Species at High Pressures and Temperatures: Revised Equations of State for Standard Partial Molal Properties of Ions and Electrolytes,” Amer. J. Sci. 288, 19–98 (1988).

    Google Scholar 

  71. Thermodynamic Properties of Individual Substances, Ed. by V. P. Glushko (Nauka, Moscow, 1981), Vol. 10 [in Russian].

    Google Scholar 

  72. J. V. Walther, “Experimental Determination of Portlandite and Brucite Solubilities in Supercritical H2O,” Geochim. Cosmochim. Acta 50, 733–739 (1986).

    Article  Google Scholar 

  73. J. V. Walther and H. C. Helgeson, “Calculation of Thermodynamic Properties of Quartz and Its Polymorphs at High Pressures and Temperatures,” Am. J. Sci. 277, 1315–1351 (1977).

    Google Scholar 

  74. J. V. Walther and M. I. Long, “Experimental Determination of Calcite Solubilities in Supercritical H2O,” in Extended Abstracts, Fifth Int. Symp. on Water-Rock Interaction. Reykjavik. Iceland, pp. 609–611 (1986).

  75. J. V. Walther and P. M. Orville, “The Extraction-Quench Technique for Determination of the Thermodynamic Properties of Solute Complexes: Application to Quartz Solubility in Fluid Mixtures,” Am. Mineral. 68, 731–741 (1983).

    Google Scholar 

  76. J. V. Walther and J. Schott, “The Dielectric Constant Approach to Speciation and Ion Pairing at High Temperature and Pressure,” Nature 332, 635–638 (1988).

    Article  Google Scholar 

  77. J. J. Wilkinson and J. D. Johnston, “Pressure Fluctuations, Phase Separation, and Gold Precipitation during Seismic Fracture Propagation,” Geology 24(5), 395–398 (1996).

    Article  Google Scholar 

  78. B. Yardley, “Earthquakes with Gold Linings,” Nature 382(6587), 210–211 (1996).

    Google Scholar 

  79. A. V. Zotov, A. V. Kudrin, K. A. Levin, et al., “Experimental Studies of the Solubility and Complexing of Selected Ore Elements (Au, Ag, Cu, Mo, As, Sb, Hg) in Aqueous Solutions,” in Fluids in the Crust (Chapman and Hall, London, 1995), pp. 95–138.

    Google Scholar 

  80. A. V. Zotov, K. A. Levin, I. L. Khodakovskii, and V. K. Kozlov, “Thermodynamic Properties of Chloride Silver Complexes in Water Solution at 273–623 K,” Geokhimiya, No. 5, 690–702 (1986).

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Original Russian Text © N.N. Akinfiev, A.V. Zotov, 2006, published in Geologiya Rudnykh Mestorozhdenii, 2006, Vol. 48, No. 1, pp. 29–50.

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Akinfiev, N.N., Zotov, A.V. Thermodynamic description of equilibria in mixed fluids (H2O-nonpolar gas) in a wide range of temperatures (25–700°C) and pressures (1–5000 bar). Geol. Ore Deposits 48, 23–42 (2006). https://doi.org/10.1134/S1075701506010028

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