Consideration of dipole–quadrupole interactions in molecular based equations of state

The thermodynamic behaviour of a number of real substances is determined by dipolar as well as quadrupolar interactions of the molecules. In equations of state (EOS) like, e.g. BACKONE separate contributions to the Helmholtz energy for the dipolar and the quadrupolar interactions are considered but no cross contributions. Here, the concept of effective dipole and quadrupole contributions is suggested in which the effective dipole strength μ_e is influenced by the quadrupole cross interaction. Similarily, the effective quadrupole strength Q_e takes into account the dipole cross interaction. In order to arrive at these effective dipolar and quadrupolar strengths, molecular simulations are performed. From the simulation results correlation equations are derived which are used in combination with BACKONE for the calculation of vapour–liquid equilibria (VLE) of real mixtures. By using these effective moments, the only required binary mixing rule parameter k_ij tends to small values of about 0.01 and becomes temperature-independent. Moreover, the VLE pressures are predicted now considerably better than without consideration of the cross contributions.     

Densities and Apparent Molar Volumes of Aqueous H<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>BO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript> Solutions at Temperatures from 296 to 573 K and at Pressures up to 48 MPa

Densities of four aqueous H₃BO₃ solutions (0.062, 0.155, 0.315, and 0.529 mol-kg^–1) have been measured in the liquid phase with a constant volume piezometer immersed in a precisely controlled liquid thermostat. Measurements were made at temperatures between 296 and 573 K and pressures from 0.82 to 48 MPa. The total uncertainties of the density, pressure, temperature, and molality measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.0005 mol-kg^–1, respectively. The accuracy of the method was confirmed by PVT measurements on pure water for two isobars (30 and 39 MPa) at temperatures from 313 to 573 K. The experimental and calculated (IAPWS formulation) densities for pure water show excellent agreement which is within their experimental uncertainties (average absolute deviation, AAD=0.012%;). Apparent and partial molar volumes were derived using the measured densities for solutions and pure water, and these results were extrapolated to zero concentration to yield the partial molar volumes of the electrolyte (H₃BO₃) at infinite dilution. The temperature, pressure, and concentration dependencies of the apparent and partial molar volumes were studied. Small pressure and concentration effects on the apparent molar volumes were found at temperatures up to 500 K. The parameters of a polynomial type of equation of state for the specific volume V_sol(P, T, m) as a function of pressure, temperature, and molality were obtained with a least-squares method using the experimental data. The root-mean-square deviation between measured and calculated values from this polynomial equation of state is ±0.2 kg-m^–3 for density. Measured values of the solution densities and the apparent and partial molar volumes are compared with data reported in the literature.     

Bubble pressures and saturated liquid molar volumes of trichlorofluoromethane—chlorodifluoromethane mixtures. Representation of refrigerant-mixtures vapor—liquid equilibrium data by a modified form of the Peng—Robinson equation of state

Experimental vapor—liquid equilibrium data and saturated liquid molar volumes of chlorodifluoromethane—trichlorofluoromethane binary mixtures have been obtained at four temperatures (298.15, 323.15, 348.15 and 373.15 K) using apparatus described previously.The experimental vapor—liquid equilibria are represented well by a modified form of the Peng—Robinson equation of state with one interaction parameter, but the mean deviation between the calculated and experimental densities is 5%.Vapor—liquid data for binary refrigerant mixtures from the literature are treated using the modified form of the Peng—Robinson equation of state with one adjusted interaction parameter in the mixing rule for a. The representation is fair and is not improved by introducing an additional parameter in the mixing rule for b.     

Comparison of methods for calculating thermodynamic properties of binary mixtures in the sub and super critical state: Lee–Kesler and cubic equations of state for binary mixtures containing either CO2 or H2S

The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO₂ or H₂S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO₂ and H₂S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee–Kesler equation; (b) two equations that included new reference fluids for the Lee–Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO₂ mixtures while for H₂S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee–Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%.     

Near-saturation (P,ρ,T) and vapor-pressure measurements of NH3, and liquid-phase isothermal (P,ρ,T) and bubble-point-pressure measurements of NH3+H2O mixtures

Near-saturation pressure, density, and temperature (P,ρ,T) and vapor-pressure measurements for NH₃ are reported over a temperature range from 279 to 392 K. Liquid-phase isothermal (P,ρ,T) and bubble-point-pressure measurements for two standard mixtures of NH₃+H₂O (x_NH3=0.8360 and 0.9057 mole fraction) are reported over a temperature range from 280 to 379 K and at pressures to 7.7 MPa. These data are compared to literature data and correlations and agree within ±3% for bubble-point pressures, ±0.005 g/cm³ for liquid densities, and ±0.0011 g/cm³ for vapor densities. A consistent data set for equation-of-state optimization at high concentrations of NH₃ is proposed.     

An equation of state for gases and liquids

We present an equation of state that can represent within experimental error most individual sets of published PVT data for most fluids, whether in the range of vapor at moderate pressures, or compressed liquids, or gases at very high temperatures and densities, any region in fact except the vicinity of the critical point. In terms of pressure the equation is P = DRT [1 + (D/T) (c₁T + c₂D - 1) / (c₃ + c₄T^{$\text{sol1}\text{2}$} + c₅D + c₆D²)] where D = 1/V, the density in mole 1^?1. The coefficients are readily determined by a least squares fit of the data. An additional term is sometimes needed if the D range is very wide, say several times D_c. Different fluids can be simultaneously represented over a limited range, such as the compressed liquid region, by a single reduced form of the equation in which all but three of the constants are the same for all, and these three (a reducing T, 1/c₁, a reducing D, 1 / c₂, and a dimensionless parameter) are characteristic of each individual fluid. The equation can also simultaneously represent many data sets for a single fluid from many labs and covering various T and D ranges. From this, a consistent representation of its thermodynamic properties can be derived.     

Extension of the exp-6 model to the simulation of vapor-liquid equilibria of primary alcohols and their mixtures

Configurational-biased Gibbs ensemble Monte Carlo simulations were performed to obtain the phase behavior of the homologous series of primary alcohols from ethanol to 1-heptanol. Molecular interactions in these systems are modeled by a newly developed exp-6 potential in combination with a Coulombic intermolecular potential. Some of exp-6 potential parameters required to describe these alcohols were taken from the previous literature data reported for methanol and n-alkanes. The oxygen's potential parameters were optimized to fit the coexistence curve of these alcohols to the experimental data. Simulated values of saturated liquid and vapor densities, vapor pressures and critical constants of the alcohols are in good agreement with experimental data. The efficiency of the new model in the prediction of binary phase diagram of water/ethanol and n-hexane/1-propanol mixtures is also evaluated. The calculated mole fractions in the vapor and liquid phases of these binary mixtures also show satisfactory agreement with the experimental data.     

Experimental determination and calculation of the critical curves for the binary systems of CO2 containing ketone, alkane, ester and alcohol, respectively

A set of variable-volume autoclave with a quartz window was used for the experimental determination of the high-pressure phase equilibria and critical curves. The critical temperatures, pressures, densities and mole volumes in the region near the critical point of CO₂ were examined for eleven binary systems of supercritical CO₂ (SC CO₂) with different kinds of substances (ketone, alkane, ester and alcohol), respectively. The critical curves of the above binary systems were also calculated using an equation of state. The equation consists of a hard body repulsion term and an additive perturbation term, which takes care of the attractive molecular interaction. The calculated data were compared with the experimental data, and yielded good agreements. At the same time, the values of the adjustable parameters, λ, k_σ and k_? were obtained. The critical curves of the above eleven binary systems at higher temperatures and pressures all belong to type I.     

A group-contribution correlation for predicting thermodynamic properties with the Perturbed-Soft-Chain Theory

The Perturbed-Soft-Chain theory (PSCT), an equation of state capable of predicting thermodynamic properties for a variety of compounds, is modified to be a group-contribution equation. The Group-PSCT (GPSCT) treats each pure compound as a sum of its constituent functional groups, and interactions among these groups are considered. The three pure-compound parameters, v*, T* and c, used in the original PSCT are calculated by using combining rules for five independent group parameters. The group parameters in this paper were determined from a correlation of the PSCT parameters.Using the GPSCT, calculated results show good agreement with experimental data. Liquid-densities and vapor pressures for twenty-six low molecular-weight compounds (alkanes, alkenes, and aromatics) have been calculated with average absolute errors less than 3.5% for liquid-densities and 7% for vapor-pressures. Though these values are somewhat larger than for the original PSCT, mixture predictions often are better for GPSCT than for PSCT, especially for mixtures involving polymers. This suggests that the GPSCT should prove useful for intermediate molecular weight (i.e., 200 – 1000) compounds for which little experimental data exists.     

Experimental Vapor Pressures and Derived Thermodynamic Properties of Aqueous Solutions of Lithium Nitrate from 423 to 623 K

Vapor pressures of six aqueous lithium nitrate solutions with molalities of (0.181, 0.526, 0.963, 1.730, 2.990, and 5.250) mol-kg^–1 have been measured in the temperature range 423.15–623.15 K with a constant-volume piezometer immersed in a precision liquid thermostat. The static method was used to measure the vapor pressure. The total uncertainty of the temperature, pressure and composition measurements were estimated to be less than 15 mK, 0.2%, and 0.014%, respectively. The vapor pressures of pure water were measured with the same apparatus and procedure to confirm the accuracy of the method used for aqueous lithium nitrate solutions. The results for pure water were compared with high-accuracy P_S–T_S data calculated from the IAPWS standard equation of state. Important thermodynamic functions (activities of water and lithium nitrate, partial molar volumes, osmotic coefficient, excess relative partial molar entropy, and relative partial molar enthalpy values of the solvent) were derived using the measured values of vapor pressure for the solution and pure water. The measured and derived thermodynamic properties for solutions were compared with data reported in the literature. The present results are consistent with most previous reported thermodynamic data for the pure water and H₂O + LiNO₃ solutions at low temperatures.     

New (p, ρ, T) data for carbon dioxide – Nitrogen mixtures from (250 to 400) K at pressures up to 20 MPa

Comprehensive (p, ρ, T) measurements on two binary mixtures (0.10 CO₂ + 0.90 N₂ and 0.15 CO₂ + 0.85 N₂) were carried out in the gas phase at seven isotherms between (250 and 400) K and pressures up to 20 MPa using a single sinker densimeter with magnetic suspension coupling. A total of 69 (p, ρ, T) data for the first mixture and 69 (p, ρ, T) data for the second are presented in this article. The uncertainty in density was estimated to be (0.02 to 0.15)%, while the uncertainty in temperature was 3.9 mK and the uncertainty in pressure was less than 0.015% (coverage factor k = 2). Experimental results were compared with densities calculated from the GERG equation of state and with data reported by other authors for similar mixtures. Results yielded that, while deviations between experimental data and values calculated from the GERG equation were lower than 0.05% in density for low pressures, the relative error at high pressures and low temperatures increased to about (0.2 to 0.3)%. The main aim of this work was to contribute to an accurate density data base for CO₂/N₂ mixtures and to check or improve equations of state existing for these binary mixtures.     

Compressed liquid densities of 1-butanol and 2-butanol at temperatures from 313 K to 363 K and pressures up to 25 MPa

(p, ρ, T) properties were determined in liquid phase for 1-butanol and 2-butanol at temperatures from 313 K to 363 K and pressures up to 25 MPa using a vibrating tube densimeter. The uncertainty is estimated to be lower than ±0.2 kg · m⁻³ for the experimental densities. Nitrogen and water were used as reference fluids for the calibration of the vibrating tube densimeter. Experimental densities of 1-butanol and 2-butanol were correlated with a short empirical equation and the 11-parameter Benedict–Webb–Rubin–Starling equation of state (BWRS EoS) using a least square optimization. Statistical values to evaluate the different correlations were reported. Published densities of 1-butanol and 2-butanol are compared with values calculated with the BWRS EoS using the parameters obtained in this work. The experimental data determined here are also compared with available correlations for 1-butanol and 2-butanol.     

Application of 1-1 modification of van der waals equation of state for saturated binary liquid mixtures

The Law-Lielmezs (L-L) modification of Van der Waals equation of state has been extended to include four hydrocarbon-hydrocarbon binary liquid mixtures for the saturated liquid-vapour equilibrium states. The values of the characteristic mixture p_m and q_m parameters have been calculated, and a relation between the values of these parameters and the molecular weight of binary mixture has been established. The proposed relation is compared with the results obtained by the use of Lielmezs, Howell and Campbell, and Soave 1980 modifications of the Redlich-Kwong equation of state.     

Vapor–liquid equilibria and density measurement for binary mixtures of o-xylene + NMF, m-xylene + NMF and p-xylene + NMF at 333.15 K, 343.15 K and 353.15 K from 0 kPa to 101.3 kPa

Isothermal vapor–liquid equilibria at 333.15 K, 343.15 K and 353.15 K for three binary mixtures of o-xylene, m-xylene and p-xylene individually mixed with N-methylformamide (NMF), have been obtained at pressures ranged from 0 kPa to 101.3 kPa over the whole composition range. The Wilson, NRTL and UNIQUAC activity coefficient models have been employed to correlate experimental pressures and liquid mole fractions. The non-ideal behavior of the vapor phase has been considered by using the Peng–Robinson equation of state in calculating the vapor mole fraction. Liquid and vapor densities were measured by using two vibrating tube densitometers. The excess molar volumes of the liquid phase were also determined. Three systems of o-xylene + NMF, m-xylene + NMF and p-xylene + NMF mixtures present large positive deviations from the ideal solution and belong to endothermic mixings because their excess Gibbs energies are positive. Temperature dependent intermolecular parameters in the NRTL model correlation were finally obtained in this study.     

Transferable step potentials for perfluorinated hydrocarbons

The step potential equilibria and discontinuous molecular dynamics (SPEADMD) model is adapted for characterizing the interaction potentials of perfluorocarbons and their mixtures with n-alkanes. We seek to explain the peculiar behavior of these systems, especially with regard to the unfavorable mixing behavior. The methodology is based on discontinuous molecular dynamics (DMD) and second order thermodynamic perturbation theory (TPT). DMD simulation is applied to the repulsive part of the potential. The effects of disperse attractions and hydrogen bonding are treated by TPT, discretizing the attractive potential into four distinct wells of variable depth. This approach accelerates the molecular simulations in general and the parameterization of the transferable potentials in particular. C₃–C₈ straight chain perfluorocarbons are characterized along with perfluorobenzene, perfluorocyclobutane, and heptafluoropropane applying explicit atom models for all fluorine atoms. Each compound is simulated at 21 densities. Interpolation with density combines with TPT to give a complete equation of state. The depths of the attractive wells are optimized by iterating on their values until the vapor pressures computed by the resulting equation of state provide the minimum deviation from experimental data.     

Phase compositions and saturated densities for the binary systems of carbon dioxide with ethanol and dichloromethane

The compositions and densities of the liquid and vapor phases of two binary systems at equilibrium were measured on a new experimental apparatus over a range of temperatures and pressures. The studied systems are: CO₂–ethanol at 313.2 and 328.2 K; CO₂–dichloromethane at 308.2, 318.2 and 328.2 K and for pressures ranging from ambient up to ca. 9 MPa. Some of our measurements are critically compared with corresponding literature values. These measurements are ideally suited for testing equation-of-state models. The recently developed quasi-chemical hydrogen-bonding (QCHB) model was used for correlating the experimental data. A satisfactory agreement was obtained between experimental and calculated phase compositions and saturated densities.     

Vapor–liquid equilibrium data for the sulfur dioxide (SO2) + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at temperatures from 288.07 to 403.19 K and pressures up to 5.38 MPa: Representation of the critical point and azeotrope temperature dependence

Isothermal vapor–liquid equilibrium data have been measured for the binary system SO₂ + R227ea (1,1,1,2,3,3,3-heptafluoropropane) at 10 temperatures between 288.07 and 403.19 K, and at pressures in the range 0.276–5.38 MPa. The peculiarity of this system is the existence of an azeotrope. The experimental method used in this work is of the static-analytic type, taking advantage of two pneumatic capillary samplers (Rolsi™, Armines’ patent) developed in the Cenerg/TEP laboratory. The data were obtained with uncertainties within ±0.02 K, ±0.0015 MPa and ±1% for molar compositions.The isothermal P, x, y data are well represented with the Peng–Robinson equation of state using the Mathias Copeman alpha function and the Wong–Sandler mixing rules involving the NRTL model.     

Vapor–liquid equilibrium of nitrogen in an equimolar hexane + decane mixture at temperatures of 258, 273, and 298 K and pressures to 20 MPa

In this work we present experimental results of P, T, x, y, for the vapor–liquid equilibrium of the ternary system: nitrogen in an equimolar hexane+decane mixture at 258, 273, and 298 K in the range 1.5–20 MPa. The solubility of nitrogen in the liquid mixture of hexane+decane is increased when the pressure is increased; however, a considerable change in the solubility values is not observed as a function of temperature in the range studied. We have correlated the experimental results using the Peng–Robinson equation of state. The standard deviation of the fit shows that the data are well correlated (within the experimental error) in the ranges of pressure and temperature studied.     

Measurement of the (p, ρ, T) relation of propane, propylene, n-butane, and isobutane in the temperature range from (95 to 340) K at pressures up to 12 MPa using an accurate two-sinker densimeter

Comprehensive (p, ρ, T) measurements on propane. propylene, n-butane, and isobutane have been carried out in the homogenous gas and liquid phases and along the (vapour + liquid) coexistence curve. The results cover a temperature range from (95 to 340) K at pressures up to 12 MPa. The measurements were performed by using an accurate two-sinker densimeter based on the Archimedes’ buoyancy principle. The total uncertainty of the measurements in density is (0.01 to 0.02)% (level of confidence 95%), except for low gas densities. Values for the second and third virial coefficients have also been determined from the measurements in the homogeneous gas regions of the fluids. The experimental results have been compared with previous results of other experimentalists and with values calculated from current equations of state. Moreover, previously unpublished results of (p, ρ, T) measurements on propane in the temperature range from (340 to 520) K at pressures up to 30 MPa are listed in the appendix.