J.P.M. Trusler

The speed of sound and derived thermodynamic properties of ethane at temperatures between 220 K and 450 K and pressures up to 10.5 MPa

Abstract The speed of sound u in gaseous ethane of mole-fraction purity 0.9999 has been measured along 17 isotherms at temperatures between 220 K and 450 K. At temperature of 300 K and above, the greatest pressure on each isotherm was chosen to correspond to that at approximately one half of the critical density. Below T =300 K, the greatest pressure on each isotherm was limited to that at which the estimated density was about 0.8 of the saturated vapour density. The measurements were made using a spherical acoustic resonator and have an estimated total uncertainty not greater than about 1·10 −4 · u ; this uncertainty is dominated by the possibility that the sample contained undetected impurities. Second and third acoustic virial coefficients have been obtained from the results and used to determine parameters in model two- and three-body intermolecular potential-energy functions for ethane. Ordinary second and third virial coefficients calculated from these models are reported. Moreover, a numerical integration of the equations that link u with the other thermodynamic properties of the fluid has been performed inside the region where the speed of sound was measured. The maximum uncertainty of the thermodynamic properties derived in this way is estimated to be 0.04 per cent for the compression factor and 0.4 per cent for the isobaric and isochoric heat capacities.

Speed of Sound of n-Hexane and n-Hexadecane at Temperatures Between 298 and 373 K and Pressures up to 100 MPa

Measurements of the speed of sound u for n-hexane and n-hexadecane at temperatures of 298.3, 323.15, 348.15, and 373.15 K and at pressures up to 100 MPa are reported. The speeds of sound, the temperatures, and the pressures are subject to an uncertainty of ±0.1%, ±0.01 K, and ±0.2 MPa, respectively. These measurements were undertaken using a new apparatus which has been constructed for measurement of the speed of sound in liquids and supercritical fluids at pressures up to 200 MPa and at temperatures between 248 and 473 K. The technique is based on a pulse-echo method with a single transducer placed between two plane parallel reflectors. The speed of sound is obtained from the difference between the round-trip transit times in the two paths. It is expected that both the precision and the accuracy of the method can be further improved.

Second acoustic virial coefficients of nitrogen between 80 and 373 K

The speed of sound in nitrogen has been measured in the temperature range 80 to 373 K and in the density range 10 to 200 mol/m3 using a spherical resonator. Values of the second acoustic virial coefficient have been determined from the results with an imprecision of no worse than 0.11 cm3/mol. This estimation of imprecision includes all known sources of systematic and random errors at the level of one standard deviation. The results are compared with values calculated from two recently proposed intermolecular potential-energy functions for this system both of which were based partially on second virial coefficient data. Although neither of these functions proved able to predict the acoustic virial coefficients to within the high precision of the present measurements, the potential of Ling and Rigby (Mol. Phys. 51 (1984) 855) gives results that deviate by less than 1 cm3/mol.

Determination of thermodynamic properties from the speed of sound

We describe methods by which all of the observable thermodynamic properties of a compressed gas, including the compressibility factor and the isochoric heat capacity, may be determined from sound speed data by numerical integration of a pair of partial differential equations. The technique may be employed over a wide range of conditions. Initial values are required. but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of analytic and numerical results. The results indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.

Densities and bubble points of binary mixtures of carbon dioxide and n-heptane and ternary mixtures of n-butane, n-heptane and n-hexadecane ☆

The densities of three mixtures of carbon dioxide and n-heptane and three mixtures of n-butane, n-heptane and n-hexadecane were measured. The binary mixtures were studied over the temperature range of 302–459 K and the pressure range of 3.61–55.48 MPa at the following carbon dioxide mole fractions: 0.2918, 0.3888 and 0.4270. The ternary mixtures were studied over the temperature range of 405–469 K and the pressure range of 0.7–24 MPa at the following n-butane mole fractions: 0.0904, 0.1564 and 0.1856 and corresponding n-heptane mole fractions: 0.7358, 0.6825 and 0.6588. The measurements were carried out in an automated isochoric instrument and their accuracy is estimated to be better than ±0.1%. The bubble points of the mixtures were also determined from an analysis of the experimental isochores in the one- and two-phase regions. The new measurements have been used to assess the performance of the Peng–Robinson equation of state and the one-fluid corresponding states model. In single phase regions, the performance of the one-fluid model is found to be superior to that of the Peng–Robinson equation. The latter performs well for bubble points provided that optimised interaction parameters are used. As an interpolation tool, the one fluid model is found to reproduce the ternary mixtures within the experimental uncertainty.

Model intermolecular potentials and virial coefficients determined from the speed of sound

A simple procedure is given for determining model two- and three-body intermolecular potential energy functions from precise measurements of the speed of sound in the gas phase. The method is applied to the pure gases argon, methane and nitrogen and results are considered for propane and the mixture (methane + propane) obtained recently by similar methods. For the pair potential, the four-parameter model proposed by Maitland and Smith is used while the consequences of three-body forces were generally assumed to be represented adequately by the triple-dipole dispersion potential of Axilrod and Teller. The effect of including additional dispersion and exchange terms in the three-body potential was investigated for argon; each of these terms is significant but their effect on the third virial coefficient may be absorbed accurately in an effective triple-dipole potential. Three or, in some cases, all four of the parameters in the pair potential were optimized, together with the triple-dipole dispersion coeffi...

Phase behaviour and density of (methane + n-butane)

Abstract The densities of six mixtures of (methane+ n -butane) were determined over the temperature range 316 to 479 K and the pressure range 8.8 to 48 MPa for mole fractions of methane between 0.3458 and 0.5333. The bubble points of the mixtures were also determined from an analysis of experimental isochores in the one- and two-phase regions. The new measurements have been used in conjunction with selected data from the literature to assess the performance of both the volume-translated Peng–Robinson equation of state and the one-fluid corresponding states model over a wide range of states. The relative strengths and weaknesses of the two models are highlighted.

Equation of state for gaseous propane determined from the speed of sound

An equation of state in the form of a truncated virial series has been developed for gaseous propane. Second, third, and fourth virial coefficients and their temperature derivatives were calculated from model two- and three-body intermolecular potentials, the parameters of which were fitted to experimental values of the speed of sound in the gas; no other data were used. The resulting model predicts accurately thermal and caloric properties of the gas over a wide range of temperatures at densities up to about one-quarter of the critical. The second and third (but not the fourth) virial coefficients are in very close agreement with directly measured values. To facilitate rapid calculation of thermodynamic properties, a look-up table for the virial coefficients and their temperature derivatives is provided together with a recommended means of interpolation.

Extended corresponding states model for fluids and fluid mixtures: I. Shape factor model for pure fluids

Abstract We present a new and accurate extended corresponded states model for the prediction of thermodynamic properties of pure fluids. This model is based on shape factors expressed as functions of the reduced temperature and density, the acentric factor and the critical compression factor. Substance-dependent coefficients were optimised against volumetric, VLE and acoustic data for the light hydrocarbons from ethane to n -pentane, ethylene, nitrogen, carbon dioxide, oxygen, argon and carbon monoxide. With this model, fluid properties are estimated largely within their experimental uncertainty. The model was tested for reduced temperatures T r in the interval 0.52≤ T r ≤3.33 and for reduced densities up to 2.8. The work reported here is a necessary precursor to the development of an extended corresponding states (ECS) equation of state for natural gas systems and mixtures of natural gas constituents.

Acoustic and Volumetric Virial Coefficients of Nitrogen

Speeds of sound in nitrogen were measured at temperatures between 170 and 400 K at amount-of-substance densities between 40 and 400 mol·m−3. From these measurements, second and third acoustic virial coefficients were obtained. The parameters of two- and three-body isotropic intermolecular potential-energy models were optimized in a simultaneous fit to the second and third acoustic virial coefficients and the ordinary second and third virial coefficients of nitrogen reported by Nowak et al. The results, which shows that the acoustic and ordinary virial coefficients are mutually consistent, may be used to predict second and third virial coefficients, and their acoustic counterparts, over a wide range of temperatures. The parameters of an anisotropic site-site potential-energy model were also obtained from a fit to the acoustic and ordinary second virial coefficients alone.