Multiphase Equilibria Research Articles

Vapor–liquid–liquid–hydrate phase equilibrium calculation for multicomponent systems containing hydrogen

The main purpose of this study was to employ the algorithm of vapor–liquid–liquid–hydrate multiphase equilibrium to the multicomponent mixtures containing hydrogen. The Patel–Teja equation of state was used to perform the vapor–liquid–liquid (V–LHC–LW) three-phase flash calculation and the Chen–Guo two-step hydrate model was employed to calculate the vapor–hydrate phase equilibria. This method is rather simple due to avoiding the complexity of simultaneous solution of the sophisticated equation group. The proposed algorithm was tested on gas-emulsion systems. The comparisons of calculated results with experimental data show that the proposed algorithm is very stable and effective.

The Thermal Stability of Molten Lithium–Sodium–Potassium Carbonate and the Influence of Additives on the Melting Point

The thermal stability of a molten LiNaK carbonate salt, potentially suitable for thermal energy storage, was studied up to a temperature of 1000 °C. The salt investigated was the eutectic Li2CO3–Na2CO3–K2CO3 in the proportions 32.1–33.4–34.5 wt. % and the study was done by simultaneous differential scanning calorimetry (DSC)/thermogravimetric–mass spectrometric (TG–MS) analysis in gas atmospheres of argon, air, and CO2. It was found that (i) under a blanket gas atmosphere of CO2 the LiNaK carbonate salt is stable up to at least 1000 °C. (ii) In an inert atmosphere of argon, the salt evolves gaseous CO2 soon after melting and begins to decompose at between 710 °C and 715 °C with acceleration in the CO2 evolution rate from the melt. An increase in the rate of weight loss is also observed after 707 °C. (iii) Under a blanket atmosphere of air, the gaseous CO2 evolution from the salt is observed to commence at 530 °C, the onset of decomposition detected by DSC analysis at 601 °C and the rapid rate of weight loss determined by TG analysis at 673 °C. The melting point of the LiNaK carbonate studied was between 400 °C and 405 °C. Thermodynamic modeling with Multi-Phase-Equilibrium (MPE) software developed in CSIRO Process Science and Engineering indicated that additives such as NaNO3, KCl, and NaOH lower the melting point of the LiNaK carbonate eutectic, and this was experimentally verified.

Development and testing of a new apparatus for the measurement of high-pressure low-temperature phase equilibria

A new apparatus for the study of high-pressure phase equilibria at low temperatures using an analytical method was designed, assembled and tested. The apparatus was specially developed for the study of multi-phase equilibria in systems containing hydrocarbons, water and hydrate inhibitors, at temperatures ranging from 213K to 353K and pressures up to 40MPa. The core of the apparatus is a variable-volume equilibrium cell, equipped with a 360° sapphire window and connected to an analytical system by three capillary samplers.The quality of the apparatus was confirmed through several tests, including the study of the system methane+water. An equilibrium point for the quaternary system methane+n-hexane+methanol+water is also presented.

Thermoelectric Properties of P-Type Ga2Te5 Based Compounds

Abstract P-type Ga2Te5 based compounds with multiphase equilibrium were prepared by spark plasma sintering and their microstructures and thermoelectric properties were evaluated in the temperature range from 319 K to 549 K. Through XRD analysis, we observed the main phase Ga2Te5, a small amount of SnTe and single element Te were observed. Results indicate that the Seebeck coefficients increase and the electrical and thermal conductivities decrease with the increase of the temperature in the entire temperature range. The highest thermoelectric figure of merit ZT of 0.16 can be achieved for Ga2SnTe5 at 549 K due to relatively low thermal conductivity and high thermal conductivity.

Simulation of the properties of a binary carbon dioxide-water mixture under sub- and supercritical conditions

A method for determining the multiphase thermodynamic equilibriums of a binary mixture expressed in pressure-enthalpy-mixture composition variables is suggested. The use of such variables, in contrast to the classical thermodynamic pressure-temperature-composition variables, makes it possible to determine not only the two-phase, but also three-phase states of a mixture. The method can be used to describe real properties of mixtures in a wide range of pressure and temperature values containing critical points; it can be helpful in modeling of the mixture flows in a porous medium. The suggested problem of calculating the multiphase equilibrium can be visually interpreted in terms of geometry by constructing a convex envelope for the thermodynamic potential of the mixture. This method is used to study the phase diagram of the carbon dioxide-water mixture.

Convex envelope method for the determination of fluid phase diagrams

In this work a new method – the convex envelope method (CEM) – for the reliable determination of fluid phase diagrams is presented. The method yields the entire phase equilibrium diagram and does not rely on the determination of individual equilibria. Formally, the CEM is based on the original idea of Gibbs interpreting all globally stable equilibrium states as those belonging to the convex envelope of the Gibbs energy over the composition space. In this work, the continuous Gibbs energy surface is approximated by an appropriate set of points. This allows a mathematically clear reformulation of the original problem as convex hull determination for a discrete set of Gibbs energy points and thus the continuous Gibbs energy surface itself. The CEM is quite generally formulated for any system with arbitrary coexisting (fluid and solid) phases. In this work it is applied to systems with multiple liquid phases only, since liquid multi-phase equilibrium diagrams are extremely important in practice for extraction and decanter design. The implementation of CEM relies on a numerical construction of the convex hull which determines the accuracy of the results. The CEM can be easily integrated in short-cut methods for analysis of separation methods based on liquid phase splitting. Therefore, the CEM is explained for the application to liquid multi-phase equilibria and validated with available experimental data and rigorous decanter simulations for several systems with complex phase behavior.

MULTIPHASE EQUILIBRIUM, PHASE STABILITY AND PHASE TRANSFORMATION IN NANOCRYSTALLINE ALLOY SYSTEMS

A nanoscale thermodynamic approach is developed to quantify the multiphase equilibrium in nanocrystalline alloy systems. The nanoscale multiphase equilibrium calculations indicate that the activities and mole numbers of phases in alloy systems change diversely as a function of the nanograin size at constant temperature, which results in distinctly different characteristics of phase stability and phase transformation behavior in nanocrystalline alloys with respect to coarse-grained polycrystalline counterparts. Take the nanocrystalline Sm–Co alloy system as an example, the diverse phase stabilities and phase transformations are demonstrated. To verify the thermodynamic predictions, a series of experiments on preparation and characterization of nanocrystalline SmCo3, Sm2Co7 and SmCo2 alloys have been performed. The experimental results are in agreement with the model calculations, which validate the present thermodynamic approach for nanoscale multiphase equilibrium.

Multiphase Equilibrium Calculations from Soave Equation of State with Chang-Twu/UNIFAC Mixing Rules for Mixtures Containing Water, Alcohols, and Esters

Various versions of the Soave–Redlich–Kwong (SRK) equation of state incorporating different mixing rules were applied to calculate vapor–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), and vapor–liquid–liquid equilibrium (VLLE) properties for the systems containing water, alcohols, and esters. The calculated results showed that the SRK equation with the T-type α function and the Chung–Twu (CT) mixing rules embedded in the UNIFAC–Lyngby model (SRK-T/CT–UNIFAC– Lyngby) not only predicts accurately the VLE properties of the constituent binaries but also represents the ternary LLE and VLLE phase behavior reasonably well. Using this model, the vapor pressure data of the pure constituent components are the only required property for the phase equilibrium calculations.

Non-iterative phase stability calculations for process simulation using discriminating functions

Phase stability calculations consume a significant part of a process or a compositional reservoir simulation CPU time as millions of two- or multi-phase equilibrium calculations on complex multicomponent mixtures need to be performed. The iterative nature of the solving methods involved in conjunction to the risk of false convergence render these computations as a hot research area. A new method is presented for generating discriminating functions of pressure, temperature and compositions which separate stable from unstable mixtures. These functions provide the same stability state predictions as the established minimum tangent plane distance since they exhibit exactly the same sign and zeroing points. Their simple explicit expressions allow for the rapid, non-iterative and robust evaluation of the stability state of the fluid under study. Being generated by using the fluid's Equation of State model they offer predictions which can be as accurate as the thermodynamic model itself. A set of examples demonstrates the accuracy of the proposed method as well as its very significant advantages with respect to computational speed.

Release of K, Cl, and S during Pyrolysis and Combustion of High-Chlorine Biomass

The release of critical ash-forming elements during the pyrolysis and combustion of corn stover has been investigated through controlled lab-scale experiments supported by multicomponent and multiphase thermodynamic equilibrium calculations. Fuel samples were treated under isothermal conditions ranging from 500 to 1150 °C, under both pyrolysis and combustion atmospheres. The volatilized material was quantified by means of mass balances based on char and ash elemental analysis, compared to a corresponding feedstock fuel analysis. Close relations between the observed K and Cl release are found, suggesting that Cl is the main facilitator for K release through sublimation of KCl, determined to begin as the reaction temperature approaches 700–800 °C. K is present in abundance relative to Cl, and the K release is found to cease as the fuel reaches complete dechlorination. In addition, around 50 wt % of the Cl is released at temperatures below 500 °C, presumably as HCl formed through ion-exchange reactions with ...

Effect of added diols (glycols) on the emulsion properties of oil, water and surfactant mixtures

We have investigated the effects of addition of various diols on the properties of water–paraffin emulsions stabilised by non-ionic surfactants. Diols do not partition to the oil phase of these emulsions to any significant extent. Diol addition causes phase inversion of the emulsions from water-in-oil (w/o) to oil-in-water (o/w) and the concentrations of the different diols required for phase inversion correlates with their tendency to adsorb at the oil–water interface. Results for the type of emulsion formed, the emulsion mean drop size and the stability of the emulsions with respect to droplet coalescence are discussed in terms of the relationships between these emulsion properties and the multiphase equilibrium liquid (microemulsion) phases from which they are derived.

A multi-scale framework for multi-phase equilibrium flash

A general multi-scale framework for multi-component, multi-phase equilibrium flash calculations, which uses information at the molecular and bulk fluid length scales, is described. The multi-scale Gibbs–Helmholtz constrained (GHC) EOS approach of Lucia (2010) is extended to include the use of (1) coarse grained NTP Monte Carlo simulations to gather pure component internal energies of departure, (2) a new linear mixing rule for internal energies of departure for mixtures, (3) a novel expression for partial fugacity coefficients for the GHC EOS, and (4) a novel flash algorithm that uses complex-valued compressibility factors and densities to assist in phase existence determination. Many numerical results for mixtures of CO 2–water, NaCl–water, and CO 2–NaCl–water are used to show that the GHC EOS flash approach is superior to all other approaches currently available. Many geometric illustrations are presented to elucidate key concepts and many experimental validations are used to substantiate claims of superiority.

The HELD algorithm for multicomponent, multiphase equilibrium calculations with generic equations of state

Abstract The HELD (Helmholtz free Energy Lagrangian Dual) algorithm is proposed to solve the isothermal, isobaric phase equilibrium problem ( P, T flash). The flash is posed as a minimisation of the Helmholtz free energy in the volume–composition space, reformulated through duality theory. The proposed solution strategy consists of: an initialisation stage, containing a stability test; a phase identification stage, in which linear and nonconvex optimisation problems are solved alternatively; and an acceleration and convergence stage. The stability test is solved with a tunneling algorithm and the nonconvex part of the second stage with a multistart approach. Examples are presented for three equations of state, SRK, SAFT-HS and SAFT-VR. Non-ideal mixtures of up to fifteen components are examined; they exhibit features such as azeotropy, liquid–liquid, and liquid–liquid–liquid equilibria. The HELD algorithm is found to be reliable over a variety of challenging phase behaviour, converging to the best known solution in all of the calculations undertaken.

The influence of temperature, pressure, salinity and capillary force on the formation of methane hydrate

We present here a thermodynamic model for predicting multi-phase equilibrium of methane hydrate liquid and vapor phases under conditions of different temperature, pressure, salinity and pore sizes. The model is based on the 1959 van der Waals–Platteeuw model, angle-dependent ab initio intermolecular potentials, the DMW-92 equation of state and Pitzer theory. Comparison with all available experimental data shows that this model can accurately predict the effects of temperature, pressure, salinity and capillary radius on the formation and dissociation of methane hydrate. Online calculations of the p–T conditions for the formation of methane hydrate at given salinities and pore sizes of sediments are available on: www.geochem-model.org/models.htm.

Preface

The 21st International Conference on Chemical Thermodynamics (ICCT-2010) was held in Tsukuba, Japan, on 1–6 August 2010, by the International Association of Chemical Thermodynamics (IACT) under the sponsorship of IUPAC. The organizing committee was chaired by Prof. T. Atake. The conference attracted more than 600 scientists from 37 different countries. During the conference period, the Rossini lecture and 9 plenary lectures were delivered. Forty invited papers and approximately 200 contributed papers were presented in 7 parallel sessions, together with about 300 poster presentations. The wide variety of fields in chemical thermodynamics is illustrated by the titles of a number of the symposia: “Fluids and fluid mixtures”, “Phase equilibria”, “Foods and pharmaceuticals”, “Biothermodynamics”, “Colloids and interfaces”, “Thermochemistry and molecular energetics”, “Environmental issues”, “Industrial applications, databases and software”, “Theory and simulation”, “Organic materials and polymers”, “Inorganic materials and metals”, “New techniques”, “Education in chemical thermodynamics”, and a special session in honor of Profs. S. Seki and H. Suga. As part of the scientific program, two workshops were also held, the titles of which are: “Energy in subsections on petroleum, coal and alternative sources”, and “Calorimetry with commercial relaxation instruments”.This issue of Pure and Applied Chemistry collects four selected plenary lectures delivered at the conference. The topics include challenges in teaching thermodynamics, new equations-of-state model of fluids and their mixtures, Gibbs energy minimization method in multiphase equilibria, and critical evaluation of thermophysical properties database in chemical process simulation. In these papers, we hope that the readers find the essence of the various aspects of current exciting research in chemical thermodynamics, which were exhibited in a lively manner during this successful conference. Other general papers presented in the symposia and workshops will be published in J. Chem. Thermodynamics, Thermochimica Acta, and Molecular Simulation.The 22nd ICCT is scheduled to be held August 2012 in Búzios, Brazil.Masaki AkaogiMakoto AratonoConference Editors

Evolution of the Adria-Europe plate boundary in the northern Dinarides: From continent-continent collision to back-arc extension

The Sava Zone of the northern Dinarides is part of the Cenozoic Adria‐Europe plate boundary. Here Late Cretaceous subduction of remnants of Meliata‐Vardaroceanic lithosphere led to the formation of a suture, across which upper plate European‐derived units of Tisza‐Dacia were juxtaposed with Adria‐derived units of the Dinarides. Late Cretaceous siliciclastic sediments,deposited on the Adriatic plate, were incorporated into an accretionary wedge that evolved during the initial stages of continent‐continent collision. Structurally deeper parts of the exposed accretionary wedge underwent amphibolite‐grade metamorphism. Grt‐Pl‐ Ms‐Bt thermobarometry and multiphase equilibria indicate temperatures between 550°C and 630°C and pressures between 5 and 7 kbar for this event. Peak metamorphic conditions were reached at around 65 Ma. Relatively slow cooling from peak metamorphic conditions throughout most of the Paleogene was possibly induced by hanging wall erosion in conjunction with southwest directed propagation of thrusting in the Dinarides. Accelerated cooling took place in Miocene times, when the Sava Zone underwent substantial extension that led to the exhumation of the metamorphosed units along a low‐angle detachment. Footwall exhumation started under greenschist facies conditions and was associated with top‐to‐the‐north tectonic transport, indicating exhumation from below European plate units. Extension postdates the emplacement of a 27 Ma old granitoid that underwent solid‐state deformation under greenschist facies conditions. The 40Ar/39Ar sericite and zircon and apatite fission track ages from the footwall allow bracketing this extensional unroofing between 25 and 14Ma. This extension is hence linked to Miocene rift‐related subsidence in the Pannonian basin, which represents a back‐arc basin formed due to subduction rollback in the Carpathians.

Computational Modelling of Oxide Surface Tensions in Secondary Metallurgy and Continuous Casting

AbstractTwo computational models were used to estimate the surface tensions of oxide systems containing SiO2, CaO, Na2O and Al2O3 as a function of temperature and composition. The compositions of the oxide melts were chosen to correspond to those of ladle slags in secondary metallurgy and to casting powders in continuous casting of steel. The first model uses Butler's equation to calculate the surface tensions of the multicomponent melts and is based on Tanaka et al.'s consideration of the ionic radii of the components as well as surface tensions and molar volumes of pure components. In the second model the same ionic radii dependent contribution is applied as activity coefficients to a constrained free energy model where the surface layer is considered as a separate phase in the system. In the model, the constrained interfacial area is analogous with a component mass balance in a traditional computation of a multiphase chemical equilibrium and surface energy with the corresponding chemical potential. Based on the results it is concluded that the effect of temperature on the surface tensions of the considered oxide melts is insignificant when compared to the effect of chemical composition. According to the validation the results agree well with published surface tension data. The multi‐component surface tension approach provides a practical method for evaluation of e.g. functioning of various casting powders in industrial steel casting practice.

Predicting microsegregation in multicomponent aluminum alloys – progress in thermodynamic consistency

Abstract Recent developments in modeling the interaction of thermodynamics and kinetics during microsegregation formation in multicomponent alloys are reported. A model accounting for solid state back diffusion, dendrite arm coarsening, dendrite tip undercooling, eutectic undercooling and thermodynamic correction of the interface concentrations is presented. By coupling the solution of the diffusion equation in the liquid and solid phases with the thermochemistry library ChemApp, the phase equilibria at the solid–liquid interface are calculated at each time step. Using an activity based method for identifying multiphase equilibria and metastable extensions of the stability range of phases, a thermodynamically consistent implementation of eutectic undercooling in multicomponent systems is achieved. The model is equipped with a userfriendly interface that allows setting the model parameters interactively and that presents the results (solute distribution, phase fractions, secondary arm spacing) in a pertinent way.

Post-kinematic recovery of fractured cordierite in the lower amphibolite facies: the significance of intra-crystal cation diffusion for retrograde partial mineral breakdown

Brittle intra-crystal fracturing during a micro- seismic event under amphibolite facies P-T conditions (ca. 4.5 kbar, 555°C) formed micro-shear zones and brittle fragments in cordierite from migmatites of the Ordovician Sierras Pampeanas (NW Argentina). During post-seismic static recovery and coarsening of crystal fragments, primary cordierite (XMg=0.65) underwent partial breakdown within the fractured and subsequently recovered and recrystallized part of primary cordierite. Post-kinematic partial primary cordierite breakdown results in the formation of secondary sillimanite, magnetite, staurolite, quartz, and secondary cordierite (XMg=0.70-0.80) within a ca. 300-500 μm thick alteration zone. Secondary cordierite, volumetrically the most important secondary phase, essentially forms by iron and magnesium diffusion and substitution. All other secondary phases form by nucleation. The retrograde breakdown occurred under near-isochemical conditions with only limited influx of hydrothermal fluids containing minor zinc, potassium, silica, and excess oxygen. The observed modal composition of the alteration zone is similar to results of thermodynamic modeling of primary cordierite breakdown, using multiphase equilibria software. This indicates that the observed reaction reflects conditions of, or close to, thermodynamic equilibrium. Although fluid was present during, and may have been an important factor contributing to, partial mineral breakdown, we consider post-kinematic recovery and recrystallization, effected by a combination of cation diffusion and elimination of dis- locations, as the key process facilitating retrograde meta- morphism and the generation of the secondary mineral assemblage in (near-) equilibrium modes.

Prediction of multiphase equilibrium using the PC-SAFT equation of state and simultaneous testing of phase stability

This work employs the PC-SAFT equation of state to illustrate how to compute phase equilibria and stability of multiphase systems. The proposed computation scheme is based on the methodology of Gupta et al. (1991) but with modifications. Phase equilibria and stability are computed simultaneously and without the need to modify the exact stability equation. This approach does not encounter difficulty when the phase fraction approaches zero. A simple initialization strategy is utilized. In addition, this work tests the predictive capability of PC-SAFT in multiphase systems of water-hydrocarbon containing systems at different pressure–temperature conditions. The dipole and quadrupole interactions were included in the PC-SAFT equation and the binary interaction parameters ( k ij ) were set to zero. The work has demonstrated the ability of PC-SAFT to successfully predict vapour–liquid–liquid equilibrium of systems containing water, hydrocarbons and ethylene glycol with or without carbon dioxide.