A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000?K and at pressures ranging from vapour pressure up to 40,000?bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.     

氨基酸季铵离子液体水溶液的密度和黏度

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Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.     

Calculation of the critical point for mixtures using mixture models based on Helmholtz energy equations of state

This paper mainly focuses on refrigerant mixtures with relatively simple critical behavior, and presents a practical and useful method for the critical point calculation for the mixtures using mixture models based on Helmholtz energy equations of state. The expression for critical point criterion suitable for this objective is derived first. Numerical manipulations to obtain a physically correct solution are described in detail. For four binary refrigerant mixtures of difluoromethane (R-32) + pentafluoroethane (R-125), R-125 + 1,1,1,2-tetrafluoroethane (R-134a), R-125 + 1,1,1-trifluoroethane (R-143a), and R-32 + propane (R-290), the critical temperatures and critical molar volumes are calculated applying the presented method. The calculation results are compared with experimental values, and the capabilities of the mixture models for the mixtures in the critical region are discussed.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

On interrelation between the internal pressure and the cohesion energy density

The question about the definition of the “internal pressure” concept is being discussed. It is shown that the previously found differential relation between the cohesion energy density and the internal pressure is one of the examples of an absolutely general interrelation between definitely connected differential functions. It is ascertained that the ratio (the internal pressure divided by the cohesion energy density) is a structuresensitive parameter inherent to the calorific (thermal) equation of a liquid state.     

Equation of state of the hard sphere liquid

Using the results of Monte Carlo simulation, equations of state of hard sphere liquids are calculated for 106 values of the fill factor η= 0.005–0.530 (step of 0.005). In the region of liquid phase stability the absolute accuracy of about 0.00001–0.00008 is reached. Correctness of the accuracy estimate is discussed. The results obtained are compared with reported equations of state of the hard sphere liquid.     

Model Equations of State for Liquid Alkali Metals

Abstract

The structure of a model equation of state for the liquid alkali metals is proposed, in response to the observed failure of the principle of corresponding states, and limited tests are presented.     

A perturbed Yukawa chain equation of state for refractory liquid metals

The perturbed Yukawa chain equation of state (EoS) has been employed to calculate the liquid density of refractory metals over a wide range of temperatures and pressures. The model uses three independent parameters: m-segment number, σ-segment size, and ε/k-segment energy. For pure components, parameters have been obtained by fitting the models to experimental data on liquid densities. Our calculations on the liquid density of tantalum, rhenium, molybdenum, titanium, zirconium, hafnium and niobium from undercooled temperatures up to several hundred degrees above the boiling point and pressures ranging from 0 to 200?MPa reproduces very accurately the experimental pVT data.     

Density estimated physicochemical properties of alanine-based ionic liquid [C7mim][Ala] and its application in selective transesterification of soybean oil

Amino acid ionic liquid (AAIL) based on alanine, 1-n-heptyl-3-methylimidazolium alanine ([C7mim][Ala]), has been prepared and characterized. Since the IL can form strong hydrogen bonds with water, trace amount of water is a problematic impurity in the IL. Using the standard addition method (SAM), the densities were measured in the temperature range from 293.15 to 343.15±0.05 K. On the basis of the experimental data of density, the surface tension , molar volume, and the molecular volume Vm, molar enthalpy of vaporization lgHm0, and the thermal expansion coefficients , for [C7mim][Ala] were estimated using semi-empirical methods. Also the interstice model has been verified with good accordance. Then the [C7mim][Ala] was taken as catalyst in the transesterification reaction with fatty acid, where soybean oil was used as raw material and methanol as reactant. The amount of catalyst, alcohol consumption, reaction time, temperature and other factors of the reaction were investigated. Using GC determination, the conversions were calculated by the internal standard method. The main ingredients of the products were identified by GC-MS as palm methyl ester and linoleic acid methyl ester only, which showed high selectivity in palmitic acid and linoleic acid.     

High-pressure vapor–liquid equilibria in the nitrogen–n-pentane system

New experimental vapor–liquid equilibrium data of the N₂–n-pentane system were measured over a wide temperature range from 344.3 to 447.9 K and pressures up to 35 MPa. A static-analytic apparatus with visual sapphire windows and pneumatic capillary samplers was used in the experimental measurements. Equilibrium phase compositions and vapor–liquid equilibrium ratios are reported. The new results were compared with those reported by other authors. The comparison showed that the pressure–composition data reported in this work are in good agreement with those determined by others but they are closer to the mixture critical point at each temperature level. The experimental data were modeled with the PR and PC-SAFT equations of state by using one-fluid mixing rules and a single temperature independent interaction parameter. Results of the modeling showed that the PC-SAFT equation fit the data satisfactorily even at the highest temperatures of study.     

Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals?

The PC-SAFT equation of state is a very popular and promising model for fluids that employs a complicated pressure-explicit mathematical function (and can therefore not be solved analytically at a specified pressure and temperature, contrary to classical cubic equations). In this work, we demonstrate that in case of pure fluids, the PC-SAFT equation may exhibit up to five different volume roots whereas cubic equations give at the most three volume roots (and yet, only one or two volume roots have real significance). The consequence of this strongly atypical behaviour is the existence of two different fluid–fluid coexistence lines (the vapour-pressure curve and an additional liquid–liquid equilibrium curve) and two critical points for a same pure component, which is obviously physically inconsistent. In addition to n-alkanes, nearly 60 very common pure components (branched alkanes, cycloalkanes, aromatics, esters, gases, and so on) were tested out and without any exception, we can claim that all of them exhibit this undesired behaviour. In addition, such similar phenomena (i.e. existence of more than three volume roots) may also arise with mixtures. From a computational point of view, most of the algorithms used for solving equations of state only search for three roots at the most and are thus likely to be inefficient when an equation of state gives more than three volume roots. To overcome this limitation, a simple procedure allowing to identify all the possible volume roots of an equation of state is proposed.     

Density improvement of the SRK equation of state

The SRK equation of state has been modified by volume translation in order to improve its accuracy both in- and outside the critical region. A temperature dependent volume correction is proposed which can match the true critical point of the pure component, and provides accurate densities for polar and non-polar pure substances both near to and far from the critical point. It can also be easily extended to mixtures, and the calculation results show that it can shift the critical locus towards experimental values and gives good results for the liquid densities of mixtures.     

Vapor–liquid equilibrium data for the nitrogen + n-octane system from (344.5 to 543.5) K and at pressures up to 50 MPa

A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers has been used to obtain new vapor–liquid equilibrium data for the N₂ + n-octane system over the temperature range from (344.5 to 543.5) K and at pressures up to 50 MPa. Equilibrium phase compositions and vapor–liquid equilibrium ratios are reported. The new results were compared with solubility data reported by other authors. The comparison showed that the solubility data reported in this work at 344.5 K are in good agreement with those determined by others at 344.3 K. The experimental data were modeled with the PR and PC-SAFT equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results from the modeling effort showed that the PC-SAFT equation was superior to the PR equation in correlating the experimental data of the N₂ + n-octane system.     

Thermodynamic properties for liquid mercury using GMA equation of state

The important known regularities and thermodynamic properties of liquid mercury have been studied based on the average potential energy. Recognised regularities, the linearity of Zeno contour, bulk modulus and secant bulk modulus as functions of temperature, isochors of pressure versus temperature and near linearity of the inverse isobaric expansion coefficient have been investigated, all evaluated using the Goharshadi–Morsali–Abbaspour equation of state. The validity of the equation of state in predicting thermophysical properties is confirmed by a statistical parameter, absolute average deviation, with a maximum value of 0.41, showing excellent agreement with the experiment at temperatures between 293.15 and 323.15?K from low to high pressures.     

A perturbed hard-sphere equation of state for alkali metals

A perturbed hard-sphere equation of state, employing a basic frame proposed by Eslami [H. Eslami, J. Nucl. Mater. 336 (2005) 135–139] has been developed for alkali metals. Following the approach introduced by Ihm et al. [G. Ihm, Y. Song, E.A. Mason, J. Chem. Phys. 94 (1991) 3839–3848], the temperature dependence of the parameters a and b has been fitted to liquid density data for potassium. The scaling parameters that are used to reduce the temperature are the temperature and density at normal boiling point. The important improvement is to omit the adjustable parameters, the well depth and the location of the minimum of pair potential, which are required to apply the earlier equation of state of Eslami. The present EoS, which can be used without fitting parameters, reproduces the volumetric behavior of liquid alkali metals with a very good accuracy. Six hundred and ninety four data points at different pressures and temperatures are examined and the average absolute deviation of predicted liquid density data compared to experiment is 1.41%.     

Estimation of Physico-chemical Properties of Ionic Liquid EPReO_4 Using Surface Tension and Density

An ionic liquid (IL) EPReO₄ (N‐ethylpyridinium rheniumate) was prepared. The density and surface tension values of the IL were determined in the temperature range of 293.15–343.15 K. The ionic volume and surface entropy of the IL were estimated by extrapolation, respectively. In terms of Glasser's theory, the standard molar entropy and lattice energy of the IL were estimated, respectively. Using Kabo's and Rebelo's methods, the molar enthalpy values of vaporization of the IL, Δ^g_lH⁰_m (298 K), at 298 K and, Δ^g_lH⁰_m (T_b), at hypothetical normal boiling point were estimated, respectively. According to the interstice model, the thermal expansion coefficient of IL EPReO₄ (α) was calculated and compared with experimental value, finding their magnitude order is in good agreement by 8.98%.