A Generalized Equation of State for High-Pressure Liquids

An equation of state （EOS） for high-pressure liquids, i.e., Tait EOS, is deduced according to isothermal 1 3V compressibility KT= -1/V· （2V/2p）T·.Based on the equation, a generalized EOS for high pressure-liquids is established by using the reduced state principle and introducing a characteristic parameter-configuration factor ξ. Reasonably satisfactory P-V-T data for many organic compounds, including some polar components, were calculated by using the equation.

Representation of Phase Behavior of Ionic Liquids Using the Equation of State for Square-well Chain Fluids with Variable Range

An equation of state （EOS） for square-well chain fluids with variable range （SWCF-VR） developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperature （pVT） and phase equilibrium of pure ionic liquids （ILs） and their mixtures. The new molecular parameters for 23 ILs were obtained by fitting their experimental density data over a wide temperature and pressure ranges. The mo- lecular parameters of ILs composed of homologous organic cation and an identical anion such as [Cxmim][NTf2] are good linear with respect to their molecular weight, indicating that the molecular parameters of homologous substances, subsequently p VT and vapor-liquid equilibria vapor-liquid equilibria （VLE） can be predicted using the generalized parameter when no experimental data were available. The new set of parameters were satisfactorily used for calculations of the property of solvent and ILs mixture and the solubility of gas in various ILs at low pressure only using one temperature-independent binary interaction parameter.

A Modification of α in SRK Equation of State and Vapor-Liquid Equilibria Prediction

Based on results of saturated vapor pressures of pure substances calculated by SRK equation of state, the factor a in attractive pressure term was modified. Vapor-liquid equilibria of mixtures were calculated by original and modified SRK equation of state combined with MHV1 mixing rule and UNIFAC model, respectively. For 1447 saturated pressure points of 37 substance including alkanes; organics containing chlorine, fluorine, and oxygen; inorganic gases and water, the original SRK equation of state predicted pressure with an average deviation of 2.521% and modified one 1.673%. Binary vapor-liquid equilibria of alcohols containing mixtures and water containing mixtures also indicated that the SRK equation of state with the modified a had a better precision than that with the original one.

EXTENSION OF SOAVE EQUATION OF STATE TO LIQUID DENSITY

On the basis of vapor pressures, volumes of saturated vapor and liquid, both parameters "a" and "b" in Soave equation of state are treated as temperature dependent and an extended Soave equation is proposed in this work. The VLE for 38 pure components including polar substances have been calculated. The comparison of calculated results with experimental data shows the prediction of liquid density is improved over Soave equation without losing the accuracy of prediction in vapor pressure and vapor density.

A NEW MODEL FOR THE SURFACE TENSION OF BINARY AND TERNARY LIQUID MIXTURES BASED ON PENG-ROBINSON EQUATION OF STATE

Based on the surface chemical potential and Peng-Robinson equation of state,a newmodel is proposed to predict and correlate the surface tensions of binary and ternary liquid mix-tures.Using this method,the surface tensions of 73 binary and 8 ternary systems are calculatedwith average relative deviations 1.35% and 3.52% respectively.The proposed model is simple, re-liable and accurate.

Modeling p VT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State

Combining Peng-Robinson （PR） equation of state （EoS） with an association model derived from shield-sticky method （SSM） by Liu et al., a new cubic-plus-association （CPA） EoS is proposed to describe the ther-modynamic properties of pure ionic liquids （ILs） and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall aver-age deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their mo-lecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter kij, satisfactory correlations of vapor-liquid equilibria （VLE） for binary mixtures of ILs ＋ non-associating solvents and ＋ associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs ＋ non-associating mixtures from CPA, lattice-fluid （LF） and square-well chain fluids with variable range （SWCF-VR） EoSs are compared.

VAPOR-LIQUID EQUILIBRIA BY EXTENDED SOAVE EQUATION OF STATE

The Soave[1]equation of state is extensively accepted because of its accuracy andsimplicity.In 1988,Tan et al.[2]suggested a modification by introducing atemperature-dependent factor to parameter"b"on the basis of statistical meaning,anda good accuracy was obtained for supercritical fluids as well as fluids approaching criti-cal conditions but not for mixtures.In the previous work,an extended Soave equa-tion of state[3]has been proposed to improve the prediction of liquid density.In thispaper,the extended equation is used to calculate vapor-liquid equilibria of mixtures atsubcritical conditions.

A G^E/Equation of State Mixing Rule for Vapor-Liquid Equilibria

A new excess Gibbs free energy/equation of state type mixing 0rule was derived byremoving the infinite pressure boundary condition imposed by Wong and Sandler.The mixing rulewas extensively tested in terms of a comprehensive data base,consisting of 52 simple nonpolar-nonpolar,carbon dioxide containing,hydrocarbon-hydrocarbon,CFC,polar-polar,nonpolar-polarbinary and multicomponent systems.Focused on the complete predictive capability,a comparisonbetween the Wong-Sandler and the mixing rule proposed was conducted.The results indicate that thenew mixing rule is in general superior to the Wong-Sandler’s,and the binary interaction parameteras required by the latter is removed,which reduces computing effort and is reliable in predictions ofvapor-liquid equilibria from low pressures to high pressures.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.

Thermal equation of state of a natural kyanite up to 8.55 GPa and 1273 K

The thermal equation of state of a natural kyanite has been investigated with a DIA-type,cubic-anvil apparatus(SAM85)combined with an energy-dispersive synchrotron X-ray radiation technique up to 8.55 GPa and 1273 K.No phase transition was observed in the studied pressure-temperature(P-T)range.The Le Bail full profile refinement technique was used to derive the unit-cell parameters.By fixing the bulk modulus K 0 as 196 GPa and its pressure derivative K0 as 4,our P-V(volume)-T data were fitted to the high temperature BircheMurnaghan equation of state.The obtained parameters for the kyanite are:V_(0)=294.05(9)Å^(3),a=2.53(11)×10^(-5)K^(-1) and(K/T)P=-0.021(8)GPa∙K^(-1).These parameters have been combined with other experimentally-measured thermodynamic data for the relevant phases to calculate the P-T locus of the reaction kyanite¼stishoviteþcorundum.With this thermodynamically constrained phase boundary,previous high-pressure phase equi-librium experimental studies with the multi-anvil press have been evaluated.

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A suitable flexible functional form for the radial distribution function G（R） is assumed for the mixture, with R as a variable. The function G（R） has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics （MD） result for pure HS and LJ fluid respectively.

Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） and Lennard Jones （L J） fluids. A suitable axiomatic form for surface tension S（r） is assumed for the pure fluid, with r as a variable. The function S（r） has an arbitrary parameter rn. S（r） = A ＋ B（d/r）/[1 ＋ m（d/r）]. We use the condition in terms of radial distribution function G（λd,η） containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of rn and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.

GC-MCSPT-A MODIFIED HARD-SPHERE THREE-PARAMETER EQUATION OF STATE WITH GROUP MODEL FOR VLE PREDICTION

The mixing rule for a new group-contribution equation of state was proposed by combining the excess Gibbs energy model with the modified Hard-Sphere Three-Parameter Equation of State designated as the MCSPT equation. Low-and high-pressure vapor-liquid equilibria of 28 binary and 9 ternary systems containing strongly polar substances were predicted by using the interaction parameters of the original and modified UNIFAC model. Predicted results have shown that the proposed GO-MCSPT equation has an extensive applicability with satisfactory accuracy.

A New Approach to Investigation of vdW Type of Equations of State

A new approach to the investigation of vdW type of equations of state (EOS) is developed by embedding a vapor pressure equation and a saturated liquid volume equation into vdW type EOS, which results in a new function AS(T). The AS(T) possesses the properties of an attractive parameter A(T), and if an EOS is accurate in the whole PVT space, then its numerical value equals A(T). As a useful tool for investigating EOS, the As(T) has been used to make comparisons among RKS, PRSVII, PT and ALS EOS, and to indicate where the shortcomings of the EOS are coming from. Based on the AS(T), a possible way to develop a real predictive equation of state is also suggested.

Extension of Huron-Vidal-type Mixing Rule to Three-parameter Harmens-Knapp Cubic Equation of State

In this paper was extended the HV-type mixing rules to Harmens-Knapp cubic equation state(HK CEOS). The new HV-type mixing rule with HK CEOS was tested for Vapor-liquid equilibrium(VLE) of different polar and nonpolar systems. The tested results are in good agreement with existing experimental data within a wide range of temperatures and pressures. In comparison with the VDW mixing rule, the new mixing rule gives much better predictions for the VLE of nonpolar and polar systems.

A four parameter cubic equation of state with temperature dependent covolume parameter

A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations;2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and;3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points Tr= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer’s acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.

A MODIFIED VDW EQUATION WITH TEMPERATURE DEPENDENT PARAMETERS FOR CALCULATING OF ASSOCIATION AND POLAR FLUID

The generalized van der Waals(vdW)equation of state was proposed by Schmidt and Wenzel(1980)and later modified by Iwai,Margerum and Lu to improve its calculations of pure component liquid densities forthe polar fluid.In this paper,we present a modified vdW equation of state by introducing a new temperaturefunction for representing α(T)and considering u to be dependent on pure component property.

Statistical mechanics and artificial intelligence to model the thermodynamic properties of pure and mixture of ionic liquids

In this paper, the volumetric properties of pure and mixture of ionic liquids are predicted using the developed statistical mechanical equation of state in different temperatures, pressures and mole fractions. The temperature dependent parameters of the equation of state have been calculated using corresponding state correlation based on only the density at 298.15 K as scaling constants. The obtained mean of deviations of modified equation of state for density of all pure ionic liquids for 1662 data points was 0.25%. In addition, the performance of the artificial neural network(ANN) with principle component analysis(PCA) based on back propagation training with28 neurons in hidden layer for predicting of behavior of binary mixtures of ionic liquids was investigated. The AADs of a collection of 568 data points for all binary systems using the EOS and the ANN at various temperatures and mole fractions are 1.03% and 0.68%, respectively. Moreover, the excess molar volume of all binary mixtures is predicted using obtained densities of EOS and ANN, and the results show that these properties have good agreement with literature.

Equation of state of initially liquid carbon monoxide and nitrogen mixture

The modified liquid perturbation variational theory and the improved vdW-1f model were applied to calculating the equation of the state of liquid CO-N2 mixture with the ratio of 1:1, 4:1 and 1:4, respectively, in the shock pressure range of 9-49 GPa. It was shown that the calculated result for CO-N2 mixture with the ratio of 1:1 is well consistent with the earlier experimental data. The thermodynamics equilibrium, chemical equilibrium and phase equilibrium were all considered in detail. It was found that Hugoniot of liquid CO-N2 mixture is moderately softened in the pressure range of 20-30 GPa and 30-49 GPa for different initial proportions, and that the Hugoniot is more softened in the latter pressure range, which means that the structural phase transition occurs near 20 GPa and 30 GPa. Since the shock pro-ductions may absorb a plenty of systematic energy, the shock temperature and pressure decline compared with the case of no chemical reaction. Pressures and temperatures increase gradually with the increase in the mole fraction of nitrogen composition. The results for the 1:1 CO-N2 mixture lie in the middle of two others. Therefore, it was shown that the modified Lorentz-Berthelor rule used in the scheme is effective to study shock-compression properties of liquid CO-N2 mixture under high temperatures and high pressures.

The Performance of EOS Models in the Prediction of Vapor-Liquid Equilibria in Asymmetric Natural Gas Mixtures

The aim of this work is to apply cubic equations of state(EOS)to vapor-liquid equilibriacalculations of gas-heavy hydrocarbon systems,which are asymmetric in molecular size and areusually found in natural gases.Investigation has been done to test the validity of the original PSRKand the cubic simplified perturbed hard-chain(CSPhC)models for global phase diagrams.Thecalculation results show that both equations overpredict vapor pressure in the near critical region.In the prediction of the solubilities of high molecular weight(MW)hydrocarbons in the naturalgas,the PSRK model gives good agreement for the dew point pressure-vapor composition diagrams.Adjustment of the pure component parameters of the CSPHC EOS for heavy components to fit thevapor-liquid equilibrium(VLE)data has been proved to give significant promoting in predictionaccuracy.However,further improvement of a van der Waals EOS,such as SRK,PT and DG modelsfor the asymmetric systems by adjusting the three pure component properties,T_c, p_c and ?