Liquid—vapor equilibrium in the system H2Ar at temperatures from 83 to 141 K and pressures to 52 MPa

Calado, J.C.G. and Streett, W.B., 1979. Liquid—vapor equilibrium in the system H₂Ar at temperatures from 83 to 141 K and pressures to 52 MPa. Fluid Phase Equilibria, 2: 275–282.Experimental measurements of liquid—vapor phase equilibria in the system H₂Ar are reported for thirteen temperatures in the range 83.09 to 141.42 K, and pressures to 52 MPa. The mixture critical line and the pressure—temperature trace of the three-phase line solid—liquid—gas have been located. These lines intersect at T = 84.0 K and P = 52.5 MPa to form an upper critical end point. The pressure—temperature trace of the three-phase line has a temperature minimum at T ? 82.5 K, P ? 20 MPa.     

Hybrid method for phase equilibrium flash calculations

Joulia, X., Maggiochi, P., Koehret, B., Paradowski, H. and Bartuel, J.J., 1986. Hybrid method for phase equilibrium flash calculations. Fluid Phase Equilibria, 26: 15–36.A new algorithm for the calculation of a two-phase equilibrium at a given temperature and pressure using various thermodynamic models is described. This algorithm is a combination of two simultaneous solution methods based on a linearization of the system of equations with or without the partial derivatives of equilibrium ratios with respect to composition. This hybrid method exploits the reliability of the first order methods, which make good progress from a poor starting point, and, if necessary, switches on special application of the Schubert method to accelerate the rate of convergence. Results are reported for liquid—liquid and liquid—vapour equilibria with special attention in the vicinity of critical points.     

Ternary phase equilibria for the sodium chloride–sodium sulfate–water system at 200 and 250 bar up to 400°C

Phase equilibria in the NaCl–Na₂SO₄–H₂O system were investigated at 200 and 250 bar for total salt concentrations ranging from 5 to 20 wt.% total salt over temperatures ranging from 320 to 400°C. In addition to providing data for this ternary system, the experiments also added information on the phase behavior of the two binary systems: NaCl–H₂O and Na₂SO₄–H₂O. For salt mixture compositions which were rich in sodium sulfate, a solid phase was observed to nucleate from the homogeneous liquid phase. Salt mixture compositions which had a high fraction of sodium chloride exhibited a vapor separation from a homogeneous liquid phase. By fitting curves to the solid–liquid and vapor–liquid separation temperatures, the temperature and composition of a constrained invariant point where liquid, solid salt and vapor are in equilibrium were estimated. These estimates were performed at discrete compositions of 5, 10, 15 and 20 wt.% total salt at pressures of 200 and 250 bar. The temperature and composition of the invariant point increased with increasing pressure following a simple thermodynamic model for boiling point elevation in a nearly ideal solution.     

Experimental densities,vapor pressures,and critical point,and a fundamental equation of state for dimethyl ether

Densities, vapor pressures, and the critical point were measured for dimethyl ether, thus, filling several gaps in the thermodynamic data for this compound. Densities were measured with a computer-controlled high temperature, high-pressure vibrating-tube densimeter system in the sub- and supercritical states. The densities were measured at temperatures from 273 to 523 K and pressures up to 40 MPa (417 data points), for which densities between 62 and 745 kg/m³ were covered. The uncertainty (where the uncertainties can be considered as estimates of a combined expanded uncertainty with a coverage factor of 2) in density measurement was estimated to be no greater than 0.1% in the liquid and compressed supercritical states. Near the critical temperature and pressure, the uncertainty increases to 1%. Using a variable volume apparatus with a sapphire tube, vapor pressures and critical data were determined. Vapor pressures were measured between 264 and 194 kPa up to near the critical point with an uncertainty of 0.1 kPa. The critical point was determined visually with an uncertainty of 1% for the critical volume, 0.1 K for the critical temperature, and 5 kPa for the critical pressure. The new vapor pressures and compressed liquid densities were correlated with the simple TRIDEN model. The new data along with the available literature data were used to develop a first fundamental Helmholtz energy equation of state for dimethyl ether, valid from 131.65 to 525 K and for pressures up to 40 MPa. The uncertainty in the equation of state for density ranges from 0.1% in the liquid to 1% near the critical point. The uncertainty in calculated heat capacities is 2%, and the uncertainty in vapor pressure is 0.25% at temperatures above 200 K. Although the equation presented here is an interim equation, it represents the best currently available.     

Experimental measurement and thermodynamic modelling of clathrate hydrate equilibria and salt solubility in aqueous ethylene glycol and electrolyte solutions

We present the extension of a recently developed method for modelling saline water to the thermodynamic prediction of phase behaviour for mixed salt–organic clathrate hydrate inhibitor aqueous solutions. Novel freezing point, boiling point and salt solubility data have been generated for NaCl–ethylene glycol (EG) and KCl–EG aqueous solutions. These data have been used in the optimisation of binary interaction parameters between salts and ethylene glycol. The extended thermodynamic model is capable of predicting complex vapour–liquid–solid (VLSE) equilibria for aqueous electrolytes and/or organic inhibitor solutions over a wide range of pressures, temperatures and inhibitor concentrations. Reliable hydrate dissociation data for two mixed salt–organic inhibitor quaternary systems (CH₄–H₂O–NaCl–EG and CH₄–H₂O–KCl–EG) have been measured at pressures up to 50 MPa. These data are used to validate the predictive capabilities of the model for hydrate equilibria. Good agreement between experimental data and predictions is observed, demonstrating the reliability of the developed model.     

Phase separation of gas–liquid and liquid–liquid microflows in microchips

Phase separation of gas–liquid and liquid–liquid microflows in microchannels were examined and characterized by interfacial pressure balance. We considered the conditions of the phase separation, where the phase separation requires a single phase flow in each output of the microchannel. As the interfacial pressure, we considered the pressure difference between the two phases due to pressure loss in each phase and the Laplace pressure generated by the interfacial tension at the interface between the separated phases. When the pressure difference between the two phases is balanced by the Laplace pressure, the contact line between the two phases is static. Since the contact angle characterizing the Laplace pressure is restricted to values between the advancing and receding contact angles, the Laplace pressure has a limit. When the pressure difference between the two phases exceeds the limiting Laplace pressure, one of the phases leaks into the output channel of the other phase, and the phase separation fails. In order to experimentally verify this physical picture, microchips were used having a width of 215 μm and a depth of 34 μm for the liquid–liquid microflows, a width of 100 μm and a depth of 45 μm for the gas–liquid microflows. The experimental results of the liquid–liquid microflows agreed well with the model whilst that of the gas–liquid microflows did not agree with the model because of the compressive properties of the gas phase and evaporation of the liquid phase. The model is useful for general liquid–liquid microflows in continuous flow chemical processing.     

Inhibition effect of 1-ethyl-3-methylimidazolium chloride on methane hydrate equilibrium

The dissociation conditions of methane hydrate in the presence of 0.1, 0.2, 0.3 and 0.4 mass fraction of 1-ethyl-3-methylimidazolium chloride (abbreviated by EMIM-Cl hereafter) were experimentally determined. A high pressure micro-differential scanning calorimeter equipped with a motorized pump was applied to measure the dissociation temperature of the (hydrate + liquid water + vapor) three-phase equilibrium under a constant pressure process with a pressure ranging from (5.0 to 35.0) MPa. The addition of EMIM-Cl would inhibit the methane hydrate formation. The most significant inhibition effect was observed at 0.4 mass fraction of EMIM-Cl in aqueous solution to lower the dissociation temperature by 12.82 K at 20.00 MPa in comparison to that of the (methane + water) system. The Peng–Robinson–Stryjek–Vera equation of state incorporated with COSMO-SAC activity coefficient model and the first order modified Huron–Vidal mixing rule were applied to evaluate the fugacity of vapor and liquid phase. A modified van der Waals and Platteeuw model with an explicit pressure dependence of the Langmuir adsorption constant was applied to determine the fugacity of hydrate phase. The predictive thermodynamic model successfully describes the tendency of phase behavior of methane hydrate in the presence of EMIM-Cl in the range from 0.1 to 0.4 mass fraction with absolute average relative deviation in predicted temperature of 0.70%.     

硝酸盐型卤水体系的综合热力学模型与多温相图预测

硝酸盐型卤水是盐湖卤水、 硝酸盐工业、 废水处理中普遍遇到的电解质溶液体系. 硝酸盐具有极高的溶解度, 实现硝酸盐型复杂电解质体系物性和相平衡的精准热力学表达依然具有挑战性. 以煤化工废水的典型体系Na⁺//NO₃^- , Cl^-, SO₄^{2 -} -H₂O为对象, 以改进的eNRTL模型为基础, 由活度系数模型、 溶液物性模型、 物种热力学模型和固液相平衡模型构成了电解质体系的综合热力学模型. 利用二元体系的冰点、 饱和蒸汽压、 等压摩尔热容、 活度系数和渗透压系数等物性数据和三元体系等温相平衡数据, 采用多目标优化方法, 获得了表达研究体系的多温特性的12组液相特征参数和7个固相物种的热力学参数. 据此完成了3个二元体系、 3个三元体系等温相平衡的准确计算和三元、 四元完整相图的预测, 适用温度达到实验所及的全部温度范围(254.65~543.15 K); 适用浓度达到饱和程度, 其中NaNO₃的浓度高达226.88 mol/kg. 三元、 四元体系的多温相图预测结果与实验数据相吻合, 并给出了9个三元、 5个四元体系零变点的完整信息.     

Theoretical modeling for thermophysical properties of cellulose: pressure/volume/temperature data

Thermo-compression process—compression of pure cellulose under high temperatures and pressures—is a recent method to produce biodegradable materials. For such processes, experimental measurements and study of properties and behavior of cellulose are difficult to carry out. To overcome these difficulties, a complete pressure–volume–temperature investigation is needed as carried out in this work. To develop a predictive thermodynamic PVT model of cellulose theoretically, the modified Sanchez and Lacombe equation of state together with the implementation of the Hoftyzer and van Krevelen group contribution method and the Boudouris modification to the Constantinou and Gani’s group contribution method were coupled to the Compressible Regular Solution theory. The developed method is a pure predictive model and to examine the accuracy of theoretically calculated PVT data by the model, some available PVT data of cellulose at temperatures from 25 to 180 °C and pressures from 19.6 to 196 MPa (219 data points) were collected from literature. The comparisons were made and the agreement between the calculations and the experimental data were acceptable with a Cumulative Absolute Relative Deviation of 0.04 %. Consequently, the model can be used for prediction of thermodynamic properties of cellulose and cellulose-containing mixtures.     

Phase behaviour of the thermotropic cubic mesogen 1,2-bis-(4- n -octyloxybenzoyl)hydrazine under pressure

The phase transition behaviour of an optically isotropic, thermotropic cubic mesogen 1,2-bis-(4-n-octyloxybenzoyl)hydrazine, BABH(8), was investigated under pressures up to 200 MPa using a high pressure differential thermal analyser, wide-angle X-ray diffraction and a polarizing optical microscope equipped with a high pressure optical cell. The phase transition sequence, low temperature crystal (Cr₂)-high temperature crystal (Cr ₁)- cubic (Cub)-smectic C (SmC)-isotropic liquid (I) observed at atmospheric pressure, is seen in the low pressure region below about 30 MPa. The cubic phase disappears at high pressures above 30–40 MPa, in conjunction with the disappearance of the Cr₁ phase. The transition sequence changes to Cr₂-SmC-I in the high pressure region. Since only the Cub-SmC transition line among all the phase boundaries has a negative slope (dT/dP) in the temperature-pressure phase diagram, the temperature range for the cubic phase decreases rapidly with increasing pressure. As a result, a triple point was estimated approximately as 31.6 ±2.0 MPa, 147.0±1.0°C for the SmC, Cub and Cr₁ phases, indicating the upper limit of pressure for the observation of the cubic phase. Reversible changes in structure and optical texture between the Cub and SmC phases were observed from a spot-like X-ray pattern and dark field for the cubic phase to the Debye-Sherrer pattern and sand-like texture for the SmC phase both in isobaric and isothermal experiments.     

Experimental study and thermodynamic modeling of the MgO–NiO–SiO2 system

The MgO–NiO–SiO₂ system has been studied by a combination of thermodynamic modeling and experimental measurements of phase equilibria. A complete literature review, critical evaluation and thermodynamic modeling of phase diagrams and thermodynamic properties of all oxide phases in the MgO–NiO–SiO₂ system at 1 atm total pressure are presented. To resolve the contradictions in the literature data, a new experimental investigation has been carried out over the temperature range from (1400 to 1650) °C using an equilibration and quenching technique followed by electron probe X-ray microanalysis (EPMA). Tie-lines between olivine and monoxide, olivine and proto-pyroxene, liquid and olivine and liquid and cristobalite have been measured. The whole set of experimental data, including the new experimental results and previously published data, has been taken into consideration in thermodynamic modeling of oxide phases in the MgO–NiO–SiO₂ system. The Modified Quasichemical Model has been used for the liquid phase. A simple random mixing model with a polynomial expansion of the excess Gibbs energy has been used for the monoxide solid solution. The models for olivine and proto-pyroxene were developed within the framework of the Compound Energy Formalism. The optimized model parameters reproduce all available thermodynamic and phase diagram data within experimental error limits.     

Phase behaviour of thermotropic banana-shaped compounds under pressure

The phase behaviour of two achiral bent core banana-shaped compounds, the hexyloxy (compound I) and decyloxy (compound II) members of the 1,3-phenylene bis[N-(2-hydroxy-4-n-alkoxybenzylidene)-4′-aminobenzoate] series was investigated under hydrostatic pressures up to 300?MPa using high pressure differential thermal analysis and light transmission methods. The reversible transition sequence crystal (Cr₁)–B₁ phase–isotropic liquid (I), observed at room pressure for compound I, remains in the pressure region up to c 70?MPa. At higher pressures a pressure-induced crystalline phase (Cr_i) appears between the Cr₁ and B₁ phases, its temperature region becoming wider with increasing pressure. The temperature vs. pressure phase diagram shows a triple point of 72.9?MPa and 160.3°C for the Cr₁, Cr_i and B₁ phases, indicating the lower limit of pressure for the Cr_i phase. In compound II the reversible transition sequence crystal (Cr₁)–B₂ phase–I is seen over the whole pressure region, and the temperature range of the B₂ phase remains unaltered. It is concluded that both the B₁ and B₂ banana phases are stable over the whole pressure region studied.     

Analysis of the Glass-Forming Ability of Fe–Er Alloys,Based on Thermodynamic Modeling

The Fe–Er phase diagram and thermodynamic properties of all its phases are assessed by means of self-consistent analysis. To refine the data on phase equilibria in the Fe–Er system, an investigation is performed in the 10–40 at % range of Er concentrations. The temperature–concentration dependences of the thermodynamic properties of a melt are presented using the model of ideal associated solutions. Thermodynamic parameters of each phase are obtained, and the calculated results are in agreement with available experimental data. The correlation between the thermodynamic properties of liquid Fe–Er alloys and their tendency toward amorphization are studied. It is shown that compositions of amorphous alloys prepared by melt quenching coincide with the ranges of concentration with the predominance of Fe₃Er and FeEr₂ associative groups that have large negative entropies of formation.     

Critical points of adsorbed phases using a 2D lattice gas equation of state

The types of critical phase diagrams for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on a two-dimensional lattice gas theory are investigated. The search for critical point conditions was done using the Hicks and Young algorithm, switching to the Heidemann and Khalil algorithm in the close of vicinity of a critical point. We observed that the model can predict critical points that represent the conditions in which a vapor-like and a liquid-like adsorbed phases collapse. The critical diagrams were classified using an analogy with the van Konynenburg and Scott scheme for classifying the critical behavior of binary bulk mixtures. The original classification scheme is based on the critical lines on the pressure–temperature plane; we used a straightforward extension based on the critical lines on the spreading pressure–temperature plane. Five of the six types of phase behavior classified by von Konynenburg and Scott were observed using this thermodynamic model. The transitions between the types of phase diagram were also observed in temperature–mole fraction projections. These results extend previous observations that suggested the possibility of very interesting phase behaviors for adsorbed mixtures. However, experimental data would be necessary to confirm the predicted types of critical diagrams.     

Study of azeotropic mixtures with the advanced distillation curve approach

Classical methods for the study of complex fluid phase behavior include static and dynamic equilibrium cells that usually require vapor and liquid recirculation. These are sophisticated, costly apparatus that require highly trained operators, usually months of labor-intensive work per mixture, and the data analysis is also rather complex. Simpler approaches to the fundamental study of azeotropes are highly desirable, even if they provide only selected cuts through the phase diagram. Recently, we introduced an advanced distillation curve measurement method featuring: (1) a composition explicit data channel for each distillate fraction (for both qualitative and quantitative analysis), (2) temperature measurements that are true thermodynamic state points that can be modeled with an equation of state, (3) temperature, volume and pressure measurements of low uncertainty suitable for equation of state development, (4) consistency with a century of historical data, (5) an assessment of the energy content of each distillate fraction, (6) trace chemical analysis of each distillate fraction, and (7) corrosivity assessment of each distillate fraction. We have applied this technique to the study of azeotropic mixtures, for which this method provides the bubble point temperature and dew point composition, completely defining the thermodynamic state from the Gibbs phase rule perspective. In this paper, we present the application of the approach to several simple binary azeotropic mixtures: ethanol + benzene, 2-propanol + benzene, and acetone + chloroform.     

High pressure phase equilibrium properties for ethane+1-butanol system at 313.15 K

Phase equilibria and saturated densities for ethane+1-butanol system at high pressures were measured using a static-circulation apparatus at 313.15 K. The experimental apparatus equipped with three Anton Paar DMA 512S vibrating tube density meters was previously developed for measuring vapor–liquid–liquid equilibrium (VLLE) at high pressures. Co-existing phase composition and saturated density of each phase can be measured by means of the apparatus with a maximum temperature and pressure of 400 K and 20 MPa, respectively. The present experimental results include vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), and VLLE. The equilibrium composition and density of each phase were determined by gas chromatography and density measurements, respectively. The experimental data were correlated with various equations of state.     

Estimation of vapour liquid equilibria of binary systems,carbon dioxide–ethyl caproate,ethyl caprylate and ethyl caprate using artificial neural networks

Vapour liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations of state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for three binary systems viz. carbon dioxide–ethyl caproate, ethyl caprylate and ethyl caprate which are of importance in supercritical extraction. The temperature range in which these models are valid is 308.2–328.2 K and the pressure range is 1.6–9.2 MPa. The average absolute deviation for all the three systems in the estimation of liquid phase mole fraction was 3% or less and less than 0.02% for the vapour phase mole fraction. The error was less compared to that estimated by SRK or Peng Robinsons equation of state.     

Phase behaviour of the thermotropic cubic mesogen 1,2-bis-(4- n -octyloxybenzoyl)hydrazine under pressure

The phase transition behaviour of an optically isotropic, thermotropic cubic mesogen 1,2-bis-(4- n -octyloxybenzoyl)hydrazine, BABH(8), was investigated under pressures up to 200 MPa using a high pressure differential thermal analyser, wide-angle X-ray diffraction and a polarizing optical microscope equipped with a high pressure optical cell. The phase transition sequence, low temperature crystal (Cr 2 )-high temperature crystal (Cr 1 ) - cubic (Cub)-smectic C (SmC)-isotropic liquid (I) observed at atmospheric pressure, is seen in the low pressure region below about 30 MPa. The cubic phase disappears at high pressures above 30-40 MPa, in conjunction with the disappearance of the Cr 1 phase. The transition sequence changes to Cr 2 -SmC-I in the high pressure region. Since only the Cub-SmC transition line among all the phase boundaries has a negative slope (d T /d P ) in the temperature-pressure phase diagram, the temperature range for the cubic phase decreases rapidly with increasing pressure. As a result, a triple point was estimated approximately as 31.6 ±2.0 MPa, 147.0 ±1.0°C for the SmC, Cub and Cr 1 phases, indicating the upper limit of pressure for the observation of the cubic phase. Reversible changes in structure and optical texture between the Cub and SmC phases were observed from a spot-like X-ray pattern and dark field for the cubic phase to the Debye-Sherrer pattern and sand-like texture for the SmC phase both in isobaric and isothermal experiments.     

Thermodynamic consistency between calorimetric acoustic and volumetric measurementents

In this work, experimental measurements of isobaric heat capacity as well as speed of sound were performed in the compressed liquid phase of n-undecane from 303.15 to 373.15 K and for pressures ranging up to 60 MPa. These results were used to estimate various thermophysical properties such as density, isentropic compressibility and isochoric heat capacity in the same ranges of pressure and temperature. All these sets of data allow checking the thermodynamic consistency between calorimetric, acoustic and volumetric properties.     

The Entropies of n-Heptane,n-Octane,n-Nonane,and n-Undecane over a Wide Range of the Liquid and Gaseous States

The entropies S of C₇–C₁₁ normal alkanes over the temperature and pressure ranges 300–620 K and 0.5–60 MPa were obtained by the integration of the experimental isobars of isobaric heat capacity C _p . The C _p data were obtained using a flow adiabatic calorimeter with calorimetric flow rate measurements. The entropy values were determined up to critical temperatures by extrapolation from the sides of liquid S′ and gas S″ phases. The p-T-S thermodynamic surfaces of the alkanes under consideration in the liquid and gas phases were constructed. A generalized temperature dependence of S′ and S″ was determined for the homologous series over the temperature range from the triple to critical point within the framework of similarity theory.