The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables

The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa₇₅, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities     

Physico-chemical models of the internal structure of partially differentiated Titan

We analyze models of the internal structure of Titan, a large icy satellite of the Saturn system. Calculations are carried out using information on the mass, mean density, moment of inertia, orbital parameters, and elastic properties of the satellite obtained by the Cassini–Huygens mission, as well as geochemical data on the composition of chondrite materials, equations of state of water and ices I, III, V, VI, and VII, and thermodynamic models for conductive heat transfer in the outer icy crust and of global convection in the interior zones of the satellite. The analysis of the models shows that models of partially differentiated Titan are most consistent; they include an outer water–ice shell, an intermediate ice–rock mantle, and an inner rock–iron core. It is shown that for the models of this type the maximum thickness of the water–ice shell is 460–470 km; it can be composed of an outer conductive crust of Ih ice 80–110 km thick and a subsurface water ocean 200–300 km deep. The maximum radius of the central rock–iron core of Titan can reach ~1300 km. The thickness of Titan’s ice–rock mantle does not exceed 2100 km at a density of 1.22–2.64 g/cm³. The model of partially differentiated Titan is feasible in the moment of inertia range of 0.312 < I/MR ² < ~0.350.     

Thermodynamics of ice polymorphs and ‘ice-like’ water in hydrates and hydroxides

Thermodynamic properties of water, in various families of hydroxides, oxihydroxides and hydrates (chlorides, chlorates, sulfates and sulfites …), have been calculated by using a large number of data available in the literature. A phase diagram of water has been used to find the first complete set of thermodynamic properties at 298 K, 1 bar of 8 ice polymorphs, from Ih (hexagonal ice, the common polymorph) to IX (very low temperature and high pressure polymorph). These results are used to illustrate the concept of ‘ice-like water’ available for a very large number of hydrated phases (noted X.H₂O) in which water is attached to the corresponding anhydrous substrate (noted X) within a large spectrum of different enthalpies (Δ_fH°) or Gibbs free energies (Δ_fG°), but within a relatively small range of others properties. Heat capacity (Cp°), entropy (S°), and volume (V°) of hydration water (X.H₂O−X=H₂O) appeared to be very close to those characterizing ice polymorphs such as ice II or ice VIII. This concept allows the authors to propose a classification of minerals in terms of affinity for water and to predict the relative stability of hydrated and dehydrated phases under climatic variations.     

基于假三元模型的透辉石-硬玉固溶体热力学性质计算

自然界中矿物多以固溶体形式存在,据其晶体化学特征计算热力学性质是开展矿物成因理论研究的基础。本文引入描述二元矿物固溶体热力学性质的假三元模型,计算得到了透辉石-硬玉固溶体系列的热力学性质。该模型通过构造一种高度有序的中间相,同时考虑长程和短程有序效应,基于热力学平衡态矿物固溶体自由能最低的规律,可以计算特定组分下矿物的平衡自由能、焓和熵等热力学参数。本文针对透辉石-硬玉固溶体体系,取绿辉石为其中间有序态,计算了其活度-成分关系和温度-组分相图等,发现绿辉石随温度升高的有序无序相变为一级相变,相变温度为1 148±25 K,与实验研究结果一致。本文获得的透辉石-绿辉石-硬玉体系的热力学参数可用于视剖面图方法研究MORB成分的岩石的榴辉岩相变质作用过程。     

Thermodynamic properties of organic iodine compounds

A critical evaluation has been made of the thermodynamic properties reported in the literature for 43 organic iodine compounds in the solid, liquid, or ideal gas state. These compounds include aliphatic, cyclic and aromatic iodides, iodophenols, iodocarboxylic acids, and acetyl and benzoyl iodides. The evaluation has been made on the basis of carbon number systematics and group additivity relations, which also allowed to provide estimates of the thermodynamic properties of those compounds for which no experimental data were available. Standard molal thermodynamic properties at 25 °C and 1 bar and heat capacity coefficients are reported for 13 crystalline, 29 liquid, and 39 ideal gas organic iodine compounds, which can be used to calculate the corresponding properties as a function of temperature and pressure. Values derived for the standard molal Gibbs energy of formation at 25 °C and 1 bar of these crystalline, liquid, and ideal gas organic iodine compounds have subsequently been combined with either solubility measurements or gas/water partition coefficients to obtain values for the standard partial molal Gibbs energies of formation at 25 °C and 1 bar of 32 aqueous organic iodine compounds. The thermodynamic properties of organic iodine compounds calculated in the present study can be used together with those for aqueous inorganic iodine species to predict the organic/inorganic speciation of iodine in marine sediments and petroleum systems, or in the near- and far-field of nuclear waste repositories.     

A multiscale homogenization model for strength predictions of fully and partially frozen soils

Soil freezing is often used to provide temporary support of soft soils in geotechnical interventions. During the freezing process, the strength properties of the soil–water–ice mixture change from the original properties of the water-saturated soil to the properties of fully frozen soils. In the paper, a multiscale homogenization model for the upscaling of the macroscopic strength of freezing soil based upon information on three individual material phases—the solid particle phase (S), the crystal ice phase (C) and the liquid water phase (L)—is proposed. The homogenization procedure for the partially frozen soil–water–ice composite is based upon an extension of the linear comparison composite (LCC) method for a two-phase matrix–inclusion composite, using a two-step homogenization procedure. In each step, the LCC methodology is implemented by estimating the strength criterion of a two-phase nonlinear matrix–inclusion composite in terms of an optimally chosen linear elastic comparison composite with a similar underlying microstructure. The solid particle phase (S) and the crystal ice phase (C) are assumed to be characterized by two different Drucker–Prager strength criteria, and the liquid water phase (L) is assumed to have zero strength capacity under drained conditions. For the validation of the proposed upscaling strategy, the predicted strength properties for fully and partially frozen fine sands are compared with experimental results, focussing on the investigation of the influence of the porosity and the degree of ice saturation on the predicted failure envelope.     

A thermodynamic model for multicomponent melts,with application to the system CaO-Al2O3-SiO2

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

Phlogopite: High temperature solution calorimetry,thermodynamic properties,Al-Si and stacking disorder,and phase equilibria

Methods have been developed for solution calorimetry of hydrous phases in molten lead borate near 700°C. These involve thermochemical cycles using dissolution and decomposition reactions of hydrous silicates and hydroxides. Preliminary results suggest that H₂O derived from the decomposition of hydroxides dissolves in molten 2PbO-B₂O₃ with an exothermic enthalpy of solution of −5.7 ±0.7 kcal mol⁻¹. Hydroxyphologopite persists metastably at 714°C and its heat of solution in 2PbO·B₂O₃ has been measured. From these new data, the standard enthalpy of formation of phlogopite from the elements at 25°C is −1485.5 ±1.5 kcal mol⁻¹. The standard free energy of formation is -1394.6 ±1.5 kcal mol⁻¹, assuming complete tetrahedral Al-Si disorder.Two structural features complicate the thermodynamics of synthetic and natural micas. The first is a varying degree of tetrahedral Al-Si disorder. Raman spectroscopic study of phlogopite synthesized above 600°C suggests a disordered Al-Si distribution. Calculations of the P-T locus of the geologically important equilibrium: Phl + 3Qtz = 3En + Sa + H₂O, using our thermochemical data, agree within experimental error with the results of calculations based on the best available phase equilibrium data only if a tetrahedrally disordered phlogopite is assumed. Such calculations are very sensitive to uncertainties in ΔH° and ΔG°, and reversed phase equilibrium experiments remain essential to obtaining reliable estimates of thermodynamic properties. In contrast to these Al-Si disordered phlogopites, some biotites of low temperature parageneses (<600°C) may have substantial Al-Si order. A variable Al-Si distribution has a substantial effect on the configurational entropy and therefore on the free energy of the mica in question. Because of these and other questions, applications of biotite equilibria to determining volatile fugacities in igneous and metamorphic petrogenesis are subject to large uncertainties.The second structural complication is stacking disorder, which is present in phlogopite synthesized at 650°C but not in the 850°C sample. The enthalpy difference between these two samples, determined by solution calorimetry, is smaller than the experimental uncertainty of ±1.0 kcal mol⁻¹. Thus there appears to be little driving force for ordering, and micas with disordered stacking sequences may persist in many geologic environments. The effect of stacking disorder on thermodynamic properties is probably very small.     

土体冻结过程中的热质迁移研究进展

土体的冻胀，融沉问题归根结底是热质迁移问题，文章概述了近年来在国际上有关这方面研究的新成果，总体上讲，冻结缘的厚度，分凝冰形成温度以及冰透镜体形成条件等作为热质迁移试验研究的重点受到关注，质的迁移研究不仅仅限制在水分的迁移，而且对于矿物质，溶质，气体等的迁移以及对水分迁移的影响都有不同程度的研究，对于冻胀预报模型，已从经验型过渡到依据基本物理，力学，热动力学理论而建立的理论模型，今后的研究发展方向是加强室内参数测试水平以及对理论模型的普遍性验证。     

Kinetics and equilibrium study of chromium adsorption on zeoliteNaX

This study aims to report Batch adsorption study of hexavalent chromium, Cr (VI) on zeoliteNaX. Kinetics of Cr (VI) adsorption and adsorption isotherms were determined by varying operating parameters such as pH, initial concentration, temperature and contact time. ZeoliteNaX was found to remove Cr (VI) in acidic solutions down to ppm level at pH of about 4. Removal rate of Cr (VI) was found to decrease as pH rises above 4.0. Langmuir, Freundlich, Temkin and Redlich-Peterson models were applied to adsorption equilibrium data to find the best amongst these models. Langmuir model with R² = 0.9711 best fits the adsorption data. The kinetics of adsorption was found to follow the first order reversible reaction. The separation parameter, R_L values of less than 1.0 i.e., 0.7369, 0.5834 and 0.4828 corresponding to initial concentrations of 10, 20 and 30 mg/L, respectively indicated that adsorption of Cr (VI) on zeoliteNaX is favoured. The estimated values of thermodynamic parameters such as heat of adsorption and standard gibbs free energy confirmed the exothermic nature of adsorption of Cr (VI) on zeoliteNaX.     

A thermodynamic formulation of hydrous cordierite

A thermodynamic formulation of hydrous Mg-cordierite (Mg₂Al₄Si₅O₁₈·nH₂O) has been obtained by application of calorimetric and X-ray diffraction data for hydrous cordierite to the results of hydrothermal syntheses. The data include measurements of the molar heat capacity and enthalpy of hydration and the molar volume. The synthesis data are consistent with a thermodynamic formulation in which H₂O mixes ideally on a single crystallographic site in hydrous cordierite. The standard molar Gibbs free energy of hydration is-9.5±1.0 kJ/mol (an average of 61 syntheses). The standard molar entropy of hydration derived from this value is-108±3 J/mol-K. An equation providing the H₂O content of cordierite as a function of temperature and fugacity of H₂O is as follows (n moles of H₂O per formula unit, n<1): $$\begin{gathered}n = {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } \mathord{\left/{\vphantom {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}}} \right.\kern-\nulldelimiterspace} {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}} \hfill \\{\text{ }}\left. {\left. { - {\text{ln}}\left( {\frac{T}{{{\text{298}}{\text{.15}}}}} \right) - \left( {\frac{{298.15}}{T} - 1} \right)} \right]} \right) \hfill \\\end{gathered}$$ Application of this formulation to the breakdown reaction of Mg-cordierite to an assemblage of pyrope-sillimanite-quartz±H₂O shows that cordierite is stabilized by 3 to 3.5 kbar under H₂O-saturated conditions. The thermodynamic properties of H₂O in cordierite are similar to those of liquid water, with a standard molar enthalpy and Gibbs free energy of hydration that are the same (within experimental uncertainty) as the enthalpy and Gibbs free energy of vaporization. By contrast, most zeolites have Gibbs free energies of hydration two to four times more negative than the corresponding value for the vaporization of water.     

Effects of pressure on aqueous chemical equilibria at subzero temperatures with applications to Europa

Pressure plays a critical role in controlling aqueous geochemical processes in deep oceans and deep ice. The putative ocean of Europa could have pressures of 1200 bars or higher on the seafloor, a pressure not dissimilar to the deepest ocean basin on Earth (the Mariana Trench at 1100 bars of pressure). At such high pressures, chemical thermodynamic relations need to explicitly consider pressure. A number of papers have addressed the role of pressure on equilibrium constants, activity coefficients, and the activity of water. None of these models deal, however, with processes at subzero temperatures, which may be important in cold environments on Earth and other planetary bodies. The objectives of this work were to (1) incorporate a pressure dependence into an existing geochemical model parameterized for subzero temperatures (FREZCHEM), (2) validate the model, and (3) simulate pressure-dependent processes on Europa. As part of objective 1, we examined two models for quantifying the volumetric properties of liquid water at subzero temperatures: one model is based on the measured properties of supercooled water, and the other model is based on the properties of liquid water in equilibrium with ice.The relative effect of pressure on solution properties falls in the order: equilibrium constants(K) > activity coefficients (γ) > activity of water (a_w). The errors (%) in our model associated with these properties, however, fall in the order: γ > K > a_w. The transposition between K and γ is due to a more accurate model for estimating K than for estimating γ. Only activity coefficients are likely to be significantly in error. However, even in this case, the errors are likely to be only in the range of 2 to 5% up to 1000 bars of pressure. Evidence based on the pressure/temperature melting of ice and salt solution densities argue in favor of the equilibrium water model, which depends on extrapolations, for characterizing the properties of liquid water in electrolyte solutions at subzero temperatures, rather than the supercooled water model. Model-derived estimates of mixed salt solution densities and chemical equilibria as a function of pressure are in reasonably good agreement with experimental measurements.To demonstrate the usefulness of this low-temperature, high-pressure model, we examined two hypothetical cases for Europa. Case 1 dealt with the ice cover of Europa, where we asked the question: How far above the putative ocean in the ice layer could we expect to find thermodynamically stable brine pockets that could serve as habitats for life? For a hypothetical nonconvecting 20 km icy shell, this potential life zone only extends 2.8 km into the icy shell before the eutectic is reached. For the case of a nonconvecting icy shell, the cold surface of Europa precludes stable aqueous phases (habitats for life) anywhere near the surface. Case 2 compared chemical equilibria at 1 bar (based on previous work) with a more realistic 1460 bars of pressure at the base of a 100 km Europan ocean. A pressure of 1460 bars, compared to 1 bar, caused a 12 K decrease in the temperature at which ice first formed and a 11 K increase in the temperature at which MgSO₄·12H₂O first formed. Remarkably, there was only a 1.2 K decrease in the eutectic temperatures between 1 and 1460 bars of pressure. Chemical systems and their response to pressure depend, ultimately, on the volumetric properties of individual constituents, which makes every system response highly individualistic.     

Unexpected phase assemblages in inclusions with ternary H2O-salt fluids at low temperatures

Phase assemblages and temperatures of phase changes provide important information about the bulk properties of fluid inclusions, and are typically obtained by microthermometry. Inclusions are synthesized in natural quartz containing an aqueous fluid with a composition in the ternary systems of H₂O-NaCl₂-CaCl₂, H₂O-NaCl-MgCl₂, and H₂O-CaCl₂-MgCl₂. This study reveals that these fluid inclusions may behave highly unpredictably at low temperatures due to the formation of metastable phase assemblages. Eutectic temperatures cannot be detected in most of the fluid inclusions containing these ternary systems. Nucleation of a variety of solid ice and salt-hydrate phases in single fluid inclusions is often partly inhibited. Raman spectroscopy at low temperatures provides an important tool for interpreting and understanding microthermometric experiments, and visualizing stable and metastable phase assemblages. Final dissolution temperatures of ice, salt-hydrates, and salt must be treated with care, as they can only be interpreted by purely empirical or thermodynamic models at stable conditions.     

Semi-empirical Gibbs free energy formulations for minerals and fluids for use in thermodynamic databases of petrological interest

The P–T partition function in statistical thermodynamics can be used to derive semi-empirical formulations of the Gibbs free energy G for minerals and fluids. Parameterization of these equations includes simultaneous regression of experimental heat capacity and molar volume data, allowing fitting, appraisal and optimization of various data sources, as required in the construction of internally consistent petrological data bases. This approach can also be extended to minerals with -transitions and to fluids by considering the Gibbs free energy as a function of pressure P, temperature T and an ordering parameter X, so that accurate modelled representation and extrapolation of the thermodynamic properties of large numbers of petrologically significant minerals and coexisting fluids can be attained. The ordering parameter is chosen to denote the equilibrium mole fraction (thermodynamic probability) of ordered clusters (structural units) in a substance when G(T,P, X)=min. The procedure is tested on existing experimental data for the system MgO–SiO₂–H₂O. The proposed Gibbs free energy formulation permits thermodynamic properties of minerals, fluids and phase equilibria to be described and extrapolated over a wide range of pressure (0–800 kbar) and temperature (20–3000 K), thus allowing effective use in thermodynamic data bases of petrological interest.     

Thermodynamic analysis of binary liquid silicates and prediction of ternary solution properties by modified quasichemical equations

Modified quasichemical equations, developed for the analysis of the thermodynamic properties of structurally ordered liquid solutions, are shown to be well-suited for use with molten silicates. For binary systems, these equations have been coupled with a least-squares optimization computer program to analyse simultaneously all thermodynamic data including phase diagrams, Gibbs energies and enthalpies of formation of compounds, activities, enthalpies of mixing, entropies of fusion, miscibility gaps, etc. In this manner, data for several binary systems have been analysed and represented with a small number of parameters. In the present article, results for the SiO₂-MgO, SiO₂-Na₂O and MgO-CaO systems are presented. The resulting equations represent all the binary data, including the phase diagrams, within or virtually within experimental error limits.From the modified quasichemical equations for ternary systems, ternary thermodynamic properties can be approximated solely from data from the subsidiary binary systems. Results for the SiO₂-CaO-Na₂O, SiO₂-CaO-MgO, and SiO₂-MgO-FeO systems are in excellent agreement with measured ternary data. Predictions for the quaternary system SiO₂-MgO-CaO-Na₂O are also presented.     

Applications of the SW96 formulation in the thermodynamic calculation of fluid inclusions and mineral-fluid equilibria

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.     

链烷烃的热力学性质与分子拓扑指数的关系

定义了一种新的连接性指数^1Y=Σk1/m^2 n^2,研究了链烷烃的标准生成焓、标准熵、标准生成吉布斯自由能等三个热力学性质与碳原子个数N，^1Y之间的定量关系，相关系数为优，其计算值与实验值较为接近，对未参与回归的正癸烷的60个异构体的三个热力学性质进行了计算，计算值与实验值较一致。     

Calculation of thermodynamic properties of hydrated borates by group contribution method

 General equations to correlate and predict the thermodynamic properties of hydrated borates were developed based on the experimental results according to their structural types. The thermodynamic properties (ΔH _f ⁰ and ΔG _f ⁰) of a hydrated borate phase are the sum of the contributions of the cations in aqueous solution, the borate polyanions, and the structural water to the corresponding thermodynamic properties. This method is called the group contribution method, and it is extensively used to calculate the thermodynamic properties of many kinds of inorganic compounds, such as silicates and clay minerals. Received: 23 November 1998 / Accepted: 11 October 1999     

Thermodynamic modeling of binary CH4-H2O fluid inclusions

This work reports the application of thermodynamic models, including equations of state, to binary (salt-free) CH₄-H₂O fluid inclusions. A general method is presented to calculate the compositions of CH₄-H₂O inclusions using the phase volume fractions and dissolution temperatures of CH₄ hydrate. To calculate the homogenization pressures and isolines of the CH₄-H₂O inclusions, an improved activity-fugacity model is developed to predict the vapor-liquid phase equilibrium. The phase equilibrium model can predict methane solubility in the liquid phase and water content in the vapor phase from 273 to 623 K and from 1 to 1000 bar (up to 2000 bar for the liquid phase), within or close to experimental uncertainties. Compared to reliable experimental phase equilibrium data, the average deviation of the water content in the vapor phase and methane solubility in the liquid phase is 4.29% and 3.63%, respectively. In the near-critical region, the predicted composition deviations increase to over 10%. The vapor-liquid phase equilibrium model together with the updated volumetric model of homogenous (single-phase) CH₄-H₂O fluid mixtures (Mao S., Duan Z., Hu J. and Zhang D. (2010) A model for single-phase PVTx properties of CO₂-CH₄-C₂H₆-N₂-H₂O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar. Chem. Geol.275, 148-160), is applied to calculate the isolines, homogenization pressures, homogenization volumes, and isochores at specified homogenization temperatures and compositions. Online calculation is on the website: http://www.geochem-model.org/.