Decay rate of critical fluctuations in ethane + carbon dioxide mixtures near the critical line including the critical azeotrope

Using the technique of photon correlation spectroscopy we have measured the decay rate of critical fluctuations in mixtures of ethane and carbon dioxide of various compositions including a near-azeotropic mixture. Our experimental data indicate that there is only one dominant mode of fluctuations and the decay rate is well described by the predictions of the mode-coupling theory with the exponent v=0.63 for all compositions. The decay rate, its background contributions, the shear viscosity, and the correlation length for the mixtures appear to interpolate simply between those of ethane and carbon dioxide.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Hydrogen component fugacity coefficients in binary mixtures with ethane: Pressure dependence

The fugacity coefficients of hydrogen in binary mixtures with ethane were measured. Data were taken using an experimental chamber which is divided into two regions by a semipermeable membrane through which hydrogen, but not ethane, can penetrate. The measurement of the gas pressures inside and outside the membrane gives the hydrogen component fugacity at a given temperature, binary mixture mole fraction, and mixture pressure. In this paper, results are reported at mixture pressures of 5.25, 6.97, 10.21, and 13.47 MPa. In each case, the temperature of the mixture was maintained at an average value of 130°C (403.15 K). The general qualitative features of the data are discussed, and comparisons are made with predictions obtained from the Redlich-Kwong and Peng-Robinson equations of state.     

Hydrogen component fugacities in binary mixtures with carbon dioxide: Pressure dependence

The fugacity coefficients of hydrogen in binary mixtures with carbon dioxide were measured isothermally using a physical equilibrium technique. This technique involves the use of an experimental chamber which is divided into two regions by a semipermeable membrane. Hydrogen can penetrate and pass through the membrane, while carbon dioxide cannot. During the approach to equilibrium, the pressure of pure hydrogen on one side of the membrane approaches the partial pressure of hydrogen in the mixture on the other side of the membrane. This allows a direct measurement of the hydrogen component fugacity at a given mixture mole fraction. In this study, results are reported for measurements made on the hydrogen + carbon dioxide binary at 130°C (403 K), with total mixture pressure of 3.45, 5.17, 8.62, 10.34, and 13.79 MPa. General trends in the experimental results are discussed, and comparisons are made with predictions from the Redlich-Kwong, Peng-Robinson, and extended corresponding-states models.     

Critical parameters of mixtures of carbon dioxide and ethane

This paper deals with an evaluation of the critical parameters reported for mixtures of carbon dioxide and ethane. Equations are presented for the critical parameters as a function of the concentration.     

The viscosity and thermal conductivity of ethane in the limit of zero density

New representations of the viscosity and thermal conductivity of ethane in the limit of zero density are provided. The correlation for the viscosity extends over the temperature range 200 to 1000 K, whereas that for thermal conductivity extends from 225 to 725 K. The behavior of each property is represented by an independent correlation of the appropriate effective collision cross section as a function of temperature. The final results are compared with experimental data as well as with earlier correlations. The accuracy of the viscosity correlation is estimated to be ±0.5 % in the temperature range 300 KT600 K, increasing to ±1.5 and ±2.5% at 200 and 1000 K, respectively. The uncertainty associated with the thermal conductivity correlation is ±2 % in the temperature range 300 KT500 K, increasing to ±3% at either end. The results of this study indicate that there is an urgent need for additional high-precision measurements of thermal conductivity especially for temperatures above 400 K.     

Assessment and improvement of viscosity models for miscible binary and ternary liquid mixtures

Abstract

Experimental viscosities of 74 binary and 11 ternary systems, ranging from ideal to non‐ideal solutions, are compared with values calculated with several different equations, including five polynomial functions, to gain an insight of each method and the way of improvement.

The 2‐constant and 3‐body equations of McAllister and Heric seem adequate for most of the binary systems except those with the complex viscosity‐composition characters. The error distribution discloses for these two equations about 80% of the predicted values show an error below 1%. The proposed two polynomials η_m=A+Bx ₁ +Cx ² ₁ and η_m=A+Bx ₁ +Cx ² ₁ +Dx ³ ₁ are superior to any binary viscosity model when evaluated on the bases of simplicity, generality and over‐all accuracy. Mean errors for all two approaches rarely exceed 2–3% even for the system exhibits a strong non‐ideal behavior.

Of all the ternary viscosity models tested, the proposed two polynomial expressions η_m=A+Bx ₁ +Cx ² ₁ +Dx ₂ +Ex ² ₂ +Fx ₁ x ₂ and η_m= A+Bx ₁ +Cx ² ₁ +Dx ₂ +Ex ² ₂ +Fx ₁ x ₂ +Gx ₁ x ² ₂ +Hx ² ₁ x ₂ are the most reliable with mean deviations generally being smaller than 2%. A 5‐parameter polynomial η_m=A+Bx ₁ +Cx ² ₁ +Dx ₂ +Ex ² ₂ proposed by us and the Ausländer formula are also recommended as two relatively simple methods of evaluating the ternary viscosities with reasonable accuracy for many practical purposes.     

The viscosity of gaseous propane and its initial density dependence

Results of five series of high-precision viscosity measurements on gaseous propane, each differing in density, are reported. The measurements were performed in a quartz oscillating-disk viscometer with small gaps from room temperature up to about 625 K and for densities between 0.01 and 0.05 mol · L^–1. The experimental data were evaluated with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficients deduced from the zero-density and initial-density viscosity coefficients for propane and for furthern-alkanes are in close agreement with the theoretical representation of the Rainwater-Friend theory for the potential parameter ratios by Bich and Vogel. A new representation of the viscosity of propane in the limit of zero density is provided using the new experimental data and some data sets from literature. The universal correlation based on the extended principle of corresponding states extends over the temperature range 293 to 625 K with an uncertainty of ±0.5 % and deviates from earlier representations by about 1 % at the upper temperature limit.     

Shear viscosity coefficients of compressed gaseous and liquid carbon dioxide at temperatures between 220 and 320 K and at pressures to 30 MPa

The shear viscosity coefficients of compressed gaseous and liquid carbon dioxide hav been measured with the torsional piezoelectric crystal method at temperatures between 220 and 320 K and at pressures to 30 MPa. The dependencies of the viscosity on pressure, density, and temperature and the dependencies of the fluidity (inverse viscosity) on molar volume and temperature have been examined. The measurements on the compressed liquid were correlated with a modified Hildebrand equation.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Argon+carbon dioxide gaseous mixture viscosities and anisotropic pair potential energy functions

The viscosities of pure gaseous carbon dioxide and argon+carbon dioxide mixtures have been measured with a capillary flow viscometer. The viscosities are relative to those of argon, in the temperature range 213 to 353 K, and considered accurate to ±0.7%. The pure-component viscosities agree closely with previous measurements. The mixture viscosities are used to calculate interaction viscosities and binary diffusion coefficients, which are compared with previous measurements. Interaction viscosities have been calculated, by use of the Mason-Monchick approximation, from the anisotropic pair potential energy functions for the unlike interaction proposed by Pack and his co-workers and by Hough and Howard. Comparison of these calculated interaction viscosities with those derived from our experiments and the higher-temperature measurements of Hobley, Matthews, and Townsend proves to be a powerful discriminant for the proposed anisotropic potential functions.Paper dedicated to Professor Joseph Kestin.     

Crossover behavior of the transport coefficients of critical binary mixtures

The behavior of the transport coefficients related to diffusion, heat conduction, and their cross-processes in fluid mixtures near the consolute point and the liquid-vapor critical line is investigated. Simple crossover equations for the critical enhancement of those coefficients are developed by incorporating a finite cutoff and time-dependent correlation functions of the order parameter and of the entropy into decoupled-mode theory integrals. It is shown that the thermal conductivity of a binary mixture is nondivergent and the crossover from the critical background in the critical point to the regular background far from the critical point is elucidated. The crossover to the behavior of the thermal conductivity in the one-component limit is also discussed.     

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.     

Thermal conductivity of organic liquid binary mixtures: Measurements and prediction method

A correlation presented in previous papers for the prediction of organic liquid thermal conductivity, , is generalized in order to estimate the thermal conductivity of the binary mixtures of organic liquids. The proposed equation contains the reduced temperature, the molar fractions, and two factors characteristic of the components. The comparison between predicted and experimental A values is developed at atmospheric pressure, taking into account data present in the literature and experimental values obtained at the Department of Energy of Ancona University, using the steady-state hot-wire method. Fifty binary mixtures are considered (28 of them are investigated by the authors at 25 and 50°C), and the mean general deviation between predicted and experimental thermal conductivity values (621 data points) is 2.5%.     

Measurements of the viscosity of compressed gaseous and liquid nitrogen + methane mixtures

The shear viscosity coefficients of three compressed gaseous and liquid nitrogen + methane mixtures have been measured at temperatures between 100 and 300 K and at pressures to about 30 MPa (4350 psia) with a piezoelectric quartz crystal viscometer. The precision of the measurements ranges from about 0.5% at high densities to about 1% at low densities. The estimated experimental error ranges from about 2% at high densities to about 4% at densities near the critical density and at supercritical temperatures near the critical temperature. The measurements have been compared with an extended corresponding states model, previously proposed for calculating the viscosities of fluid mixtures. Differences between the measured and calculated viscosities are discussed.     

Thermodynamic and transport properties of fluids and fluid mixtures in the extended critical region

A practical representation of the thermodynamic properties and the transport coefficients related to diffusion, heat conduction, and their cross-processes in pure fluids and binary mixtures near the liquid-vapor critical line is developed. Crossover equations for the critical enhancement of those coefficients incorporate the scaling laws near the critical point and are transformed to the regular background far away from the critical point. The crossover behavior of the thermal conductivity and the thermal diffusion ratio in binary mixtures is also discussed. A comparison is made with thermal-conductivity data for pure carbon dioxide, pure ethane, and carbon dioxide add ethane mixtures.     

Initial density dependence of experimental viscosities and of calculated diffusion coefficients of the binary vapor mixtures methanol-benzene and methanol-cyclohexane

The paper reports experimental results for the viscosity of the vapor mixtures methanol-benzene (five mole fractions with densities up to 1.5kg·m^–3 and 0.022 mol·L ^–1) and methanol-cyclohexane (four mole fractions with densities up to 1.9kg·m^–3 and 0.026 mol·L ^–1). In analogy to the pure components, the measurements on the mixtures were carried out with an oscillating-disk viscometer with small gaps, completely made of quartz, beginning as near as possible to room temperature and continuing to a maximum temperature of 630 K. A first evaluation by means of the Chapman-Enskog theory of dilute gases has shown differences in the resulting values of the interaction viscosity _ij ⁽⁰⁾ in the limit of zero density exceeding the experimental errors. Consistent results were obtained by taking into account the initial density dependence of the viscosity within the framework of the modified Enskog theory for gaseous mixtures. The values of _ij ⁽⁰⁾ were also used to estimate binary diffusion coefficients of the mixtures.     

The thermal conductivity and viscosity of acetic acid-water mixtures

The viscosity and thermal conductivity of acetic acid water mixtures were measured over the entire composition range and at temperatures ranging from 293 to 453 K. Viscosity measurements were performed with a high-pressure viscometer and thermal conductivity was measured using a modified transient hot-wire technique. A mercury filled. glass capillary was used as the insulated hot wire in the measurements. The l iscosity data showed unusual trends with respect to composition. At it given temperature. the viscosity was seen to increase with increasing acid concentration, attain a maximum. and then decrease. The thermal conductivity, on the other hand, decreased monotonically with acid concentration. A generalized corresponding-states principle using water and acetic acid as the reference fluids was used to predict both viscosity and thermal conductivity with considerable sucres.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–34, 1994, Boulder. Colorado, U.S.A.     

Correlation of the zero-density viscosity of polyatomic gases

Correlations are presented for the dilute-gas viscosities of three gases with multipole moments of increasing order: carbon dioxide (quadrupolar), methane (octopolar), and sulfur hexafluoride (hexadecapolar). These are based on highquality experimental data and are estimated to have an uncertainty of ±0.3% near room temperature, rising to ±1.5% at the extremes of temperature considered (200 to 1000 K). A comparison of these correlations with the two-parameter corresponding-states correlation developed by Kestin and co-workers for monatomic systems indicates systematic deviations, particularly at low temperatures. Model calculations designed to investigate the influence of a quadrupole term in the intermolecular pair potential on the viscosity coefficient indicate that these systematic deviations can be ascribed to such long-range multipolar interactions and suggest the basis for a new, more general three-parameter corresponding-states procedure.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermodynamic behavior of mixtures of methane and ethane in the critical region

An isomorphic equation of state for near-critical binary mixtures is used to represent equation of state and specific heat data for mixtures of methane and ethane in a substantial range of densities and temperatures around the critical line.     

Measurements of the viscosity and density of three hydrocarbons and the three associated binary mixtures versus pressure and temperature

The dynamic viscosity η and density ρ of the pure substances (heptane, methylcyclohexane, 1-methylnaphthalene) and of the three associated binary mixtures (heptane+methylcyclohexane, heptane+1-methylnaphthalene, methylcyclohexane+1-methylnaphthalene) were measured as a function of temperatureT (303.15, 323.15, and 343.15 K) and pressureP(≤100 MPa). For the binary mixtures the mole fractionx of each component was successively 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, and 1. The total experimental results represent 432 different points: 54 for the pure substances and 378 for the binary mixtures (x≠0 and 1).     

Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region

We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.