Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Densities and Refractive Indices of Binary Mixtures of Benzene with Triethylamine and Tributylamine at Different Temperatures

Experimental densities, ρ, and refractive indices, n _D for binary liquid mixtures of benzene with triethylamine (TEA) and tributylamine (TBA) have been measured as a function of composition in the temperature range from 278.15 to 318.15 K. The excess molar volume, V ^E , and its temperature dependence, dV ^E /dT for the binary mixtures were calculated using the experimental data. The values of V ^E for the mixtures were also estimated by using the Flory statistical theory and refractive index.     

Equation of State of He-H2 and He-D2 Dense Fluid Mixtures at High Pressures and Temperatures

The fluid variational theory is used to calculate the Hugoniot equation of state (EOS) of He, D₂, He + H₂, and He + D₂ fluid mixtures with different He:H₂ and He:D₂ compositions at high pressures and temperatures. He, H₂, and D₂ are the lightest elements. Therefore, the quantum effect is included via a first-order quantum correction in the framework of the Wigner-Kirkwood expansion. An examination of the reliability of the above computations is performed by comparing experiments and calculations, in which the calculation procedure used for He and D₂ is adopted also for He + D₂ and He + H₂, since no experimental data for the mixtures are available to conduct these comparisons. Good agreement in both comparisons is found. This result may be seen as an indirect verification of the calculation procedures used here, at least, in the pressure and temperature domains covered by the experimental data for He and D₂ used for comparisons, which is nearly up to 40 GPa and 10⁵ K. Also, the equation of state of He + H₂ fluid mixtures with different compositions is predicted over a wide range of temperatures and pressures.     

A Thermodynamic Property Model for the Binary Mixture of Methane and Hydrogen Sulfide

A thermodynamic property model with new mixing rules using the Helmholtz free energy is presented for the binary mixture of methane and hydrogen sulfide based on experimental P_ρ T_x data, vapor–liquid equilibrium data, and critical-point properties. The binary mixture of methane and hydrogen sulfide shows vapor–liquid–liquid equilibria and a divergence of the critical curve. The model represents the existing experimental data accurately and describes the complicated behavior of the phase equilibria and the critical curve. The uncertainty in density calculations is estimated to be 2%. The uncertainty in vapor–liquid equilibrium calculations is 0.02 mole fraction in the liquid phase and 0.03 mole fraction in the vapor phase. The model also represents the critical points with an uncertainty of 2% in temperature and 3% in pressure. Graphical and statistical comparisons between experimental data and the available thermodynamic models are discussed     

Viscosities of six 1-Alkanols at temperatures in the range 298–348 K and pressures up to 200 MPa

Viscosities of six higher 1-alkanols (1-hexanol, 1-octanol, 1-decanol, 1-dodecanol, 1-tetradecanol, and 1-hexadecanol) have been determined at temperatures from 298 to 348 K and pressures up to 200 MPa. The viscosity measurements were performed using a falling-body viscometer with an uncertainty of ±5%. Simple equations are presented to express the experimental viscosities as a function of temperature and pressure within the experimental uncertainty. The relationship between the viscosity and the density of these alkanols is discussed in terms of the significant structure theory extended to high pressures.     

Viscosity Measurements and Correlation of the Squalane + CO<Subscript>2</Subscript> Mixture

Experimental results for the viscosity of squalane + CO₂ mixtures are reported. The viscosities were measured using a rolling ball viscometer. The experimental temperatures were 293.15, 313.15, 333.15, and 353.15 K, and pressures were 10.0, 15.0, and 20.0 MPa. The CO₂ mole fraction of the mixtures varied from 0 to 0.417. The experimental uncertainties in viscosity were estimated to be within ±3.0%. The viscosity of the mixtures decreased with an increase in the CO₂ mole fraction. The experimental data were compared with predictions from the Grunberg–Nissan and McAllister equations, which correlated the experimental data with maximum deviations of 10 and 8.7%, respectively.     

Prediction of transport properties of dense gases and liquids by the Peng-Robinson (PR) equation of state

An attempt is made in this work to combine the Enskog theory of transport properties with the simple cubic Peng-Robinson (PR) equation of state. The PR equation of state provides the density dependence of the equilibrium radial distribution function. A slight empirical modification of the Enskog equation is proposed to improve the accuracy of correlation of thermal conductivity and viscosity coefficient for dense gases and liquids. Extensive comparisons with experimental data of pure fluids are made for a wide range of fluid states with temperatures from 90 to 500 K and pressures from 1 to 740 atm. The total average absolute deviations are 2.67% and 2.02% for viscosity and thermal conductivity predictions, respectively. The proposed procedure for predicting viscosity and thermal conductivity is simple and straightforward. It requires only critical parameters and acentric factors for the fluids.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Correlation for the Carbon Dioxide and Water Mixture Based on The Lemmon–Jacobsen Mixture Model and the Peng–Robinson Equation of State

Models representing the thermodynamic behavior of the CO₂–H₂O mixture have been developed. The single-phase model is based upon the thermodynamic property mixture model proposed by Lemmon and Jacobsen. The model represents the single-phase vapor states over the temperature range of 323–1074 K, up to a pressure of 100 MPa over the entire composition range. The experimental data used to develop these formulations include pressure–density–temperature-composition, second virial coefficients, and excess enthalpy. A nonlinear regression algorithm was used to determine the various adjustable parameters of the model. The model can be used to compute density values of the mixture to within ±0.1%. Due to a lack of single-phase liquid data for the mixture, the Peng–Robinson equation of state (PREOS) was used to predict the vapor–liquid equilibrium (VLE) properties of the mixture. Comparisons of values computed from the Peng–Robinson VLE predictions using standard binary interaction parameters to experimental data are presented to verify the accuracy of this calculation. The VLE calculation is shown to be accurate to within ±3 K in temperature over a temperature range of 323–624 K up to 20 MPa. The accuracy from 20 to 100 MPa is ±3 K up to ±30 K in temperature, being worse for higher pressures. Bubble-point mole fractions can be determined within ±0.05 for CO₂.     

Anharmonic effects in the specific heat of aluminum

The specific heat at constant pressure, C _p , of aluminum has been measured by Leadbetter between 300 and 772 K and by Brooks and Bingham between 330 and 893 K. Both sets of data are converted to the specific heat at constant 0 K volume, C _v0, by the Slater-Overton method, based on the equation of state and not the Debye type of theory. Corrections to the work of Overton are given. Our analysis shows that the C _v0 obtained from Leadbetter's data remains below 3R up to 750 K, whereas it becomes >3R for the Brooks and Bingham data in the temperature range 650–850 K. Calculations of C _v0 (harmonic + anharmonic) from three pseudopotentials are reported for (a) Harrison modified point ion potential with Hubbard exchange and correlation factor in the dielectric function, (q); (b) Ashcroft pseudopotential with the same (q) as in (a); and (c) Dagens-Rasolt-Taylor (DRT) M2 pseudopotential with Geldart-Taylor (q). The shape of the C _v0 curve is found to be similar for all three potentials. For DRT potential, C _v0 reaches 3R at 700 K, whereas the other two barely approach 3R about 900 K. The anharmonic contribution to C _v0 is a factor of two larger for the Dagens et al. compared to the other two potentials. There is a marked difference between the C _v0 curve from the analysis of the Brooks and Bingham data and the theoretical curves. It appears that the experimental points are too high from about 500 K up. The C _v0 curve from Leadbetter's data is very similar to the three theoretical curves, but the results appear to be too low. A remeasurement of the specific heat from 500 K to the melting point is needed.     

Deriving Analytical Expressions for the Ideal Curves and Using the Curves to Obtain the Temperature Dependence of Equation-of-State Parameters

Different equations of state (EOSs) have been used to obtain analytical expressions for the ideal curves, namely, the Joule–Thomson inversion curve (JTIC), Boyle curve (BC), and Joule inversion curve (JIC). The selected EOSs are the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Deiters, linear isotherm regularity (LIR), modified LIR (MLIR), dense system equation of state (DSEOS), and van der Waals (vdW). Analytical expressions have been obtained for the JTIC and BC only by using the LIR, MLIR, and vdW equations of state. The expression obtained using the LIR is the simplest. The experimental data for the JTIC and the calculated points from the empirical EOSs for the BC are well fitted into the derived expression from the LIR, in such a way that the fitting on this expression is better than those on the empirical expressions given by Gunn et al. and Miller. No experimental data have been reported for the BC and JIC; therefore, the calculated curves from different EOSs have been compared with those calculated from the empirical equations. On the basis of the JTIC, an approach is given for obtaining the temperature dependence of an EOS parameter(s). Such an approach has been used to determine the temperature dependences of A ₂ of the LIR, a and b parameters of the vdW, and the cohesion function of the RK. Such temperature dependences, obtained on the basis of the JTIC, have been found to be appropriate for other ideal curves as well.     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).