The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa

A thermodynamic property formulation for standard dry air based upon experimental P––T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.     

Prediction of the Viscosity of Supercritical Fluid Mixtures

A method for predicting the viscosity of supercritical, multicomponent fluid mixtures, at any density, from the zero-density viscosity of pure components is presented. The method is based upon the results for a rigid-sphere model, suitably interpreted to apply to real fluids, and on the finding that the excess viscosity of pure supercritical fluids can be adequately described by a density function independent of temperature. The density range of the method extends to twice the critical density of the pure component with the smallest critical density. The only exception is for the methane-rich mixtures where the mixture density should not exceed 12000 mol·m^–3. The uncertainty ascribed to the predictions made by this method is of the order of ±5%.     

Molar heat capacity at constant volume for air from 67 to 300 K at pressures to 35 MPa

Measurements of the molar heat capacity at constant volumeC _v for air were conducted with an adiabatic calorimeter. Temperatures ranged from 67 to 300 K, and pressures ranged up to 35 MPa. Measurements were conducted at 17 densities which ranged from gas to highly compressed liquid states. In total, 227C _v values were obtained. The air sample was prepared gravimetrically from research purity gases resulting in a mole fraction composition of 0.78112 N₂ + 0.20966 O₂ + 0.00922 Ar. The primary sources of uncertainty are the estimated temperature rise and the estimated quantity of substance in the calorimeter. Overall, the uncertainty (± 2) of theC _v values is estimated to be less than ± 2% for the gas and ±0.5% for the liquid.Nomenclature C _v Molar heat capacity at constant volume, J · mol^–1 K^–1 - C _v ⁰ Molar heat capacity in the ideal-gas state, J · mol^–1 · K^–1 - V _bomb Volume of the calorimeter containing sample, cm³ - P Pressure, MPa - P Pressure rise during a heating interval, MPa - T Temperature, K - T ₁,T ₂ Temperature at start and end of heating interval, K - T Temperature rise during a heating interval, K - Q Calorimetric heat energy input to bomb and sample, J - Q ₀ Calorimetric heat energy input to empty bomb, J - N Moles of substance in the calorimeter, mol - Fluid density, mol · dm^–3     

Determination of the Critical Point of Gold

Wire-shaped gold specimens are placed in a new, improved high-pressure vessel, which is part of a fast capacitor-discharge circuit and in which static pressures above 600 MPa can be reached with distilled water as the pressure-transmitting medium. The specimens are self-heated resistively by a current pulse. The current through the specimen, the voltage drop across it, and its temperature are recorded as a function of time with submicrosecond resolution. The radial expansion of the specimen is determined with a CCD camera, Experiments are performed at different pressures. When the critical pressure is exceeded, there is no liquid–gas phase transition; hence, no sudden change in the thermal expansion rate is observed. The results for temperature, pressure, and specific volume at the critical point of gold are as follows: T _c =7400±1100 K, p _c=530±20 MPa, and v _c=0.13±0.03 × 10^–3m³·kg^–1.     

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).     

A Generalized Model for the Thermodynamic Properties of Mixtures

A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.     

Dew Point, Liquid Volume, and Dielectric Constant Measurements in a Vapor Mixture of Methane + Propane Using a Microwave Apparatus

An apparatus based on a microwave resonant cavity has been used to measure dew points and liquid volume fractions in a zC₃H₈+(1–z)CH₄ mixture with z=0.250±0.001 mole fraction. The microwave cavity is optimized for the measurement of small liquid volume fractions in lean natural gases. Argon and carbon dioxide were used to calibrate the resonator for dielectric constant and liquid volume measurements in mixtures. Estimated uncertainties are 1×10^–4 for dielectric constants and (0.05 K, 0.05 MPa) for dew points. The novel use of multiple cavity modes, each sensitive to different liquid volume regimes, substantially improves the reliability of liquid volume measurements. Liquid volume fractions can be resolved to better than 0.01%. Densities inferred from (P,T,) measurements agree within 0.6% of equation of state (EOS) densities with an estimated uncertainty of 0.1%. Liquid volume fractions measured with the microwave apparatus compare well with values determined using a conventional PVT cell. Fourteen dew points were measured at ten different temperatures. From these data, the mixture cricondentherm is estimated to be (293.45±0.05) K, which is 0.15 K higher than the value predicted using the Peng–Robinson equation of state.     

Measurements of the viscosity of n-heptane + n-undecane mixtures at pressures up to 75 MPa

New absolute measurements of the viscosity of binary mixtures of n-heptane and n-undecane are presented. The measurements, performed in a vibrating-wire instrument, cover the temperature range 295–335 K and pressures up to 75 MPa. The concentrations studied were 40 and 70%, by weight, of n-heptane. The overall uncertainty in the reported viscosity data is estimated to be ±0.5%. A recently extended semiempirical scheme for the prediction of the thermal conductivity of mixtures from the pure components is used to predict successfully both the thermal conductivity and the viscosity of these mixtures, as a function of composition, temperature, and pressure.     

A Study of Lennard–Jones Equivalent Analytical Relationships for Modeling Viscosities

An analytical representation of the viscosity–density–temperature relationship of the Lennard–Jones (LJ) fluid, over wide ranges of temperature and density, is critically assessed and combined with an LJ pressure–density–temperature equation of state to allow LJ viscosity calculations at a given temperature and pressure. Both LJ equivalent analytical relationships (EARs) are accurate. The potential of using an LJ-based model to represent the viscosities of real fluids is evaluated in two steps. First, the qualitative trends generated by the two combined LJ EARs are studied. Second, viscosity predictions for real, relatively simple, fluids are performed. For these, it is assumed that a real fluid behaves as an LJ fluid having a critical temperatureT _cand a critical pressureP _cexactly matching the real-fluid experimental values ofT _candP _c. Such an assumption is equivalent to supposing that real fluids behave as LJ fluids with effective intermolecular potential parameters consistent with the experimental critical coordinates. The viscosity predictions are based only on molecular weight,T _c, andP _c. The quantitative evaluation is relative to a database of 30 relatively simple compounds including 4 noble gases and the olefinic and aliphatic straight-chain hydrocarbons through 8 carbon atoms. Conditions for the evaluation ranged from 0.6 to 3 for reduced temperatures and from 0 to 3 for LJ reduced densities. The average error is usually less than 10% for vapor and supercritical viscosity and usually less than 25% for liquid viscosity. In its present form, the methodology is actually a corresponding-states model where the reference fluid is an LJ fluid.     

Determination of the compressibility factorZ(p,T) of three methane-ethane mixtures using the dielectric constant method

The compressibility behavior of three mixtures of the CH₄ C₂ H₆, system has been investigated experimentally by means of the dielectric constant method. Precise ( ± 1 ppm) measurements of the dielectric constant () as a function of the pressure (P) along one isotherm (T) are combined with the first three dielectric virial coefficients (A,B, andC) in order to obtain accurate values of the molar density (p). The compressibility factorZ=P/( _p RT) was obtained from the measured values ofp,P, andT. The coefficientA, is determined from the measurements of as a function ofP, while the higher-order coefficients (B, andC,) are obtained by an expansion technique. We report the measured values ofZ at 295.15 K up to 12 MPa for three mixtures of CH₄-C₂-H₆ containing, respectively. 9.54, 35.3, and 75.4% (molar) of ethane. Their exact composition was determined by weighing during the mixing process. The first three dielectric virial coefficients and the mixed second dielectric virial coefficient for the CH₄,-C₂, H₆ system agree with the calculated or the literature values within the limits of uncertainties. For the mixture containing 90.46% CH₄+C₂H₆, deviations in compressibility are of the order of 0.4% from GERG.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Thermal conductivity andPVT measurements of pentafluoroethane (refrigerant HFC-125)

By means of the transient and steady-state coaxial cylinder methods, the thermal conductivity of pentafluoroethane was investigated at temperatures from 187 to 419 K and pressures from atmospheric to 6.0 MPa. The estimated uncertainty of the measured results is ±(2–3)%. The operation of the experimental apparatus was validated by measuring the thermal conductivity of R22 and R12. Determinations of the vapor pressure andPVT properties were carried out by a constant-volume apparatus for the temperature range 263 to 443 K, pressures up to 6 MPa, and densities from 36 to 516 kg m^–3. The uncertainties in temperature, pressure, and density are less than ±10 mK, ±0.08%, and ±0.1%, respectively.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Phase diagram and concentration susceptibility of 3He-4He mixtures near the tricritical point

The inverse concentration susceptibility (/\x) _T of ³He-⁴He mixtures has been calculated from high-resolution vapor-pressure measurements and in situ measurements of the dielectric constant very close to the tricritical point. The measurements have been fitted to a scaling-law equation of state. In the normal fluid a logarithmic correction term was necessary to obtain a good fit. In the superfluid a regular correction term, proportional to (x – x _t)², was evaluated. New measurements of the phase-separation curve confirm our earlier measurements on the ³He-rich side and extend the measurements much closer to the tricritical point on the ⁴He-rich side. The tricritical point is at temperature T = 0.8669 ± 0.0005 K and mole fraction x = 0.6716 ± 0.0014.Work performed under the auspices of the U. S. Department of Energy.     

Vapor–Liquid Equilibrium Data for the Sulfur Dioxide (SO<Subscript>2</Subscript>) + Difluoromethane (R32) System at Temperatures from 288.07 to 403.16 K and at Pressures up to 7.31 MPa

Isothermal vapor–liquid equilibrium data have been measured for the binary system R32 (difluoromethane) + SO₂ at eight temperatures between 288.07 and 403.16 K, and at pressures in the range 0.417–7.31 MPa. The experimental method used in this work is of the static–analytic type, taking advantage of two pneumatic capillary samplers (Rolsi^TM, Armines patent) developed in the CENERG/TEP laboratory. The data were measured with uncertainties within ±0.02 K and ±0.0015 MPa, respectively, for temperatures and pressures and ±1% for molar compositions as a result of careful calibrations. 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.     

A new apparatus for the measurement of the isobaric heat capacity of liquid refrigerants

A new automated adiabatic flow calorimeter was developed which enables one to measure the isobaric heat capacity, C _p, of pure fluids and their mixtures in the liquid phase. The calorimeter has been carefully designed to keep the heat loss from the sample fluid as small as possible being regarded as negligible. The experimental apparatus constitutes a closed circuit of the sample circulation using a combination of two mounted metallic bellows and a metering pump. The present apparatus is designed to measure C _p at temperatures to 500 K and pressures to 15 MPa and is also applicable to measurements in the critical region as well as the region near the saturated liquid state because of its excellent mass flow rate control stability and the high adiabatic efficiency of the calorimeter. The C _p of liquid refrigerant 114 (R114) has been measured at temperatures from 275 to 415 K and pressures up to 3.2 MPa including the critical region with experimental uncertainty of less than ±0.4%. The heat capacity of saturated liquid R114 has also been derived from the data measured in the single phase.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Virial equation of state of helium, xenon, and helium-xenon mixtures from speed-of-sound and burnettPρT measurements

The virial equation of state was determined for helium, xenon, and helium-xenon mixtures for the pressure and temperature ranges 0.5 to 5 MPa and 210 to 400 K. Two independent experimental techniques were employed: BurnettPρT measurements and speed-of-sound measurements. The temperature-dependent second and third density virial coefficients for pure xenon and the second and third interaction density virial coefficients for helium-xenon mixtures were determined. The present density virial equations of state for xenon and helium-xenon mixtures reproduce the speed-of-sound data within 0.01% and thePρT data within 0.02% of the pressures. All the results for helium are consistent, within experimental errors, with recent ab initio calculations, confirming the accuracy of the experimental techniques.     

Transverse response of3He-A for the parallel plate geometry: Coupled fluid and orbital motion

We have studied the transverse response of³He-A for the parallel plate geometry, employing the hydrodynamics of Graham. When particle-hole symmetry is employed to set certain reactive and dissipative coefficients to zero, the four modes have frequencies _1,2 ^± =–(s _1,2 ^± )ik², wheres _1,2 ^± =a_1,2±ib_1,2are constants andk is the wavevector magnitude. Away fromT _c the fluid and orbital motions are strongly coupled. Experimental generation of these modes is considered.     

He4 State Equation Below 0.8 K

This work develops the Helmholtz potential A(ρ, T) for He⁴ below 0.8 K. Superfluid terms, related to temperature and momentum gradients, are neglected with negligible loss of accuracy in the derived state properties (specific heats, first sound velocity, expansivity, compressibility, etc.). Retained terms are directly related to a bulk fluid compressibility plus phonon and roton excitations in this quantum fluid. The bulk fluid compressibility is found from the empirical equation c₁³ ≈ c₁₀³ + b; P, where c₁ is the velocity of first sound, P is the pressure, and c₁₀ and b are constants; this empirical equation is found to apply also to other helium temperature ranges and to other fluids. The phonon excitations lead to a single temperature-dependent term in A(ρ ,T) up to 0.3 K, with only two more terms added up to 0.8 K. The roton potential, negligible below about 0.3 K, is a single term first derived 60 years ago but little used in more recent work. The final A(ρ ,T) is shown to fit available experimental specific heat data to about ±2% or better. The magnitude of the pressure-independent Gruneisen parameter below 0.3 K is typical of highly compressed normal liquids. Extension of the equation above 0.8 K is hampered by lack of data between 0.8 and 1.2 K     

An experimental study of the thermodynamic properties of 1,1-difluoroethane

Experimental vapor pressures andP--T data of an important alternative refrigerant, 1, 1-difluoroethane (HFC-152a), have been measured by means of a constant-volume method coupled with expansion procedures. SixtyP--T data were measured along eight isochores in a range of temperaturesT from 330 to 440 K, at pressuresP from 1.6 to 9.3 MPa, and at densities from 51 to 811 kg·m^–3. Forty-six vapor pressures were also measured at temperatures from 320 K to the critical temperature. The uncertainties of the temperature and pressure measurements are within ±7mK and ±2kPa, respectively, while the uncertainty of the density values is within ±0.1%. The purity of the sample used is 99.9 wt%. On the basis of the measurements along each isochore, five saturation points were determined and the critical pressure was determined by correlating the vapor-pressure measurements. The second and third virial coefficients for temperatures from 360 to 440 K have also been determined.     

Volumetric measurements under pressure for 2,2,4-trimethylpentane at temperatures up to 353.15 K and for benzene and three of their mixtures at temperatures up to 348.15 K

(p, V, T) data have been obtained in the form of volume ratios relative to 0.1 MPa for benzene (298.15 to 348.15 K), 2,2,4-trimethylpentane (TMP) (313.15 to 353.15 K), and their mixtures near 0.25, 0.5, and 0.75 mole fraction of benzene (313.15 to 348.15 K) for pressures up to near the freezing pressures for benzene and the mixtures, and up to 400 MPa for TMP. Isothermal compressibilitiesκ _T, isobaric expansivitie α, changes in heat capacity at constant pressureΔC _p, and excess molar volumesV ^E have been determined from the data. Literature data at atmospheric pressure have been used to convert theΔC _p toC _p at several temperatures. The isobars for α over the temperature range 278.15 to 353.15 K for TMP intersect near 47 MPa and reverse their order in temperature when plotted against pressure; normalization of the α's by dividing the values at each temperature by the α at 0.1 MPa prevents both the intersection and the reversal of the order. TheV ^E are positive and have an unusual dependence on pressure: they increase with temperature and pressure so that the order of the curves for 0.1, 50, and 100 MPa changes in going from 313.15 to 348.15 K.