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.     

A test of the modified Enskog theory for the transport properties of liquids

The modified Enskog theory (MET) has been applied to various fluids in the liquid range (between the triple point and the critical point), and the viscosity, thermal conductivity, and self-diffusion coefficients have been calculated. The temperature dependence of the covolume has been introduced explicitly, bypassing the use of virial coefficients. The agreement is generally acceptable and sometimes good. There is an evident regularity in the results when the reduced temperature is introduced as an independent variable.     

Correlation of the transport properties of simple fluids at low temperatures and high pressures based on the generalized Eucken relation and the molecular dynamics of hard sphere fluid

A generalized correlation is developed for the viscosity and thermal conductivity of isotropic fluids under high pressures (up to 200 MPa) and low temperatures (down to 85 K). Two known observations have been taken into consideration in the development of the correlation. First, the Alder correction factors for the Enskog theory values of transport coefficients obtained from molecular dynamics simulations for hard sphere fluids are incorporated. The inclusion of these corrections in the theory makes it possible to describe correctly the density dependence of the hard sphere viscosity and thermal conductivity at high pressures. The hydrodynamic cage effect, which is manifested in the molecular motions of dense fluid systems, is thus correctly accounted for. Second, the generalized Eucken relation, which relates the thermal conductivity to the viscosity, is incorporated. As a consequence, an internally consistent correlation is obtained, which can adequately predict the behavior of the thermal conductivity from given values of viscosity. Tests on simple fluids, such as argon, krypton, etc., show that the correlation is valid within a few percent for the entire fluid range where experimental data are available for comparison, and also along the vapor-liquid saturation line, with the exclusion of the critical region. Furthermore, since the variables appearing in the theory are in reduced form, a corresponding states correlation is established for isotropic fluids.     

Accurate transport properties and second virial coefficients for helium based on a state-of-the art interatomic potential

Second virial coefficients and transport properties of helium are presented based on a state-of-the-art interatomic potential which was constructed with the use of a multiproperty fit. The experimental potential employed to produce these properties accurately reproduces a wide range of bulk and microscopic data and agrees well with ab initio calculations which were not available at the time of its construction. Virial coefficients of ³He and ⁴He are presented from 2 to 600 K, and transport properties of pure ³He and ⁴He gases and ³He-⁴He mixtures are presented from 5 to 6000 K.     

The MIDAS Data-Bank System for the transport properties of fluids

The development of the MIDAS Data-Bank System from its origin as part of the first DECHEMA properties data project in 1977 is described. The system concentrates the rapidly increasing amount of data for the viscosity and thermal conductivity for pure fluids and fluid mixtures by evaluation of the most reliable data sets. The data sets are represented by density-temperature correlations which are the customary method to correlate transport properties. To allow for a direct calculation of the transport properties from given pressures and temperatures, a new type of equation has been developed. As an example, the simultaneous representation of the viscosity and thermal conductivity of oxygen by one transport equation of state is discussed.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Cubic equations of state for transport properties

A method is presented for the prediction of the background contribution of residual thermal conductivities and residual viscosities of nonpolar or slightly polar substances. The method is based on the concept of transport equations of state describing the transport properties in terms of pressure and temperature by pressure explicit equations similar to thermal equations of state. The transport equation of state is derived from a generalized cubic thermal equation of state and a universal function for the density dependence of the residual part of the transport properties. A comparison of calculated and recommended values of the thermal conductivity of 35 and the viscosity of 23 substances yields an absolute average deviation of 6% for the thermal conductivity and of 5% for the viscosity. The Maxwell condition is applied to the generalized transport equation of state to predict consistently the transport properties along the vapor-liquid coexistence curve.     

The thermal conductivity of dense fluids using revised Enskog theory

A predictive method designed to obtain the thermal conductivities of one-component dense fluids is described. This method is based on the revised Enskog theory. Here, an effective state-dependent hard-sphere diameter is used to obtain the hard-sphere diameter needed by the revised Enskog theory in order to deal with actual fluids. In addition, we introduce the contribution of the internal degrees of freedom through the Mason-Monchick procedure. Our predictions for noble gases and hydrocarbons, at high density, are compared with predictions coming from the conformal solution model, with empirical correlation schemes, and with experimental data. A very satisfactory agreement is found.     

Density effects in internal-energy transport in polyatomic gases

The revised Enskog theory is used in a heuristic way to modify the Wang Chang-Uhlenbeck quantum kinetic equation for polyatomic gases close to thermodynamic equilibrium. The density effects predicted for the total and internal thermal conductivities are in qualitative agreement with recent molecular dynamic calculations, suggesting that inelastic effects should be included in dense fluid transport theory. Paper dedicated to Professor Edward A. Mason.     

Correlation of dense fluid self-diffusion,shear viscosity,and thermal conductivity coefficients

A general procedure has been developed for simultaneously fitting any two of the self-diffusion coefficient, the viscosity (as the fluidity), and the thermal conductivity (as its reciprocal) as Dymond reduced coefficients, (D*,*,*), to a simple function of the volume and the temperature for dense fluids. For example,D*=₁+₂ V _r/(1+₃,/V _r), whereV _r=V[1-₁(T–T _r)-₂(T–T _r)²].T _r is any convenient temperature, here 273.15 K. AsV _r is common to the two properties, only eight coefficients, _j and _k are required. Such reduced transport-coefficient curves are geometrically similar for members of groups of closely related compounds. The procedure has been extended to give family curves for such groups by fitting a pair of transport properties for three substances from the group in a single regression. Overall, fewer coefficients are required than for other schemes in the literature, and the fitting functions used are simpler. The curves so constructed can be used for the correlation of data obtained from different sources, as well as interpolation and, to a limited extent, extrapolation. A comparison is made for a number of compotmd groups between simultaneous fits of the pairs (D– ), (D–), and (–)Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Correlation and prediction of dense fluid transport coefficients. I. n-alkanes

Recent accurate measurements of the self-diffusion coefficient for n-hexadecane and n-octane and of the viscosity coefficient for n-heptane, n-nonane, and n-undecane over wide pressure ranges have been used to provide a critical test of a previously described method, based on consideration of hard-sphere theory, for the correlation of transport coefficient data. It is found that changes are required to the universal curve for the reduced viscosity coefficient as a function of reduced volume and, also, to the parameters R _D, R , and R which were introduced to account for effects of nonspherical molecular shape. The scheme now accounts most satisfactorily for the self-diffusion, viscosity, and thermal conductivity coefficient data for all n-alkanes from methane to hexadecane at densities greater than the critical density.     

Correlation and prediction of dense fluid transport coefficients. V. Aromatic hydrocarbons

A previously described method, based on consideration of hard-sphere theory, is used for the simultaneous correlation of the coefficients of self-diffusion, viscosity, and thermal conductivity for benzene, toluene, o-, m-, and p-xylene, mesitylene, and ethylbenzene in excellent agreement with experiment, over extended temperature and pressure ranges. Values are given for the roughness factors R _D , R , and R , and the characteristic volume, V ₀, is expressed as a function of both carbon number and temperature.     

The initial density dependence of transport properties: Noble gases

The usual procedure that the transport properties at atmospheric pressure are identified with values in the limit of zero density cannot be accepted for all reduced temperatures T ^*. It is shown in the framework of the Rainwater-Friend theory for noble gases, as a good example, that for T ^*<1 the effect of the initial density dependence has different signs for viscosity and thermal conductivity and amounts to a few percent, when data at atmospheric pressure are compared with zero-density values. An improved representation of the monomer-dimer contribution to the second transport virial coefficients of the Rainwater-Friend theory is presented in the paper. This is based, among others, on the author's own experimental data of the initial density dependence of viscosity of polytomic gases.     

Correlation and prediction of dense fluid transport coefficients. VII. Refrigerants

A recently developed scheme, based on considerations of hard-sphere theory, is used for the simultaneous correlation of the coefficients of viscosity and thermal conductivity for the refrigerants R11, R12, R22, R32. R124, R125, R134a, R141b, and R152a in excellent agreement with experiment, over extended temperature and pressure ranges. Values for the roughness factors and correlations for the characteristic volume are presented. The overall average absolute deviations of the experimental viscosity and thermal conductivity measurements from those calculated by the correlation are 2.1 and 2.3%, respectively, over a temperature range from 200 to about 10 K below the critical temperature and a pressure range from saturation to about 40 MPa. Since the proposed scheme is based on recent and accurate density values, a Tail-type equation was also employed to correlate successfully the density of the refrigerants. The overall average absolute deviation of the experimental density measurements from those calculated by the correlation is ±0.08%.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

An improved correlation for the calculation of liquid thermal conductivity

Eighteen correlations appearing in the literature for the prediction of thermal conductivity, , of liquids are critically analyzed, and their reliability is checked using coherent input data and selected experimental values. The best results are obtained using the Reid, Sherwood, and Prausnitz correlation with a mean deviation of about 8% between predicted and experimental values. An improved correlation is proposed starting from the Viswanath equation, chosen because of its simplicity and convenience. The values of thermal conductivity obtained by this new correlation agree with the experimental values within 1%.     

Corrections to the smooth hard-sphere theory of thermal conductivity for internal energy transport: Application to methane

Thermal conductivities have been calculated for dense fluid methane from the exact smooth hard-sphere expression valid for monoatomics with core sizes derived from fitting self-diffusion and viscosity data. The results are lower than experimental values by about 16% at all densities greater than the critical density. This difference is attributed to the effect of internal energy transport on this property.     

Cubic equations of state for transport properties: An equation for the thermal conductivity of oxygen

A scheme for the development of equations for the transport properties in terms of pressure and temperature, so-called transport equations of state, is presented. The surfaces of transport properties and density as a function of pressure and temperature reveal similarities, which become even more evident when the residual transport property as a function of pressure and temperature is considered. Even the spinodals of transport and thermal properties coincide in the p, T plane, as can be shown mathematically and as was already empirically found for water and oxygen. Based on these similarities a cubic transport equation of state is evaluated for the residual thermal conductivity of oxygen. The new equation is only a little less accurate than the already established virial transport equation of state for oxygen. It is, however, much simpler and needs only a few parameters. The accuracy is still good enough for practical applications. The results demonstrate that cubic equations of state can describe transport properties and are a basis for generalized estimation methods for the transport properties of fluids.     

Status of the round robin on the transport properties of R134a

The paper contains a status report on an international project coordinated by the Subcommittee on Transport Properties of Commission 1.2 of the International Union of Pure and Applied Chemistry. The project has been conducted to investigate the large discrepancies between the results reported by various authors for the transport properties of R134a. The project has involved the remeasurement of the transport properties of a single sample of R134a in nine laboratories throughout the world in order to test the hypothesis that at least part of the discrepancy could be attributed to the purity of the sample. This paper provides an intercomparison of the new experimental results obtained to data in this project for the viscosity and the thermal conductivity in both gaseous and liquid phases. The agreement between the viscosity data from the laboratories contributing to the project was improved with several techniques, now producing consistent results. This suggests that the purity of the samples of R134a used in previous work was at least partly reponsible for the discrepancies observed. For the thermal conductivity in the liquid phase the results of the measurements are also more consistent than before, although not for all experimental techniques. Not all of the previous measurements suffered from significant sample impurities, so the present measurements on a consistent high-purity sample can he used to detect data sets which are outhers, possibly because of impurities. Identification of laboratories and techniques with systematic differences may require the examination of data for several fluids. The implications for future measurements of the transport properties of other refrigerants are significant.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

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%.     

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.