Helmholtz-Type Equations of State for Hydrocarbon Refrigerant Mixtures of Propane/n-Butane, Propane/Isobutane, n-Butane/Isobutane, and Propane/n-Butane/Isobutane

Highly accurate thermodynamic property models for binary and ternary hydrocarbon mixtures containing propane, n-butane, and isobutane have been developed. In the present model, reliable equations of state explicit in Helmholtz free energy for these three hydrocarbons that have already been developed by the present authors have been adapted. The excess term used to represent the contribution of mixing was optimized for each binary mixture by using the available experimental thermodynamic property data including PTx, isochoric heat capacity, and saturation properties (bubble-point pressures, mole fractions in the vapor phase, and saturated vapor- and liquid-densities) as input data. A generalized correction for the three binary mixtures, besides the ideal mixing, consists of only four terms in its functional form, the structure of which was determined by simultaneous optimization to the input data for the three binary mixtures by employing a stepwise regression analysis. The bank of terms, that is a matrix of candidate terms applied for the regression, was carefully prepared through detailed observation of the nonideal mixing representation of the experimental data of the three binary mixtures. No additional adjustable parameters were used in the present model for the ternary propane/n-butane/isobutane mixture. Based on comparisons with the available experimental data and values from the developed equations of state, the present models for the three binary and the ternary hydrocarbon mixtures accurately represent most of the reliable experimental data. In addition, the graphical tests of the derived thermodynamic properties show that the models, including that for the ternary mixture, provide a physically sound representation of all the thermodynamic properties over the entire fluid phase.     

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%.     

Equations of State for Technical Applications. II. Results for Nonpolar Fluids

New functional forms have been developed for multiparameter equations of state for non- and weakly polar fluids and for polar fluids. The resulting functional forms, which were established with an optimization algorithm which considers data sets for different fluids simultaneously, are suitable as a basis for equations of state for a broad variety of fluids. The functional forms were designed to fulfill typical demands of advanced technical applications with regard to the achieved accuracy. They are numerically very stable and their substance-specific coefficients can easily be fitted to restricted data sets. In this way, a fast extension of the group of fluids for which accurate empirical equations of state are available becomes possible. This article deals with the results found for the non- and weakly polar fluids methane, ethane, propane, isobutane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, argon, oxygen, nitrogen, ethylene, cyclohexane, and sulfur hexafluoride. The substance-specific parameters of the new equations of state are given as well as statistical and graphical comparisons with experimental data. General features of the new class of equations of state such as their extrapolation behavior and their numerical stability have been discussed in a preceding article. Results for typical polar fluids will be discussed in a subsequent article.     

Statistical Approach to Calculate Thermodynamic Properties for Propane

The paper describes a mathematical model to compute equilibrium thermodynamic properties in the fluid phase of pure hydrocarbons with the aid of classical thermodynamics and statistical associating chain theories. In the present paper thermodynamic properties for propane, as an example of hydrocarbon substances, are calculated. To calculate the thermodynamic properties of real fluids, models based on the Lennard–Jones intermolecular potential were applied. To calculate the thermodynamic properties of real fluids with the aid of classical thermodynamics, Miyamoto–Watanabe (MW) equations, developed in terms of the Helmholtz energy were used. Analytical results obtained by statistical thermodynamics are compared with the MW model and show relatively good agreement.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1-4, 2002, London, United Kingdom.     

Simulation d'une machine frigorifique à absorption fonctionnant avec des mélanges d'alcanes

We propose in this article an absorption chiller operating with binary alkane mixtures as an alternative to compression machines. It is an installation using low-level energy at a temperature below 150 °C (waste heat or solar energy) and operating with environmentally friendly fluids. Ten mixtures are considered and compared with two cooling mediums of the condenser and the absorber: the ambient air at 35 °C and the water at 25 °C. For an air-cooled chiller, the COP reaches 0.37 for the n-butane/octane system. This value remains 27% lower than that of an ammonia/water installation operating under the same conditions. For a water-cooling chiller, the n-butane/octane and propane/octane systems give a COP of about 0.63, which is comparable to that of the ammonia/water system. When n-butane is used as refrigerant, the machine works at a pressure under 5 bars, which is an advantage compared with machines working with ammonia/water mixtures.     

Measurements of the Liquid Viscosities of Mixtures of n-Butane, n-Hexane, and n-Octane with Squalane to 30 MPa

The viscosities of liquid mixtures of n-butane, n-hexane, and n-octane with squalane that represent model mixtures of refrigerants with refrigeration oil were measured at temperatures between 273.15 and 333.15 K, and at pressures from 0.1 to 30 MPa, by using a falling body viscometer. The uncertainty of the measurements was estimated to be no larger than 2.9%. The experimental viscosity values were fitted to a Tait-like equation within 2.8%. There are larger deviations between the experimental data and calculated values predicted by the equation of Kanti et al., which is derived from the Flory theory. By introducing an interaction parameter of the energetic mixing rule into the equation, the deviations were significantly reduced.     

The Effect of Model Internal Flexibility Upon NEMD Simulations of Viscosity

The influence of model flexibility upon simulated viscosity was investigated. Nonequilibrium molecular dynamics (NEMD) simulations of viscosity were performed on seven pure fluids using three models for each: one with rigid bonds and angles, one with flexible angles and rigid bonds, and one with flexible bonds and angles. Three nonpolar fluids (propane, n-butane, and isobutane), two moderately polar fluids (propyl chloride and acetone), and two strongly polar fluids (methanol and water) were studied. Internal flexibility had little effect upon the simulated viscosity of nonpolar fluids. While model flexibility did affect the simulated viscosity of the polar fluids, it did so principally by allowing a density-dependent change in the dipole moment of the fluid. By using a rigid model with the same geometry and dipole moment as the average flexible molecule at the same density, it was shown that the direct effect of flexibility is small even in polar fluids. It was concluded that internal model flexibility does not enhance the accuracy of viscosities obtained from NEMD simulations as long as the appropriate model geometry is used in the rigid model for the desired simulation density.     

An experimental investigation and modelling of the thermodynamic properties of isobutane–compressor oil solutions: Some aspects of experimental methodology

This paper presents experimental data for the solubility, density and capillary constant for solutions of natural refrigerant isobutane with commercial mineral compressor oil Azmol over a wide range of temperatures and concentrations. Based on information for the capillary constant, the surface tension of the solutions isobutane/Azmol is determined. The experimental data were obtained in the temperature range from 303 K to 363 K and at pressures up to 1.7 MPa using static methods. The experimental data obtained for the solutions of the natural refrigerant isobutane with the commercial mineral compressor oil Azmol are sufficiently described with the help of correlations based on the theory of thermodynamic similarity. The paper reports variation of the vapor pressure, density, capillary constant and surface tension as a function of concentration for the isobutane/Azmol solutions. The enthalpy of liquid phase of the isobutane/Azmol solutions is calculated. The analysis of the behaviour of the excess thermodynamic functions is carried out. The paper examines experimental and methodical uncertainties in the investigation of thermodynamic properties of the refrigerant/oil solutions (ROS). The influence of the time taken to establish thermodynamic equilibrium in the experimental cell on the uncertainty of the experimental data for gas-saturated mixtures such as ROS is discussed. Information about the changing concentration of refrigerant in the liquid phase of the ROS and in the surface layer of the liquid phase of the ROS at increasing temperature is presented. In addition, the experimental data for the density, surface tension and refractive index of the mineral compressor oil Azmol are reported.     

Interaction coefficients for 15 mixtures of flammable and non-flammable components

Bubble pressures were measured for 15 binary mixtures, each composed mainly of one flammable and one non-flammable component. The mixtures were trichlorofluoromethane + isopentane, pentafluoroethane + 1,1,1-trifluoroethane, 1,1-dichloro-2,2,2-trifluoroethane+{1,1-dichloro-1-fluoroethane or isopentane}, 1,1,1,2-tetrafluoroethane+{1,1-difluoroethane or propane or cyclopropane or isobutane}, difluoromethane +{pentafluoroethane or 1,1,1,2-tetrafluoroethane or 1,1-difluoroethane}. Also studied were mixtures of 1,1-difluoroethane+{cyclopropane or propane or butane or isobutane}, which comprise two flammable components. The measurements were made at approximately equimolar compositions using either a vapour-liquid equilibrium apparatus over a range of temperatures, or a static pressure measurement at 273.15K. The bubble pressures were used to determine interaction coefficients that characterize the non-ideal behaviour of these fluid mixtures. The interaction coefficients are used in equation-of-state models for the thermodynamic properties of refrigerant mixtures.     

Performance and heat transfer characteristics of hydrocarbon refrigerants in a heat pump systemPerformance et caractéristiques de transfert de chaleur des frigorigènes hydrocarbures utilisés dans un système de pompe à chaleur

Performance of a heat pump system using hydrocarbon refrigerants has been investigated experimentally. Single component hydrocarbon refrigerants (propane, isobutane, butane and propylene) and binary mixtures of propane/isobutane and propane/butane are considered as working fluids in a heat pump system. The heat pump system consists of compressor, condenser, evaporator, and expansion device with auxiliary facilities such as evacuating and charging unit, the secondary heat transfer fluid circulation unit, and several measurement units. Performance of each refrigerant is compared at several compressor speeds and temperature levels of the secondary heat transfer fluid. Coefficient of performance (COP) and cooling/heating capacity of hydrocarbon refrigerants are presented. Experimental results show that some hydrocarbon refrigerants are comparable to R22. Condensation and evaporation heat transfer coefficients of selected refrigerants are obtained from overall conductance measurements for subsections of heat exchangers, and compared with those of R22. It is found that heat transfer is degraded for hydrocarbon refrigerant mixtures due to composition variation with phase change. Empirical correlations to estimate heat transfer coefficients for pure and mixed hydrocarbons are developed, and they show good agreement with experimental data. Some hydrocarbon refrigerants have better performance characteristics than R22.     

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carlo (CBMC) simulations ofn-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties ofn-butane and other longern-alkanes such asn-hexane andn-heptane when they are confined in different zeolites are presented. The changes in the conformational properties ofn-butane andn-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of thegauche population as compared to the pure unconfined fluid. Contribution No. 1260 from the Solid State and Structural Chemistry Unit     

Testing of propane/isobutane mixture in domestic refrigeratorsEtude sur un mélange propane/isobutane dans les réfrigérateurs domestiques

The performance of a propane/isobutane (R290/R600a) mixture was examined for domestic refrigerators. A thermodynamic cycle analysis indicated that the propane/isobutane mixture in the composition range of 0.2 to 0.6 mass fraction of propane yields an increase in the coefficient of performance (COP) of up to 2.3% as compared to CFC12. For the actual tests, two commercial refrigerators of 299 and 465 l were used. For both units, all refrigeration components remained the same throughout the tests, except that the length of the capillary tube and amount of charge were changed for the mixture. Each refrigerator was fully instrumented with more than 20 thermocouples, two pressure transducers, and a digital watt/watt-h meter. For each unit, both ‘energy consumption test’ and ‘no load pull-down test’ were conducted under the same condition. The experimental results obtained with the same compressor indicated that the propane/isobutane mixture at 0.6 mass fraction of propane has a 3–4% higher energy efficiency and a somewhat faster cooling rate than CFC12. The mixture showed a shorter compressor on-time and lower compressor dome temperatures than CFC12. In conclusion, the proposed hydrocarbon mixture seems to be an appropriate long term candidate to replace CFC12/HFC134a from the viewpoint of energy conservation requiring minimal changes in the existing refrigerators.     

Vapor-Liquid Equilibrium of Carbon Dioxide With Isobutane and n-Butane: Modified Leung-Griffiths Correlation and Data Evaluation

The Leung-Griffiths model as modified by Moldover and Rainwater is used to correlate high-pressure vapor-liquid equilibria of mixtures of carbon dioxide with n-butane and isobutane. Model correlations are compared against 10 independent experimental sources for these mixtures. Agreement is generally very good and comparable to mutual experimental discrepancies. The utility of the model as a data evaluation technique is demonstrated in that small suspect regions have been identified in certain data sets and the model predictions have been confirmed by subsequent measurements that agree with the model better than the earlier data.     

Predicting the High-Pressure Phase Equilibria of Binary Mixtures of n-Alkanes Using the SAFT-VR Approach

The phase behavior of selected alkane binary mixtures is studied using SAFT-VR, a version of the statistical associating fluid theory for potentials of variable attractive range (SAFT). We treat the n-alkane molecules as chains formed from united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. We use a simple relationship between the number of carbon atoms in the n-alkane molecule and the number of segments in the united atom chains in order to predict the phase behavior of n-butane with other n-alkanes. The calculated vapor pressures and saturated liquid densities of the pure components are fitted to experimental data from the triple point to the critical point. These optimized parameters are rescaled by the respective experimental critical points and used to determine the critical lines and phase behavior of the mixtures. We use the Lorentz-Berthelot combining rule for the unlike interactions. We predict the phase behavior of n-butane + n-alkane binary mixtures, concentrating mainly on the critical region. The gas-liquid critical lines predicted by SAFT-VR for the n-alkane mixtures are in excellent agreement with the experimental data, and improve significantly on the results obtained with the simpler SAFT-HS approach where the attractive interactions are treated at the mean-field level.     

Prediction of enthalpy and entropy departures using a two-fluid corresponding-states principle

The generalized corresponding-states principle (GCSP), based on the properties of two nonspherical reference fluids, has been shown to be a powerful technique for the correlation and prediction of thermodynamic properties. In this work we show GCSP calculations of enthalpy and enropy departures for pure fluids and fluid mixtures. The mixtures studied include those conforming well to traditional corresponding states theory (e.g., n-pentane + n-octane), as well as those that have not hitherto been amenable to such treatments (e.g., n-pentane + ethanol). It is shown that the GCSP method works well for all classes of mixtures and compares favorably with other methods of prediction. The use of cubic equations of state to represent the reference fluids gives the GCSP method flexibility while maintaining accuracy in the prediction. No adjustable parameters are required in the GCSP calculations of enthalpy and entropy departures.     

The Viscosity of Gaseous n-Butane and Its Initial Density Dependence

New relative high-precision measurements of the viscosity of gaseous n-butane were carried out in an oscillating-disk viscometer. Seven series of measurements were performed between 298 and 627 K. in the density range from 0.01 to 0.05 mol·L^–1. Isotherms recalculated from the original experimental data were analyzed with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficient deduced from the zero-density and initial-density viscosity coefficients for n-butane are in good agreement with the representation of the Rainwater–Friend theory. The new experimental data and some data sets from the literature were used to develop a representation for the viscosity of n-butane in the limit of zero density on the basis of the extended principle of corresponding states. It has been shown that an individual correlation is needed to represent the experimental data between 293 and 627 K with an uncertainty of ±0.4%.     

Solubility of polymers in supercritical fluids

The phase separation of solutions of monodisperse polystyrene samples of molecular weight 9000 in pure and also binary mixtures ofn-butane andn-pentane has been examined under both subcritical and supercritical conditions over the whole concentration range using a variable-volume view cell capable of operating at up to 100 MPa and 500 K. The phase behavior of these solutions is discussed in terms of the coexistence curves and the theoretical predictions based on the mean-field lattice-gas theory.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Lennard–Jones Chain Model for Self-Diffusion of n-Alkanes

The Lennard–Jones chain model, which was developed from the equation for the self-diffusion coefficient in a Lennard–Jones fluid and the molecular dynamics simulation data of a tangent hard-sphere chain fluid, is used to calculate the self-diffusion coefficient of n-alkanes. n-Alkanes are characterized by a Lennard–Jones segment diameter, a segment–segment interaction energy, and a chain length expressed as the number of segments. The equation represents the experimental self-diffusion coefficients with an average absolute deviation of 3.93% for 16 n-alkanes covering wide ranges of temperature and pressure. The correlated results are compared with those of the rough Lennard–Jones model. A generalized version of the Lennard–Jones chain model is presented which requires only the carbon number in order to predict n-alkane self-diffusivity.