Search

Geobarometers are commonly used to determine the pressure (and hence depth) of magmatic bodies. For instance, at equilibrium, the concentration of dissolved volatiles in a vapor-saturated melt can be used as a barometer: this is the pressure of vapor-saturation P s a t v . Most determinations of P s a t v assume that melt and vapor contain only oxidized C-O-H species. However, sulfur is the third most abundant volatile element in magmas, and oxygen fugacity f O 2 exerts a strong influence on the speciation of the melt and vapor. To explore how S and f O 2 afect calculations of P s a t v , we model a Hawaiian tholeiite that contains both reduced and oxidized C-O-H-S species in the melt and vapor. We find that excluding reduced CO-H species in the system can result in significant underestimations of P s a t v under reducing conditions (ΔFMQ < 0). The efect of S on P s a t v is small except in the vicinity of the "sulfur solubility minimum" (SSmin; 0 < ΔFMQ < +2), where excluding S-bearing species can result in underestimates of P s a t v . The implications of these results depend on the volatile concentration of the system being investigated, its fO2, and the melt composition and temperature. Our results suggest there will be little impact on P s a t v calculated for mid-ocean ridge basalts because their f O 2 is above where reduced C-O-H species become important in the melt and vapor and yet below the SSmin. However, the f O 2 of ocean island and arc basalts are close enough to the SSmin and their S concentrations high enough to influence P s a t v . However, high-CO2 and high-H2O concentrations are predicted to reduce the efect of the SSmin. Hence, P s a t v calculated for shallowly trapped melt inclusions and matrix glass are more afected by the SSmin than deeply trapped melt inclusions. Lunar and martian magmas are typically more reduced than terrestrial magmas, and therefore accurate P s a t v calculations for them require the inclusion of reduced C-O-H species. [ABSTRACT FROM AUTHOR]

Silicate vapors play a key role in planetary evolution, especially dominating early stages of rocky planet formation through outgassed magma ocean atmospheres. Our open-source thermodynamic modeling software "VapoRock" combines the MELTS liquid model with gas-species properties from multiple thermochemistry tables. VapoRock calculates the partial pressures of 34 gaseous species in equilibrium with magmatic liquid in the system Si–Mg–Fe–Al–Ca–Na–K–Ti–Cr–O at desired temperatures and oxygen fugacities (f O2, or partial pressure of O2). Comparison with experiments shows that pressures and melt-oxide activities (which vary over many orders of magnitude) are reproduced to within a factor of ∼3, consistent with measurement uncertainties. We also benchmark the model against a wide selection of igneous rock compositions including bulk silicate Earth, predicting elemental vapor abundances that are comparable to (Na, Ca, and Al) or more realistic than (K, Si, Mg, Fe, and Ti) those of the closed-source MAGMA code (with maximum deviations by factors of 10–300 for K and Si). Vapor abundances depend critically on the activities of liquid components. The MELTS model underpinning VapoRock was calibrated and extensively tested on natural igneous liquids. In contrast, MAGMA's liquid model assumes ideal mixtures of a limited set of chemically simplified pseudospecies, which only roughly approximates the nonideal compositional interactions typical of many-component natural silicate melts. Finally, we explore how relative abundances of SiO and SiO2 provide a spectroscopically measurable proxy for oxygen fugacity in devolatilized exoplanetary atmospheres, potentially constraining f O2 in outgassed exoplanetary mantles. [ABSTRACT FROM AUTHOR]

Adopted by the Intergovernmental Oceanographic Commission (IOC) of UNESCO in 2010 and the International Union of Geodesy and Geophysics (IUGG) in 2011, the Thermodynamic Equation of Seawater 2010 (TEOS-10) is the current geophysical standard for the thermodynamic properties of humid air, seawater and ice. TEOS-10 equations for evaporation and sublimation enthalpies are derived mathematically from the thermodynamic potential of a »sea air« model, denoting a multi-phase equilibrium composite of the geophysical aqueous mixtures. To estimating evaporation rates from the ocean, Dalton equations in various versions are implemented in numerical climate models. Some of those equations appear to be biased on climatic time scales if compared with proper thermodynamic driving forces. Such equations may lead to a spurious amplification of the hydrological cycle and an implied effect of cooling oceans. As an unbiased alternative, Dalton equations are proposed in terms of TEOS-10 relative fugacity (RF) or its conventional relative humidity (RH) approximations. With respect to RH uncertainties or trends, the substantial sensitivity of the evaporation flux may be estimated to be as much as 5 W m−2 per 1 %rh. Within a maximum error of only 0.04 %rh, sea-surface RF may be approximated in terms of dew-point or frost-point temperatures using a simple formula. [ABSTRACT FROM AUTHOR]

This study uses simulations to explore the energy distributions involved in the adsorption of methane gas in shales. Molecular mechanics calculations were carried out using the Forcite module in BIOVIA material studio software. The critical challenge in molecular-scale simulations remains the need to improve the description of the gas adsorption prior to up-scaling to a realistic scenario. Resolving this challenge requires the implementation of multi-scale techniques that employ atomistic/molecular-level results as input. Thus, it is pertinent that the appropriate molecular data on CH4 gas interaction with shale is obtained. This study provides empirical data on CH4 sorption/adsorption in shale at the molecular level to confirm the CH4 storage potential of shales. The effect of pressure on the CH4 sorption/adsorption was also investigated. A vital aspect of this study is elucidating the energy distribution and dominant energy that controls CH4 sorption/adsorption to serve as a basis for the exploitation of CH4 in productive shales. Following the intensive simulation exercise, the average total energy of CH4 sorption varied from approximately -30 to -120 kcal/mol with increase in pressure from 500 to 2500 psi, suggesting increasing thermodynamic stability. The results indicated that van der Waals energy is the major sorption energy with values ranging from 60 to -250 kcal/mol as the sorption pressure increased, while electrostatic energy recorded the least contribution. The total adsorption energy increased from -5 to -16 kcal/mol for reservoir pressure range of 1-15 MPa. This energy distribution data confirmed the possibility of CH4 adsorption on shale under reservoir pressure conditions. [ABSTRACT FROM AUTHOR]

While noble metals often occur as minor components in host minerals in various ore deposits, little theoretical assessment exists to predict the occurrence of these metals. Here, we probe the fundamental controls responsible for the occurrence of trace elements in host minerals through first-principles calculations. We apply the theoretical model to understanding the debated issues concerning the occurrence of gold (Au) in pyrite, in which the valence of Au is ascribed to either positive or negative values. Our results indicate that (1) both positive and negative valent Au may occur in pyrite and (2) higher sulfur fugacity and lower temperature lead to more Au+ occupying Fe sites in pyrite. These findings suggest that chemical states and speciation of the Au in host pyrite are ultimately controlled by temperature and sulfur fugacity, providing insight into the formation conditions of ore deposits and facilitating strategy design for beneficiation. [ABSTRACT FROM AUTHOR]

A set of 1-atm gas-mixing experiments (n = 31) was run using Re wire loops at low-oxygen fugacity (ƒO2, within one half-log unit of the Fe–FeO buffer) and temperatures of 1175–1400 °C to explore the compositional dependence of the Fe2+–Mg olivine–liquid exchange coefficient, K D , Fe 2 + - Mg ol / liq , under conditions where corrections for liquid Fe3+ are small. The bulk compositions used for these experiments include a picrite, a high-alumina basalt, and a suite of three MORB compositions with variable Fe/Mg. The K D , Fe 2 + - Mg ol / liq values from the n = 14 experiments run on pre-saturated Re wire loops were fit to a regular solution model that relates K D , Fe 2 + - Mg ol / liq to temperature, melt composition, and olivine composition. Fe2+–Mg exchange in the experiments is well-described using two parameters: the SiO2 content of the liquid and the coexisting olivine composition. Combining our experiments with a literature compilation of low-pressure, low-ƒO2 experiments (largely on non-terrestrial bulk compositions) produced a combined data set spanning a broad region of composition space (e.g., liquid TiO2 and Na2O + K2O contents up to 18.4 wt% and 8.4 wt%, respectively). Fitting this expanded experimental database required two additional liquid compositional terms: Ti, and a Si-(Na + K) cross-term. Because the Fe3+ content of all of the experimental liquids is low, the compositional variation seen in K D , Fe 2 + - Mg ol / liq is effectively independent of the compositional effects on liquid Fe3+/Fe2+ ratios. Given olivine–liquid Mg or Fe2+ partition coefficient information, it is possible to eliminate the explicit dependence of K D , Fe 2 + - Mg ol / liq on olivine composition, enabling a simple iterative approach for calculating the composition of coexisting olivine given only the bulk composition (and Fe3+/Fe2+ ratio) of an olivine-saturated liquid. [ABSTRACT FROM AUTHOR]

Motivated by recent studies of supersymmetric black holes, we revisit the phase diagram of AdS black holes, whether BPS or not, with particular emphasis on the role of rotation. We develop BPS thermodynamics systematically and, in many explicit examples, we study its striking similarities with more familiar AdS black holes, as well as some differences. We highlight an important fugacity that preserves BPS saturation but is not captured by the supersymmetric index. [ABSTRACT FROM AUTHOR]

Crystals retain an imprint of the dynamic changes within a magma reservoir and hence contain invaluable information about the evolving conditions inside volcanic plumbing systems. However, instead of telling a single, simple story, they comprise overprinted evidence of numerous processes relating to temperature, pressure and composition that drive crystal precipitation and dissolution in magmatic systems. To decipher these different elements in the story that crystals tell, we attempt to identify the observational signatures of a simple, yet ubiquitous process: crystal precipitation and dissolution during magma cooling. To isolate this process in a complex magmatic system with intricate dynamic feedbacks, we assume that synthetic crystals precipitate and dissolve rapidly in response to deviations from thermodynamic equilibrium. In our crystalline‐scale simulations, synthetic crystals drag along the cooler‐than‐ambient melt in which they precipitated and can drive a temperature‐dependent, crystal‐driven convection. We analyze the non‐dimensional conditions for this coupled convection and record the heterogeneous thermal histories that synthetic crystals in this flow regime experience. We show that many synthetic crystals dissolve, loosing their thermal record of the convection. Based on our findings, we suggest that heterogeneity in the thermal history of crystals is more indicative of local, crystal‐scale processes than the overall, system‐wide cooling trend. Plain Language Summary: Similar to tree rings, crystals tell a story of their past through their sequential growth records. However, unlike trees, crystals are dynamic and can travel throughout the magmatic domain. We hypothesize that this mobility may result in a bias in the crystal record and prevent it from accurately recording the magma reservoir history. In order to understand what patterns natural sample crystals would record during cooling, we built a simulator that tracks individual crystals and the thermal environment they experience. We simulate how crystals drive flow, but also precipitate and dissolve in response to temperature change. Our results show that each synthetic crystal has a unique record of its past that is dependent on the temperature distribution within its vicinity. Additionally, most of the synthetic crystals dissolve in the convection, so we lose their record. Overall, the synthetic crystals in our simulation can reproduce some of the variable patterns that are often found in natural samples, suggesting that real crystals are imperfect witnesses of the magmatic dynamics they are exposed to. Key Points: Crystals in convection preserve the least information about the most dynamic flow domainCrystals in convection show signs of dissolution, suggesting a slower than actual cooling rateCrystals can record cooling, heating, and complex thermal histories even during steady cooling [ABSTRACT FROM AUTHOR]

Decades of study have documented several orders of magnitude variation in the oxygen fugacity fO2) of terrestrial magmas and of mantle peridotites. This variability has commonly been attributed either to differences in the redox state of multivalent elements (e.g., Fe3+/Fe2+) in mantle sources or to processes acting on melts after segregation from their sources (e.g., crystallization or degassing). We show here that the phase equilibria of plagioclase, spinel, and garnet lherzolites of constant bulk composition (including whole-rock Fe3+/Fe2+) can also lead to systematic variations infO2 in the shallowest ~100 km of the mantle. Two different thermodynamic models were used to calculate fO2 vs. pressure and temperature for a representative, slightly depleted peridotite of constant composition (including total oxygen). Under subsolidus conditions, increasing pressure in the plagioclase-lherzolite facies from 1 bar up to the disappearance of plagioclase at the lower pressure limit of the spinel-lherzolite facies leads to anfO2 decrease (normalized to a metastable plagioclase-free peridotite of the same composition at the same pressure and temperature) of ~1.25 orders of magnitude. The spinel-lherzolite facies defines a minimum in fO2 and increasing pressure in this facies has little influence on fO2 (normalized to a metastable spinel-free peridotite of the same composition at the same pressure and temperature) up to the appearance of garnet in the stable assemblage. Increasing pressure across the garnet-lherzolite facies leads to increases infO2 (normalized to a metastable garnet-free peridotite of the same composition at the same pressure and temperature) of ~1 order of magnitude from the low values of the spinel-lherzolite facies. These changes in normalized fO2 reflect primarily the indirect effects of reactions involving aluminous phases in the peridotite that either produce or consume pyroxene with increasing pressure: Reactions that produce pyroxene with increasing pressure (e.g., forsterite + anorthite ^ Mg-Tschermak + diopside in plagioclase lherzolite) lead to dilution of Fe3+-bearing components in pyroxene and therefore to decreases in normalizedfO2, whereas pyroxene-consuming reactions (e.g., in the garnet stability field) lead initially to enrichment of Fe3+-bearing components in pyroxene and to increases in normalizedfO2 (although this is counteracted to some degree by progressive partitioning of Fe3+ from the pyroxene into the garnet with increasing pressure). Thus, the variations in normalizedfO2 inferred from thermodynamic modeling of upper mantle peridotite of constant composition are primarily passive consequences of the same phase changes that produce the transitions from plagioclase ^ spinel ^ garnet lherzolite and the variations in Al content in pyroxenes within each of these facies. Because these variations are largely driven by phase changes among Al-rich phases, they are predicted to diminish with the decrease in bulk Al content that results from melt extraction from peridotite, and this is consistent with our calculations. Observed variations in FMQ-normalized fO2 of primitive mantle-derived basalts and peridotites within and across different tectonic environments probably mostly reflect variations in the chemical compositions (e.g., Fe3+/Fe2+or bulk O2 content) of their sources (e.g., produced by subduction of oxidizing fluids, sediments, and altered oceanic crust or of reducing organic material; by equilibration with graphite-or diamond-saturated fluids; or by the effects of partial melting). However, we conclude that in nature the predicted effects of pressure-and temperature-dependent phase equilibria on the fO2 of peridotites of constant composition are likely to be superimposed on variations in fO2 that reflect differences in the whole-rock Fe3+/Fe2+ ratios of peridotites and therefore that the effects of phase equilibria should also be considered in efforts to understand observed variations in the oxygen fugacities of magmas and their mantle sources. [ABSTRACT FROM AUTHOR]

An aerodynamic conical nozzle levitator (CNL) has been used to measure the melting temperatures of refractory ceramics. The well‐established method of cooling traces has been adapted to allow measurements for air‐sensitive samples using a controlled atmosphere, where the oxygen partial pressure can be adjusted and monitored in real time. In this study, we explain the details of a system that we developed for use at the Spallation Neutron Source (Oak Ridge National Laboratory). Measurements of the melting behavior of (Fe,Cr,Al)3O4 spinels were made between log (PO2 (atm)) of −0.7 and −5. The melting temperature of hercynite is found to be oxygen potential dependent, ranging between 1692 and 1767°C at log (PO2) values from −4.42 to −0.70. [ABSTRACT FROM AUTHOR]

We have first attempted to build a simplified model to map the interaction of quarks and gluons, which is calibrated by thermodynamical quantities like entropy density, obtained from the calculation of lattice quantum chromodynamics (LQCD). With respect to the entropy density of the standard non-interacting massless quark gluon plasma (QGP), its interacting values, from the LQCD simulation, are reduced as we go from higher to lower temperatures through the crossover of the quark–hadron phase transition. By parameterizing the increasing degeneracy factor or increasing interaction fugacity or decreasing the thermal width of quarks and gluons with temperature, a temperature profile of LQCD thermodynamics has been obtained. Using that interaction picture, the shear viscosity and electrical conductivity are calculated. Both face phase-space reduction due to the interaction. The fluidity, quantified from the shear viscosity to entropy density ratio, is not affected by the interaction picture when the temperature-dependent degeneracy factor or fugacity approaches are considered, but the temperature-dependent thermal width picture suggests that interaction might have some role in the fluidity of QGP and is probably one of the reasons for getting a (nearly) perfect fluid nature. [ABSTRACT FROM AUTHOR]

The aim of this study is twofold: to explore, first, the influence of the intellectual and social conditions on the transfer of thermodynamics to chemistry and thereby the making of chemical thermodynamics, and second, the way that this knowledge was transferred from Europe to America. Consequently, it is of interest to examine the methodological approaches used by physicists and chemists to transfer thermodynamics to chemistry, to evaluate the potential of this science to offer solutions to existing chemical problems, and to discuss the attitude of the scientific community towards these new ideas. The development of chemical thermodynamics in America followed a different route compared to the European experience. Although it was transferred from Europe, it had distinctive characteristics imposed by a different traditional, intellectual and social milieu. This study focuses on the content of the transferred knowledge to America and the direction that this knowledge assumed by the American scientists. As a paradigm, the chemical thermodynamics of Gilbert Newton Lewis will be considered. • The intellectual and social factors on the transfer of thermodynamics to chemistry. • Physicists and chemists on the genesis and development of chemical thermodynamics. • The content of the new knowledge that was transferred from Europe to America. • The appropriation of chemical thermodynamics by the American scientists. • The resistance the chemical thermodynamics felt in Europe and America. [ABSTRACT FROM AUTHOR]

Abstract A algorithm coupled with modified Patel-Teja equation of state and Chen-Guo hydrate model is developed to conduct vapor-liquid-semiclathrate multiphase flash calculation for TBAB containing systems. To quantitatively describe the gas consumption ability of semiclathrate slurry, a new concept, i.e., the apparent liquid phase, is introduced. The Patel-Teja equation of state (PT EOS) combined with a Debye-Hückel electrostatic term is chosen to describe the fugacity of TBAB in aqueous solution and calculated gas solubility in aqueous phase. The Chen-Guo hydrate model is extended to calculate the fugacity of TBAB in semiclathrate phase. Several parameters in Chen-Guo model for TBAB are retuned by correlating phase equilibrium data. A mathematical approach based on the secant iteration is successfully applied to solve flash calculation. Results from flash calculations are in satisfactory agreement with experimental data reported in other literature. This new algorithm provides an extended range of calculations for semiclathrate phases, such as amounts of semiclathrate formed, and then, the contributions of absorption and hydration upon separation performance can be quantitatively described. In addition, multistage separation are simulated using this flash algorithm. The effects of TBAB concentration of solution, initial gas liquid volume ratio, temperature, and pressure on separation efficiency are systematically discussed from the perspective of thermodynamics and mass balance. [ABSTRACT FROM AUTHOR]

A thermodynamic model is developed to calculate the fugacity coefficients and partial molar volumes of hydrogen at infinite dilution in water at 647.1–2000 K and pure water densities between 0 and 1500 kg m −3 . The model is based on the predicted values of DCFI (the dimensionless integral of the infinite dilution hydrogen - water direct correlation). Values of DCFI at low water densities are calculated from accurately known second cross virial coefficients; at high water densities predictions are based on the relations from the theory of a mixture of hard spheres; DCFI values at intermediate water densities are interpolated using a variant of corresponding-states correlation. Predicted values of the hydrogen fugacity coefficients at infinite dilution in water are compared with experimental data and results of the literature equations of state. The included Excel spreadsheet allows calculations provided that values of T , P , ρ 1 ∗ , and κ T for pure water are entered by a user. [ABSTRACT FROM AUTHOR]

Peridotites dredged from mid-ocean ridges and glassy mid-ocean ridge basalts (MORB) transmit information about the oxygen fugacity fo2) of Earth’s convecting upper mantle to the surface. Equilibrium assemblages of olivine+orthopyroxene+spinel in abyssal peridotites and Fe3+/ΣFe ratios in MORB glasses measured by X-ray absorption near-edge structure (XANES) provide independent estimates of MORB source region fo2, with the former recording fo2 approximately 0.8 log units lower than the latter relative to the quartz-fayalite-magnetite (QFM) buffer. To test cross-compatibility of these oxybarometers and examine the compositional effects of changing fo2 on a peridotite plus melt system over a range of Earth-relevant fo2, we performed a series of experiments at 0.1 MPa and fo2 controlled by CO-CO2 gas mixes between QFM-1.87 and QFM+2.23 in a system containing basaltic andesite melt saturated in olivine, orthopyroxene, and spinel Oxygen fugacities recorded by each method are in agreement with each other and with the fo2 measured in the furnace. Measurements of fo2 from the two oxybarometers agree to within 1σ in all experiments. These results demonstrate that the two methods are directly comparable and differences between fo2 measured in abyssal peridotites and MORB result from geographic sampling bias, petrological processes that change fo2 in these samples after separation of melts and residues, or abyssal peridotites may not be residues of MORB melting. As fo2 increases, spinel Fe3+ concentrations increase only at the expense of Cr from QFM-1.87 to QFM-0.11. Above QFM, Al is also diluted in spinel as the cation proportion of Fe3+ increases. None of the three spinel models tested, MELTS (Ghiorso and Sack 1995), SPINMELT (Ariskin and Nikolaev 1996), and MELT_CHROMITE (Poustovetov and Roeder 2001), describe these compositional effects, and we demonstrate that MELTS predicts residues that are too oxidized by >1 log unit to have equilibrated with the coexisting liquid phase. Spinels generated in this study can be used to improve future thermodynamic models needed to predict compositional changes in spinels caused by partial melting of peridotites in the mantle or by metamorphic reactions as peridotites cool in the lithosphere. In our experimental series, where the ratio of Fe2O3/FeO in the melt varies while other melt compositional parameters remain nearly constant, experimental melt fraction remains constant, and Fe3+ becomes increasingly compatible in spinel as fo2 increases. Instead of promoting melting, increasing the bulk Fe3+/ΣFe ratio in peridotite drives reactions analogous to the fayalite-ferrosilite-magnetite reaction. This may partly explain the absence of correlation between Na2O and Fe2O3 in fractionation-corrected MORB. [ABSTRACT FROM AUTHOR]

Storage and transport of silicate melts in the Earth's crust and their emplacement on the planet's surface occur almost exclusively at sub-liquidus temperatures. At these conditions, the melts undergo crystallization under a wide range of cooling-rates, deformation-rates, and oxygen fugacities ( f O 2 ). Oxygen fugacity is known to influence the thermodynamics and kinetics of crystallization in magmas and lavas. Yet, its influence on sub-liquidus rheology remains largely uncharted. We present the first rheological characterization of crystallizing lavas along natural cooling paths and deformation-rates and at varying f O 2 . Specifically, we report on apparent viscosity measurements for two crystallizing magmatic suspensions 1) at log ⁡ f O 2 of −9.15 (quartz–fayalite–magnetite buffer, QFM, −2.1) and 2) in air. These fugacities span a range of reduced to oxidized conditions pertinent to magma migration and lava emplacement. We find that: 1) crystallization at constant cooling-rates results in a quasi-exponential increase in the apparent viscosity of the magmatic suspensions until they achieve their rheological cut off temperature ( T cutoff ), where the melt effectively solidifies 2) the rheological departure and T cutoff increase with increasing f O 2 and 3) increasing f O 2 results in decreased crystallization-rates. Based on the experimental results and by comparison with previous rheological isothermal studies we propose a generalisation of the effect of f O 2 on the dynamic rheological evolution of natural magmatic and volcanic suspensions. We further discuss the implications for magmatic transport in plumbing and storage systems (e.g. conduits, dikes and magma chambers) and during lava flow emplacement. [ABSTRACT FROM AUTHOR]

This study presents a thermodynamic framework for predicting hydrate equilibrium pressure of gas species including methane, ethane, propane, nitrogen, carbon dioxide and hydrogen sulfide and their mixtures. For this purpose, Peng–Robinson–Stryjek–Vera equation of state (PRSV-EOS) along with modified Huron-Vidal (MHV1) mixing rule and UNIQUAC model were employed to calculate fugacity and activity coefficient of water in equilibrated fluid phases. To represent phase behavior of solid hydrate, a modified version of van der Waals and Platteeuw (vWd-P) model was utilized which accounts for guest interaction with water molecules beyond first shell of cavity and also asymmetry of encapsulated molecules and cage structure. In addition, dissolution of gas compounds in aqueous phase and subsequent non-ideality of water was taken into account. It was realized that both physical phenomena are of marked influence on the prediction accuracy. In contrast to conventional modelling approaches which scarify some part of equilibrium data to regress some adjustable parameters, advantageously, our model does not require any pre-matching. It was observed that present framework gives accurate prediction for equilibrium pressure of hydrates of CH 4 , C 2 H 6 , C 3 H 8 , CO 2 , N 2 and H 2 S with overall average absolute percent deviation (AAPD) 3.2, 3.4, 3.7, 1.5, 2.8 and 1.3, respectively. Also, incipient pressure of hydrate formed by binary gas mixtures comprised of aforementioned single components could accurately be predicted by proposed approach, which is detailed in the manuscript. Overall, formation pressures predicted by proposed modelling approach are more accurate (or at least comparable) to outstanding models presented in the hydrate literature. [ABSTRACT FROM AUTHOR]

Abstract: Raman spectroscopy yields information about the internal vibrational modes of covalently bonded molecules, which are sensitive to the local molecular environment. As such, Raman spectra of a gas composed of covalently bonded molecules collected at different temperatures and/or pressures show variations in band positions and other spectral features, reflecting molecular‐scale interactions (attraction and repulsion) among gas particles associated with the local physical and chemical environment. Because the molecules interact, gases are nonideal, and fugacity is the fundamental thermodynamic quantity that describes partial pressures of gases, adjusted to account for the nonideality. The fugacity of a substance is generally obtained from thermodynamic calculations rather than by direct analysis or measurement and, as such, is conceptually nebulous. Here, we perform spectroscopic analyses of a gas mixture of known composition at variable and known pressures and couple these results with thermodynamic calculations of gas fugacities. We show that Raman peak shifts in gas mixtures are directly correlated to fugacities of the component gas species. Our results thus provide experimental evidence that fugacities of gases can be estimated from Raman spectra collected in situ. By this approach, the thermodynamic quantities fugacity and the related thermodynamic property activity are linked directly with underlying molecular‐scale phenomena, according to the vibrational properties of molecular species. This represents a tractable method to efficiently obtain large datasets on thermodynamic properties of gas mixtures, and with some adjustments, may lead to a viable method for developing nonideal mixing rules for other substances, such as crystalline solid solutions, aqueous ions, and electrolytes. [ABSTRACT FROM AUTHOR]

A thermodynamic model to predict three phase (L-H-V and I-H-V) equilibria of gas hydrates is presented. In this model we have employed a fugacity based approach where the hydrate phase is modeled using van der Waals-Platteeuw solid solution theory and the liquid phase activity coefficients are determined from the modified UNIFAC method. For the vapour phase fugacity calculations we have investigated three equations of state (EOS): Peng-Robinson-Stryjek-Vera (PRSV), Patel-Teja (PT) and Soave-Redlich-Kwong (SRK). This model employs only parameters reported in the literature. The coexistence pressures predicted by our model for the sI hydrates of methane, carbon dioxide and ethane are in reasonable agreement with experiments, whereas our model overestimates the coexistence pressures for the sII clathrates of nitrogen and propane. The predicted cage occupancies are found to increase with increasing temperature in the L-H-V equilibria. For I-H-V equilibria the cage occupancy is observed to decrease with temperature. We have also estimated the solubility of each guest in the liquid phase (for L-H-V equilibria) using the Henry’s law. The solubilities predicted using all three EOS are in good agreement for all guest molecules, with the exception of nitrogen where at relatively higher temperatures the estimates from the PRSV EOS are noticeably lower than the corresponding predictions from the PT and SRK EOS. [ABSTRACT FROM AUTHOR]

This study presents a multiphase (water, supercritical fluid and solid species) thermodynamic model applicable to the sequestration of supercritical CO 2 in a saline aquifer at high pressures, which accounts for the effects of water activity, solid activity, supercritical fluid fugacity and aqueous species activities. The model is formulated using mass action laws, species and charge balances, a new correlation for species activity coefficients based on the Davies equation, supercritical fluid fugacities (Peng-Robinson equation of state), water activity (a new explicit form in terms of state variables and salinity), corrected equilibrium constants of aqueous reactions as functions of pressure, temperature and salinity, water-supercritical partitioning (Krichevsky-Ilinskaya correction to Henry's law), and a new model for water-solid partitioning. The effects of high pressures to 60 MPa – consistent with sequestration at depths to 6000 m – are examined in detail. The model is applied to the scCO 2 - H 2 O - CaCO 3 (s) - Na + - Cl − system, revealing substantial discrepancies between this and previous geochemical models in the effect of pressure and salinity on the chemical equilibrium constants of geochemical reactions. Several calculations of the model are compared to those of Saaltink et al. (2013) and Springer et al. (2012). [ABSTRACT FROM AUTHOR]

In this communication, a thermodynamic consistency test is performed on the isothermal solubility of hydrogen in alkenes and vapor-liquid equilibrium data for systems containing hydrogen and alkenes. The improved Peng-Robinson equation of state was used for this purpose. The fugacity coefficient of each component and compressibility factor of liquid and vapor phases were calculated by this equation of state. Thermodynamic consistency tests have been performed by rewriting the Gibbs-Duhem equation in terms fugacity coefficient and using the area test method. The results showed that most of the equilibrium data of the liquid phase were consistent, but for the vapor phase less than one-half of the data was consistent. [ABSTRACT FROM AUTHOR]

The present study is a comparative study of three equations, namely the Clausius-Clapeyron, Van't Hoff and Hildebrand (to calculate crystal-liquid fugacity ratio (CLFR) of drug compounds), to select the best model in predicting the intestinal absorption and develop a new classification system based on dose number ( D ) and CLFR. The required thermodynamic parameters [melting point, enthalpy of fusion (Δ H ) and the differential molar heat capacity (∆ C )] were experimentally obtained by differential scanning calorimetry. Pharmacokinetic data [the human intestinal absorption ( F ) and apparent permeability of Caco-2 ( P _Caco-2)] and D were obtained from the literature. The highest value of CLFR was found for diclofenac with the value of 88.78, 87.29, and 87.84 mol% from Clausius-Clapeyron, Van't Hoff, and Hildebrand approaches, respectively. The lowest CLFR value was seen for memantine with the value of 14.3 × 10 and 26 × 10 mol% from Van't Hoff and Hildebrand equations, respectively. Statistical comparison with the Wilcoxon signed rank test showed that the CLFR values calculated by three equations are different. CLFR values of more than 1 mol% correspond to the complete intestinal absorption ( F ). There was a sigmoidal dependency between CLFR and F , similar to the dependency between P _Caco-2 and F . In these modeling, the excellent correlations were obtained in all three models as evidenced by a good coefficient of determination ( r ) without a significant difference in the average absolute error. A new classification system from Hildebrand model based on D and CLFR was developed and was in agreement with the biopharmaceutics classification system (70.5%) and the biopharmaceutical drug disposition system (65.6%). This modeling approach can be a valuable tool for scientists as an alternative for intestinal permeability in the biopharmaceutical classification system to develop new oral drugs. The CLFR obtained from Hildebrand model is also more convenient than the Clausius Clapeyron model, because the former does not need to calculate ∆ C (difficult step in calculating CLFR) for drug compounds. This new classification can help to develop the new drug product in industrial and academic research, without necessary in vivo experiments. [ABSTRACT FROM AUTHOR]

Titanomagnetite-melt partitioning of Mg, Mn, Al, Ti, Sc, V, Co, Ni, Cu, Zn, Ga, Zr, Nb, Mo, Hf and Ta was investigated experimentally as a function of oxygen fugacity ( fO) and temperature ( T) in an andesitic-dacitic bulk-chemical compositional range. In these bulk systems, at constant T, there are strong increases in the titanomagnetite-melt partitioning of the divalent cations (Mg, Mn, Co, Ni, Zn) and Cu/Cu with increasing fO between 0.2 and 3.7 log units above the fayalite-magnetite-quartz buffer. This is attributed to a coupling between magnetite crystallisation and melt composition. Although melt structure has been invoked to explain the patterns of mineral-melt partitioning of divalent cations, a more rigorous justification of magnetite-melt partitioning can be derived from thermodynamic principles, which accounts for much of the supposed influence ascribed to melt structure. The presence of magnetite-rich spinel in equilibrium with melt over a range of fO implies a reciprocal relationship between a(FeO) and a(FeO) in the melt. We show that this relationship accounts for the observed dependence of titanomagnetite-melt partitioning of divalent cations with fO in magnetite-rich spinel. As a result of this, titanomagnetite-melt partitioning of divalent cations is indirectly sensitive to changes in fO in silicic, but less so in mafic bulk systems. [ABSTRACT FROM AUTHOR]

This research article proposes the use of a novel variant of the HS algorithm (harmony search), i.e. SFHS (self-regulated fret width harmony search algorithm), for calculating and predicting fugacity and activity coefficients in binary mixtures. Parameter selection was carried out based on preliminary results with different standard test functions. Different previously reported systems were selected, at 25 ° C and 40 ° C, and at low and moderate pressure levels. Moreover, two solutes were selected: carbon dioxide and ethane. Different solvents, both polar and nonpolar, were selected with comparative purposes. Activity and fugacity coefficients were calculated using the Redlich-Kwong state equation and Lewis rule, along with the sfhs algorithm, assuming both solutes in vapor phase. Consistency of the activity coefficients was analyzed by the Redlich-Kister strategy. Results were very close to those found experimentally by other authors, and most of them did not differ in more than one percentage unit. [ABSTRACT FROM AUTHOR]

The fugacity or partial pressure of CO 2 in surface water (fCO 2w) is a key parameter to determine air-sea CO 2 fluxes and the evolution of ocean acidification. Despite its importance some key physical chemical characteristics are not fully resolved, notably its dependence on temperature. The fCO 2w is mostly measured by autonomous underway systems near in situ sea surface temperature (SST). Subsurface measurements are commonly carried out on individual (discrete) samples at a fixed temperature, normally 20 °C. Here, the underway system observations are compared with co-located discrete observations to determine the consistency of these types of measurements. The co-located discrete fCO 2w at 20 °C and underway fCO 2w measurements at SST are used to infer the temperature dependence of CO 2. In addition, calculated fCO 2w from total alkalinity (TA) and total dissolved inorganic carbon (DIC) are compared with the underway and discrete fCO 2w measurements. For 21 cruises spanning the major ocean basins from 1992 to 2020 a temperature dependence of 4.13 ± 0.01% °C−1 is determined in close agreement with a widely used previous empirical estimate of 4.23 ± 0.02% °C−1 for North Atlantic surface water. The temperature dependency of calculated fCO 2w from TA and DIC using recommended constants is 4.10% °C−1 for 17 cruises where there are co-located measurements of fCO 2w , TA and DIC. • 30 years of surface water CO 2 observations from research cruises show excellent consistency • A temperature dependence of CO 2 fugacity in seawater of 4.13 ± 0.01% °C−1 is determined • The temperature dependence shows good agreement with theoretical estimates [ABSTRACT FROM AUTHOR]

The high-pressure phases Fe4O5 and Fe5O6 have recently been added to the list of known iron oxides. As mixed-valence phases, it has been suggested that they could form in the Earth’s mantle once the dominant minerals become saturated in ferric iron. The possibility that Fe4O5 could exist in the mantle is also supported by the fact that it forms extensive solid solutions with both Mg2+ and Cr3+. In this study, we present the results of high-pressure and high-temperature multi-anvil experiments performed between 5 and 24 GPa at 1000–1400 °C aimed at constraining the stability field of the Fe4O5 phase. We combine these results with published phase equilibria, equation of state and Fe–Mg partitioning data to estimate the thermodynamic properties of Fe4O5, Fe5O6 and the (Mg,Fe)2Fe2O5 solid solution. Using our thermodynamic model, the oxygen fugacity at which the high-pressure iron oxides become stable is calculated and the redox stability of (Mg,Fe)2Fe2O5 in an assemblage of olivine and pyroxene is calculated as a function of the bulk Fe/(Fe + Mg) ratio. Fe4O5 and (Mg,Fe)2Fe2O5 are stable at oxygen fugacities higher than the diamond stability field and are, therefore, unlikely to be found as inclusions in diamonds. The stability field of Fe5O6, on the other hand, extends to oxygen fugacities compatible with diamond formation. Using the Mg–Fe solid solution model, we show that Fe4O5-structured phases would be restricted to aluminium-poor environments in the mantle such as dunites or silica–iron oxide-rich sediments transported into the mantle via subduction. [ABSTRACT FROM AUTHOR]

A generalized thermodynamic framework for correlating the vapor-liquid equilibria of aqueous primary, secondary and tertiary alkanolamine solutions is presented. The model uses Universal Functional Activity Coefficient (UNIFAC) and translated modified Peng-Robinson equation of state to correlate the activity and fugacity effects of the solution, respectively. New UNIFAC binary interaction parameters are reported for aqueous monoethanolamine, diethanolamine and N-methyldiethanolamine solutions for a wide range of temperature, pressure and concentration. The results are in excellent agreement with experimental data. [ABSTRACT FROM AUTHOR]

Experiments were performed to determine the sulfur solubilities of hydrous basalts from Vesuvius, Etna and Stromboli (Italy). The melts were equilibrated at 1050 and 1200 °C with H 2 O and sulfur (added as pyrrhotite), and at pressures ranging from 250 to 2000 bar. Most experiments were performed under oxidising conditions (NNO + 2), and a few under reducing conditions (NNO − 1), with melt water contents of 0.5–3.5 wt.%. Sulfur contents in glasses were determined by electron microprobe and range from 860 up to 6700 ppm. No compositional effect is found between the three alkali basaltic melts. The fugacities of S-bearing species were derived using an MRK equation of state applied to an O–H–S fluid, knowing H 2 and H 2 O fugacities, and range from 50 up to 3000 bar. A thermodynamic species-based model is derived from our results along with available data in the literature, assuming that sulfur dissolution results from the additive contributions of both H 2 S and SO 2 dissolution reactions. Compared to similar models developed for silicic melts, basalt compositions requires the incorporation of an Fe term, which accounts for the strong association between Fe and S in silicate melts, and considers the elevated Fe content of mafic melts. The model shows that, at any fixed f S 2 , the sulfur solubility in hydrous basalt displays a pronounced minimum around NNO, the position of which depends on temperature. The minimum in sulfur solubility coincides with the redox range were the abundance of S 2 in the fluid reaches its maximum compared to either H 2 S or SO 2 species. Such a minimum in solubility is in agreement with experimental constraints at 1 bar under carefully controlled f O 2 and f S 2 . Calculated proportions of dissolved species in the melt depend on the prevailing f S 2 and f O 2 , being in general agreement with available spectroscopic models. Calculations of gas saturation pressures, which classically consider only H 2 O and CO 2 dissolved volatiles, are strongly affected by S-bearing species. At f O 2 close to, or higher than, NNO + 1, omission of sulfur species may result in underestimates of gas saturation pressures of 1 kbar or more. The same happens at f O 2 below NNO − 1. [ABSTRACT FROM AUTHOR]

As part of an initiative to evaluate commercial chemicals for their effects on human and environmental health, Canada recently evaluated decamethylcyclopentasiloxane (D5; CAS no. 541-02-06), a high-volume production chemical used in many personal care products. The evaluation illustrated the challenges encountered in environmental risk assessments and the need for the development of better tools to increase the weight of evidence in environmental risk assessments. The present study presents a new risk analysis method that applies thermodynamic principles of fugacity and activity to express the results of field monitoring and laboratory bioaccumulation and toxicity studies in a comprehensive risk analysis that can support risk assessments. Fugacity and activity ratios of D5 derived from bioaccumulation measures indicate that D5 does not biomagnify in food webs, likely because of biotransformation. The fugacity and activity analysis further demonstrates that reported no-observed-effect concentrations of D5 normally cannot occur in the environment. Observed fugacities and activities in the environment are, without exception, far below those corresponding with no observed effects, in many cases by several orders of magnitude. This analysis supports the conclusion of the Canadian Board of Review and the Minister of the Environment that D5 does not pose a danger to the environment. The present study further illustrates some of the limitations of a persistence-bioaccumulation-toxicity-type criteria-based risk assessment approach and discusses the merits of the fugacity and activity approach to increase the weight of evidence and consistency in environmental risk assessments of commercial chemicals. Environ Toxicol Chem 2015;34:2723-2731. © 2015 The Authors. Environmental Toxicology and Chemistry Published by Wiley Periodicals, Inc. on behalf of SETAC. [ABSTRACT FROM AUTHOR]

This research assesses the thermodynamic consistency of recent marine CO 2 system measurements in United States coastal waters. As one means of assessment, we compared aragonite saturation states calculated using various combinations of measured parameters. We also compared directly measured and calculated values of total alkalinity and CO 2 fugacity. The primary data set consists of state-of-the-art measurements of the keystone parameters of the marine CO 2 system: dissolved inorganic carbon (DIC), total alkalinity (TA), CO 2 fugacity ( f CO 2 ), and pH. This study is the first thermodynamic CO 2 system intercomparison based on measurements obtained using purified meta cresol purple as a pH indicator. The data are from 1890 water samples collected during NOAA's West Coast Ocean Acidification Cruise of 2011 (WCOA2011) and NOAA's Gulf of Mexico and East Coast Carbon Cruise of 2012 (GOMECC-2). Calculations of in situ aragonite saturation states (Ω A ) near the saturation horizon exhibited differences on the order of ± 10% between predictions based on the (DIC, TA) pair of measurements vs. the (pH, DIC), ( f CO 2 , DIC), or ( f CO 2 , pH) pairs. Differences of this magnitude, which are largely attributable to the imprecision of Ω A calculated from the (DIC, TA) pair, are roughly equivalent to the magnitude of Ω A change projected to occur over the next several decades due to ocean acidification. These observations highlight the importance of including either pH or f CO 2 in saturation state calculations. Calculations of TA from (pH, DIC) and ( f CO 2 , DIC) showed that internal consistency could be achieved if minor subtractions of TA (≤ 4 μmol kg − 1 ) were applied to samples of salinity < 35. The extent of thermodynamic consistency is also exemplified by the small offset between TA calculated from (DIC, pH) and that calculated from (DIC, f CO 2 ): ~ 3 μmol kg − 1 , which is similar to the accuracy of the TA measurements. Systematic trends can be detected in the offsets between measured and calculated parameters, but for this high-quality data set the magnitude of methodological improvements required to achieve exact thermodynamic consistency is quite small. [ABSTRACT FROM AUTHOR]

A version of the Widom-Rowlinson model is considered, where particles of $$q$$ types coexist, subject to pairwise hard-core exclusions. For $$q\le 4$$ , in the case of large equal fugacities, we give a complete description of the pure phase picture based on the theory of dominant ground states. [ABSTRACT FROM AUTHOR]

Solution chemistry is at the heart of many research areas in the pure and applied sciences. In fact, for more than a century, experimental as well as theoretical work on solution properties and phase equilibria involving liquid/fluid solutions in general, and aqueous liquid/fluid solutions in particular, have held prominent positions in (bio-)physical chemistry. The scientific insights gained thereby are invaluable and have not only contributed decisively to the creation of the formal structure of chemical thermodynamics but have also paved the way for the development of practically useful molecular- based models describing real solution behavior. In the first part of this review, I shall present a concise overview of the thermodynamic formalism relevant in solubility studies on liquid/fluid nonelectrolyte systems. In the second part, selected aspects of solubility data reduction and data correlation will be touched upon, including a critical evaluation of some popular approximations and a survey of current estimation technique for indispensable auxiliary quantities, such as virial coefficients and partial molar volumes at infinite dilution. One of the goals will be to clarify issues frequently overlooked and to dispel misconceptions encountered in the literature. Pride of place will be given to the Henry fugacity (also known as Henry's law constant), which is one of the most misunderstood thermodynamic quantities, and to various caloric quantities derived via van't Hoff analysis of high-precision solubility data. [ABSTRACT FROM AUTHOR]

Fugacity is considered the proper real-gas substitute for the partial pressure commonly used to describe ideal-gas mixtures. However, in several fields such as geophysics, meteorology, or air conditioning, partial pressure is still preferred over fugacity when non-equilibrium conditions of humid air are quantified. One reason may be that for ambient air, the deviations from ideal-gas behavior are small, another that explicit correlation equations for the fugacity of water vapor in humid air are scarce in the literature. This situation has improved with the publication of the new oceanographic standard TEOS-10, the International Thermodynamic Equation of Seawater 2010, which provides highly accurate values for the chemical potential and the fugacity of water vapor in humid air over wide ranges of pressure and temperature. This paper describes the way fugacity is obtained from the fundamental equations of TEOS-10, and it derives computationally more convenient virial approximations for the fugacity, consistent with TEOS-10. Analytically extracted from the TEOS-10 equation of state of humid air, equations for the 2nd and 3rd virial coefficients are reported and compared with correlations available from the literature. The virial fugacity equation is valid in the temperature range between $${-}80\,^{\circ }\hbox {C}$$ and +200 $$^{\circ }\hbox {C}$$ at pressures up to 5 MPa, and between $${-}130\,^{\circ }\hbox {C}$$ and +1000 $$^{\circ }\hbox {C}$$ at low pressures such as those encountered in the terrestrial atmosphere at higher altitudes. [ABSTRACT FROM AUTHOR]

We have studied the ferrous (Fe 2+ ) and ferric (Fe 3+ ) iron concentrations in Al-free Fe containing Mg-silicate perovskite (Mg-Pv) at pressure ( P ), temperature ( T ), and oxygen fugacity ( f O 2 ) conditions related to the lower mantle using a thermodynamic model based on ab initio calculations. We consider the oxidation reaction and the charge disproportionation reaction, both of which can produce Fe 3+ in Mg-Pv. The model shows qualitatively good agreement with available experimental data on Fe 3+ / Σ Fe ( Σ Fe = total Fe in system), spin transitions, and equations of state. We predict that under lower-mantle conditions Fe 3+ / Σ Fe determined by the charge disproportionation is estimated to be 0.01–0.07 in Al-free Mg-Pv, suggesting that low Al Mg-Pv in the uppermost pyrolitic mantle (where majoritic garnet contains most of the Al) and in the harzburgitic heterogeneities throughout the lower mantle contains very little Fe 3+ . We find that the volume reduction by the spin transition of the B-site Fe 3+ leads to a minimum Fe 3+ / Σ Fe in Mg-Pv at mid-mantle pressures. The model shows that configurational entropy is a key driving force to create Fe 3+ and therefore Fe 3+ content is highly temperature sensitive. The temperature sensitivity may lead to a maximum Fe 3+ / Σ Fe in Mg-Pv in warm regions at the core–mantle boundary region, such as Large Low Shear Velocity Provinces (LLSVPs), potentially altering the physical (e.g., bulk modulus) and transport (e.g., thermal and electrical conductivities) properties of the heterogeneities. [ABSTRACT FROM AUTHOR]

Thermodynamic analysis of equilibria involving minerals of the lower mantle of pyrolite composition and crystalline carbon-bearing compounds indicates that the range of oxygen fugacity values at which diamond can be formed is separated from the region in which Fe-rich metallic alloy is generated by a field in which Fe carbides are stable. This implies that diamond can be formed in the lower mantle under more oxidizing conditions than those thought to be dominant in this geosphere. The absence of a metallic phase from the lower-mantle diamond-bearing mineral assemblage is consistent with the high (approximately 1%) Ni concentration in the ferropericlase found as inclusions in diamonds (Fe-rich metallic alloy is able to intensely extract Ni). An elevated redox potential also follows from the occurrence of carbonate phases found among mineral inclusions in lower-mantle diamonds. The main reason for a local increase in oxygen fugacity in the lower mantle may be shifts of redox equilibria toward a decrease in the amount, and then the disappearance of the Fe-Ni alloy with increasing temperature. An important role in the formation of diamond may be played by the generation of carbonate-phosphate and silicate melts in high-temperature zones and the migration of these melts and their interaction with wall rocks. [ABSTRACT FROM AUTHOR]

An equilibrium mixture of monoclinic pyrrhotite and pyrite was synthesized in the eutectic AlCl3- KCl melt at 525 K. The reaction 7FeS2(cr) + 12Ag(cr) = 8Fe0.875S(cr) + 6Ag2S(cr) was studied by an electromotive force technique in an all-solid-state electrochemical cell with an Ag+-conductive solid electrolyte in Ar at atmospheric pressure: (-) Pt ∣ Ag ∣ AgI ∣ Ag2S, Fe0.875S, FeS2 ∣ Pt (+). In the 490-565 K temperature range a linear electromotive force vs. temperature trend was obtained from which the temperature dependence of the sulfur fugacity was determined for the monoclinic pyrrhotitepyrite equilibrium: logfS2(mpo+py) = 14.079 - 14406·T-1, (500 < T/K < 565). In addition, standard thermodynamic functions were calculated for monoclinic pyrrhotite Fe0.875S at 298 K and atmospheric pressure: ΔGf(mpo, 298.15 K) = -(136 200 ± 3000) J/mol, S°(mpo, 298.15 K) = (66.7 ± 1.3) J/(mol·K), ΔHf(mpo, 298.15 K) = -(157 400 ± 3000) J/mol. Gaseous sulfur, S2--ideal gas at 1 bar (105 Pa) pressure--was taken as a standard state for sulfur. [ABSTRACT FROM AUTHOR]

Asphaltene precipitation is a sophisticated issue in the upstream oil industry, worldwide, and has detrimental effect on a verity of production processes; it damages the properties of the reservoir and causes an unfavorable and significant decrease in oil production. In spite of numerous studies to predict asphaltene behavior, the effect of temperature on asphaltene precipitation during pressure depletion at reservoir conditions is still obscure in the literature. In this study the PVT data as well as experimental data of asphaltene precipitation at reservoir conditions of an Iranian light oil samples is used, and the asphaltene precipitation and deposition envelops (APE and ADE) of the oil are developed using solid thermodynamic modeling. [ABSTRACT FROM PUBLISHER]

Partitioning of sulphur between liquid Fe-rich metals and silicates ( ) was investigated at temperatures from 1800 °C to 2400 °C, pressures from 2 to 23 GPa and oxygen fugacities from 3.5 to 1.5 log units below the iron–wüstite buffer, using multi-anvil apparatus. The results are combined with previous experimental works to refine a multi-variable thermodynamic model of . Sulphur appears to become more siderophile with increasing pressure and FeO content of the silicate melt, and less siderophile with increasing temperature and with Si, C, O, Fe and Ni contents of the metal. We then modelled the behaviour of sulphur in the course of planetary accretion, using different possible scenarios of mantle dynamics and evolution with time of oxygen fugacity. We investigated three end-member models for metal–silicate segregation of the incoming impactors: (i) the planetary mantle does not mix and is kept chemically stratified, (ii) the magma ocean is continuously mixed chemically, and (iii) both the magma ocean and the solid lower mantle are well mixed. We show that if S is accreted along the accretion, whatever the oxidation path, its distribution between core and mantle can lead to the observed S concentration of the mantle ( ) and to the estimations of S content of the core (from its depletion in the mantle relative to the other elements with the same volatility). In the case of an Earth built with reduced material, to explain the present-day S found in the mantle, it is necessary that both the magma ocean and the solid lower mantle mix at each major step of the planetary accretion. S could also be accreted in the last 10 to 20% of Earth's growth and reach its observed present terrestrial abundances if the magma ocean is chemically mixed along the accretion. Consequently, our models show that the S terrestrial abundances do not formally require an S accretion in a late veneer but can be explained by a core–mantle equilibration alone. [ABSTRACT FROM AUTHOR]

The incorporation of H into olivine is influenced by a significant number of thermodynamic variables (pressure, temperature, oxygen fugacity, etc.). Given the strong influence that H has on the solidus temperature and rheological behavior of mantle peridotite, it is necessary to determine its solubility in olivine over the range of conditions found in the upper mantle. This study presents results from hydration experiments carried out to determine the effects of pressure, temperature, and the fugacities of HO and O on H solubility in San Carlos olivine at upper mantle conditions. Experiments were carried out at 1-2 GPa and 1,200 °C using a piston-cylinder device. The fugacity of O was controlled at the Fe-FeO, FeO-FeO, or Ni-NiO buffer. Variable duration experiments indicate that equilibration is achieved within 6 h. Hydrogen contents of the experimental products were measured by secondary ion mass spectrometry, and relative changes to the point defect populations were investigated using Fourier transform infrared spectroscopy. Results from our experiments demonstrate that H solubility in San Carlos olivine is sensitive to pressure, the activity of SiO, and the fugacities of HO and O. Of these variables, the fugacity of HO has the strongest influence. The solubility of H in olivine increases with increasing SiO activity, indicating incorporation into vacancies on octahedral lattice sites. The forsterite content of the olivine has no discernible effect on H solubility between 88.17 and 91.41, and there is no correlation between the concentrations of Ti and H. Further, in all but one of our experimentally hydrated olivines, the concentration of Ti is too low for H to be incorporated dominantly as a Ti-clinohumite-like defect. Our experimentally hydrated olivines are characterized by strong infrared absorption peaks at wavenumbers of 3,330, 3,356, 3,525, and 3,572 cm. The heights of peaks at 3,330 and 3,356 cm correlate positively with O fugacity, while those at 3,525 and 3,572 cm correlate with HO fugacity. [ABSTRACT FROM AUTHOR]

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site. [ABSTRACT FROM AUTHOR]

Abstract: This study investigates the metal–silicate partitioning of Pb and U (D Pb and D U, respectively) during core-mantle differentiation of terrestrial planets. For this, we equilibrated a molten CI-chondrite model mantle-composition with various Fe-rich alloys in the system Fe–C–Ni–Si–S in a multi-anvil over a range of P, T, f O2 (3–8GPa, 2073–2373K and from 1.5 to 5 log units below the iron-wüstite (IW) buffer). The chemical compositions of the run products and contents in Pb and U trace elements were determined using electron microbe and laser ablation inductively coupled plasma-mass spectrometry, respectively. We combined our new data set with pre-existing results in similar chemical systems to refine the major parameters controlling the D Pb and D U values, based on thermodynamical calculations. We show: (i) a significant increase of the metal–silicate partition coefficients, from ∼1 to ∼50 for D Pb and from ∼10−5 to 10−2 for D U with the addition of sulfur. (ii) At a fixed f O2, the presence of C in the metal favors U and Pb partitioning toward the silicate melt, when S produces the opposite trend. (iii) Temperature plays a non-negligible role in D Pb value. Although the results suggest that the Pb depletion observed in the present-day bulk silicate Earth can be explained by core-mantle segregation at high-pressure in a deep-magma ocean, at conditions similar to that previously refined based on the behavior of many siderophile elements, such as Ni and Co, we will also discuss the possibility of late S-rich phases segregating to the core. [Copyright &y& Elsevier]

• Solid-liquid–vapor equilibria of mixture containing carbon dioxide are calculated. • Predictive cubic equations of state are used to describe the fluid phases. • Binary interaction parameters based on vapor–liquid equilibria are used in equilibrium calculations. • Solid fugacity models including a new one are used to describe solid CO 2. • An analytical expression is derived to express melting curve. Carbon capture and sequestration / utilization using cryogenic conditions have found attention due to lower energy penalty compared to other separation methods. In cryogenic processes, carbon dioxide is likely to desublimate from a vapor phase or freezes out from a liquid phase. This study deals with phase equilibrium calculations where solid carbon dioxide forms in the presence of vapor phase (SLV), liquid phase (SLE), or both (SLVE). Two of the successful solid fugacity models are used with predictive cubic equations of state (EOSs) in calculating the phase equilibrium of carbon dioxide mixtures. The advantages and limitations of the models are discussed. In addition, a new fugacity model which describes solid carbon dioxide along solid–liquid coexistence curve is developed. This model remedies the previous models and is used from low to very high pressure. This model reduces to an analytical expression for describing carbon dioxide melting curve. When coupled with the predictive cubic EOSs, this model satisfactorily describes the SVE, SLE, and SVLE of carbon dioxide mixtures. [ABSTRACT FROM AUTHOR]

Mutual interaction of redox pairs was evaluated using the concept of intrinsic oxygen fugacity in a melt. A 'rose of $f_{O_2 } $ trends' was proposed for the visualization of possible directions of mutual oxidation/reduction of redox pairs for a given melt composition. Missing thermodynamic data were estimated for vanadium redox pairs in sodium disilicate melt, and the V/V/V/V tetrad was quantitatively described. The redistribution of vanadium in different valence states was estimated during quenching to glass of model iron-free and natural iron-bearing melts. [ABSTRACT FROM AUTHOR]

Abstract: The solubilities of solid oxides in the vapor phase of water are considered as the gas phase chemical reactions of metal oxides and water with the formation of hydroxides of metals and their hydrates. The necessary thermodynamic properties of hydroxides and their hydrates in the ideal gas state are obtained by quantum chemical calculations or in a few cases are evaluated from available experimental data. The values of the fugacity coefficients of components of gas mixtures are estimated by the empirical relation , where stands for the fugacity coefficient of pure water and the parameter k is evaluated by counting the groups (OH, H2O, O) of the molecule of a dissolved compound, which can form hydrogen bonds with water molecules. Considered examples include the calculations of the steam solubility of MoO3(s), ZnO(s), and Cu2O(s) at 573–1273K and up to water density of 300kgm−3 in comparison with available experimental data. It was found that the speciation of Mo(VI) is absolutely dominated by a single form MoO2(OH)2, while in the Zn(II) and Cu(I) steam mixtures both hydroxides and their hydrates contribute appreciably to the material balance of metals. There is a clear tendency to the dehydration of dominating forms with an increase of temperature. The agreement of the experimental and calculated solubility values can be termed satisfactory (for Cu2O(s)–H2O at least for temperatures of 623.2 and 673.2K), considering the difficulties of gas-phase solubility experiments, uncertainties of the data based on quantum chemical calculations, and the simplicity of the model to predict values. [Copyright &y& Elsevier]

Abstract: In this paper, we present a simple thermodynamic model to describe phase behavior of gas hydrates with CH4, C2H6, C3H8, N2, CO2 and their mixtures as guests. The model is based on equality of water fugacity in the liquid water and hydrate phases. The van der Waals and Platteeuw model is applied for calculating the fugacity of water in the hydrate phase. The Stryjek and Vera modification of Peng–Robinson (PRSV2) equation of state is used to evaluate the fugacity of water in the vapor and liquid phases. Binary interaction parameters are adjusted as a linear function of temperature. The Vapor–Liquid–Equilibria for the pure gas hydrates former have been predicted within 2.87% absolute average relative deviation and for the gas mixtures have been predicted within 3.43% absolute average deviation. The pure gas hydrate formation conditions have been predicted within 2.27% absolute average deviation. The hydrate formation conditions of gas mixtures have been predicted within AAD 3.72%. The results are in good agreement, demonstrating the reliability of the thermodynamic approach used in this work. [Copyright &y& Elsevier]

Phase transitions are not usually seen in the time domain. Here, we report on the finding of critical times at which a physical observable, in the thermodynamic limit, becomes nonanalytic as a function of time. We find that the coherence of a probe spin coupled to a many-body system vanishes at times in one-to-one correspondence to the Lee-Yang zeros of the partition function of the many-body system. In the thermodynamic limit, the Lee-Yang zeros form a continuum cut in the complex plane of fugacity and the probe spin coherence presents sudden death and birth at the critical times corresponding to the Yang-Lee singularities. These results provide new experimental possibilities in many-body physics. [ABSTRACT FROM AUTHOR]

Very accurate empirical thermodynamic potential functions are available for fluid water, ice, seawater, and humid air covering wide ranges of temperature and pressure conditions, including those of the terrestrial hydrosphere and atmosphere. These potential functions are formulated as international standards endorsed by the International Association for the Properties of Water and Steam (IAPWS). A related seawater standard referred to as the International Thermodynamic Equation of Seawater 2010 (TEOS-10) was adopted in 2009 by UNESCO for oceanography. Here, the formulations available from TEOS-10 for the description of the vapor pressure of ice and for thermodynamic properties of humid air, in particular, the relative humidity, are reviewed. It is concluded that the IAPWS formulation for the sublimation pressure is superior in uncertainty and range of validity over other available correlation equations, and that relative fugacity is a physically reasonable generalization of relative humidity for the case of non-ideal gases or equilibria with moist substances. [ABSTRACT FROM AUTHOR]

Abstract: An analytical expression for the vapor pressure of ionic liquids based on the Peng–Robinson equation of state is proposed. The method uses the concept of zero-pressure fugacity previously presented in the literature and that has been found to work well in the range of low vapor pressures (lower than 0.1Pa), where the values of vapor pressure of ionic liquids, up to moderate temperatures, are found. The parameters of the equation of state are generalized in terms of ionic liquid properties and results are compared with experimental data, showing average absolute deviations below 8%. The advantage of the proposed analytical expression is its solid thermodynamic foundation, the generalization of the model parameters, and its acceptable accuracy for engineering calculations. [Copyright &y& Elsevier]

Abstract: The fugacity coefficients of Si(OH)4 are evaluated from solubilities of solid phases of SiO2 in the vapor phase of water. The virial equation of state, truncated at the third virial coefficient, is employed to describe the fugacity coefficients of Si(OH)4. The temperature dependencies of the second, B 12, and the third, C 112, cross virial coefficients for H2O–Si(OH)4 interactions are approximated by empirical relations. It is found that silica–water interactions in the vapor phase are significantly more non-ideal compared to water–water interactions. Knowledge of B 12 and C 112 allows calculation of solubilities of quartz (Q) and amorphous silica (AS) in steam up to the density of 200kgm−3 in satisfactory agreement with available data, and should provide reasonable solubility values at temperatures where no experimental results exist. The calculated values of the solubility of Q and AS in saturated vapor up to the critical temperature of water, T c, are tabulated. The partial molar properties of dilute solutes close to the critical point of water are governed by the Krichevskii parameter, the value of which for Si(OH)4 is evaluated from available data (mainly vapor–liquid distribution constants for silica) to be equal to −187±10MPa. The knowledge of the thermodynamic properties of Si(OH)4 in the ideal gas state and in the state of the standard solution in liquid water allows calculating Henry’s constant, k H, for Si(OH)4 up to 623.15K at water saturation pressure . The theoretically-based equation, containing the Krichevskii parameter, allows extrapolating k H values all the way toward the critical temperature of water. This, in turn, makes possible calculation of the solubility of quartz and amorphous silica in liquid water at at all temperatures up to T c. The presented results should be useful for modeling solid–liquid–vapor, solid–vapor and liquid–vapor equilibria in the H2O–SiO2 system at steam densities up to 200kgm−3. [Copyright &y& Elsevier]

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions. [ABSTRACT FROM AUTHOR]