Thermodynamic properties for the alternative refrigerants

Models commonly used to calculate the thermodynamic properties of refrigerants are summarized. For pure refrigerants, the virial, cubic, Martin-Hou, Benedict-Webb-Rubin, and Helmholtz energy equations of state and the extended corresponding states model are discussed. High-accuracy formulations for 16 refrigerants are recommended. These models may be extended to mixtures through the use of mixing rules applied either to the parameters of the equation of state or to some property of the mixture components. Mixtures of a specific composition may also be modeled as a pseudo-pure fluid. Five mixture models, employing four distinct approaches, have been compared by a group working under the auspices of the International Energy Agency. These comparisons show all five models to be very capable in representing mixture properties. No single model was best in all aspects, but based on its combination of excellent accuracy and great generality, we recommend the mixture Helmholtz energy model as the best available.Experimental data are essential to both fit the adjustable parameters in property models and to assess their accuracy. We present a survey of the data available for mixtures of the HFC refrigerants R32, R125, R143a, R134a, and R152a and for mixtures of the natural refrigerants propane, butane, isobutane, and carbon dioxide. More than 60 data references are identified. Further data needs include caloric data for additional mixtures, comprehensive pressure-density-temperature data for additional mixture compositions, and improved accuracy for vapor-liquid equilibria data.     

Vapor-liquid equilibrium and volumetric properties calculations for solutions in the supercritical carbon dioxide

The calculations of gas solubilities in supercritical solvents require equations of state remaining accurate in the critical range, which are difficult to obtain with classical models. In this work, the Helmholtz energy of a mixture is considered as the sum of the Helmholtz energies of pure components taken at a constant packing fraction and of a residual term which may have the form of a RedlichKister, Van Laar, NRTL, UNIQUAC, or UNIFAC function. Thus it is possible to assign to a given component an equation of state whose form is different from that of the others. This model has been applied to binary systems containing supercritical carbon dioxide. The results are improved with respect to those obtained with the classical model for vapor-liquid equilibria and for volumetric properties.     

Simplified Gradient Theory Modeling of the Surface Tension for Binary Mixtures

In this work, the gradient theory was combined with the volume translation Peng-Robinson and Soave Redlich-Kwong equations of state (VTPR and VTSRK EOSs) and the influence parameter correlation to predict the surface tension of binary mixtures. The density profiles of mixtures across the interface were assumed to be linearly distributed to simplify the gradient theory model. The only two inputs of the theory are the Helmholtz free-energy density of the homogeneous fluid and the influence parameter of the inhomogeneous fluid. The VTPR and VTSRK equations of state were applied to determine the Helmholtz free-energy density and the bulk properties. The influence parameter of the inhomogeneous fluid was calculated from a correlation published previously (Lin et al. Fluid Phase Equilib 254:75, 2007). The only adjustable coefficient of the simplified gradient theory was set equal to zero, which made the theory predictive. The surface tension predicted by this model shows good agreement with experimental data for binary non-polar and polar mixtures.     

Pseudo-Pure Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C

Pseudo-pure fluid equations of state explicit in Helmholtz energy have been developed to permit rapid calculation of the thermodynamic properties of the refrigerant blends R-410A, R-404A, R-507A, and R-407C. The equations were fitted to values calculated from a mixture model developed in previous work for mixtures of R-32, R-125, R-134a, and R-143a. The equations may be used to calculate the single-phase thermodynamic properties of the blends; dew and bubble point properties are calculated with the aid of additional ancillary equations for the saturation pressures. Differences between calculations from the pseudo-pure fluid equations and the full mixture model are on average 0.01%, with all calculations less than 0.1% in density except in the critical region. For the heat capacity and speed of sound, differences are on average 0.1% with maximum differences of 0.5%. Generally, these differences are consistent with the accuracy of available experimental data for the mixtures, and comparisons are given to selected experimental values to verify accuracy estimates. The equations are valid from 200 to 450 K and can be extrapolated to higher temperatures. Computations from the new equations are up to 100 times faster for phase equilibria at a given temperature and 5 times faster for single-phase state points given input conditions of temperature and pressure.     

一种提高低温流体比体积计算精度的方法

采用了一个既能提高立方型状态方程比体积计算精度，又不影响气液平衡条件的简单摩尔修正项来改进PR方程比体积的计算。本文对19种低温流体给出其修正项的值，计算饱和蒸气和液体比体积，并与未修正的PR方程的计算值比较，结果表明这种修正能显著提高低温流体（包括量子流体氢、氦和强极性的氨气）饱和液体比体积的计算精度，并对蒸气比体积的计算也略有改进。     

On two-parameter equations of state and the limitations of a hard sphere Peng-Robinson equation

Simple two-parameter equations of state are exceptionally effective for calculations on systems of small, uncomplicated molecules. They are therefore extremely useful for vapour-liquid equilibrium calculations in cryogenic and light hydrocarbon process design. In a search for further improvement three two-parameter equations of state with a co-volume repulsion term and three with a hard sphere repulsion term have been investigated. Their characteristic constants at the critical point have been compared. The procedure for fitting the two parameters to empirical data in the subcritical region was analysed. A perturbed hard sphere equation with a Peng-Robinson attraction term was shown to be unsuitable for application over a wide range of p, T conditions. A similar equation with a Redlich-Kwong attraction term gives good service in the cryogenic range.     

An equation of state for predicting vapour-liquid equilibria of the system N2ArO2

An equation of state for the N₂ArO₂ mixtures is developed from the equations of state of the pure components by using new combination rules. The equation of state has twenty coefficients and represents the whole fluid regions of the mixtures and the pure components including the liquid and the two-phase regions with high accuracy. The equation of state permits the calculation of vapour-liquid equilibria in the total pressure and composition ranges. The accuracy of the predicted bubblepoint temperatures is about 0.1 K and that of the vapour compositions 0.2 mole %. Reliable caloric and volumetric saturation properties are also given by the equation of state.     

Vapour-liquid equilibria measurements for carbon dioxide with normal and isobutane from 250 to 280 K

Vapour-liquid equilibria measurements were made on binary mixtures of carbon dioxide with normal and isobutane at 250, 260, 270 and 280 K. Both liquid and vapour compositions were measured. The data were correlated using the Peng-Robinson equation of state, and values are given for the activity coefficients and the excess Gibbs free energy, G_E. The heat of mixing is estimated from the temperature dependence of G_E.     

A cubic equation of state for the prediction of N2-Ar-O2 phase equilibrium

A new two-parameter cubic equation of state is proposed and shown to be particularly useful for calculation of vapour-liquid equilibrium of the nitrogen-argon-oxygen system. It finds application in an economical and at the same time accurate computational procedure for equilibria at temperatures up to 140 K and pressures up to 30 atm. Bubblepoint calculations show average errors of 0.15 mole % in vapour concentrations and 0.08 K in equilibrium temperature. The equation of state is also promising for natural gas systems.     

Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a

A mixture model explicit in Helmholtz energy has been developed that is capable of predicting thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, and R-152a. 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 equation that is applied to all mixtures used in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate thermodynamic properties of mixtures, including dew and bubble point properties and critical points, generally within the experimental uncertainties of the available measured properties. It incorporates the most accurate published equation of state for each pure fluid. The estimated uncertainties of calculated properties are ±0.25% in density, ±0.5% in the speed of sound, and ±1% in heat capacities. Calculated bubble point pressures are generally accurate to within ±1%.     

Direct Prediction of Cricondentherm and Cricondenbar Coordinates of Natural Gas Mixtures using Cubic Equation of State

A numerical algorithm is presented for direct calculation of the cricondenbar and cricondentherm coordinates of natural gas mixtures of known composition based on the Michelsen method. In the course of determination of these coordinates, the equilibrium mole fractions at these points are also calculated. In this algorithm, the property of the distance from the free energy surfaces to a tangent plane in equilibrium condition is added to saturation calculation as an additional criterion. An equation of state (EoS) was needed to calculate all required properties. Therefore, the algorithm was tested with Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and modified Nasrifar-Moshfeghian (MNM) equations of state. For different EoSs, the impact of the binary interaction coefficient (k _ij) was studied. The impact of initial guesses for temperature and pressure was also studied. The convergence speed and the accuracy of the results of this new algorithm were compared with experimental data and the results obtained from other methods and simulation softwares such as Hysys, Aspen Plus, and EzThermo.     

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%.     

VLE data for CO2-CF2Cl2, N2-CO2, N2-CF2Cl2 and N2-CO2-CF2Cl

Knowledge about vapour-liquid (VLE) is required as a basis of reliable calculations for separation processes. Correlations available for the prediction of T, p, x, y data are less accurate for mixtures at high pressures and mixtures containing supercritical components. The results of VLE experiments are reported and compared with data calculated with equations of state.     

A comparison among five equations of state in predicting the inversion curve of some fluids

Five equations of state, modified Peng-Robinson by Danesh et al. (MPR1), modified SRK equation of state by Mathias and Copeman (MSRK), Vdw11, Harmens-Knapp (HK) and modified Peng-Robinson equation of state by Ruzy (MPR2) were compared in predicting of the inversion curve of some fluids. This enable us to judge the accuracy of the results obtained from different equations of state. MSRK and HK equations of state give good prediction of the low-temperatures branch of the inversion curve and are closely matched with the experimental inversion curve. As a corollary to the present study, we have perceived that the agreement of the MPR2 and Vdw11 equations of state with the inversion curve are inadequate. We also calculated maximum inversion temperature and maximum inversion pressure for every component used in this work.     

Equipment using a “static-analytic” method for solubility measurements in potentially hazardous binary mixtures under cryogenic temperatures

A new apparatus designed to study, at cryogenic temperatures, thermodynamic equilibria of potentially explosive binary systems such as hydrocarbon-oxygen mixtures is described herein. This equipment has an equilibrium cell which was especially designed to minimize hazards while allowing accurate phase equilibrium measurements. Reliability of results, obtained with this equipment has been verified by working on the nitrogen-propane system, for which data are already available in literature, over a large range of compositions and at various temperatures. Four isothermal curves describing liquid phase compositions at 109.98, 113.77, 119.75 and 125.63 K have been determined. Our experimental data are represented within 2% in compositions and in pressures through the Peng-Robinson equation of state implying Mathias-Copeman alpha function and Huron-Vidal mixing rule. Comparisons to literature allow pointing out: good agreement is observed with Kremer and Knapp data (1983) while the three sets of Poon and Lu data (1974) presenting systematic positive deviation are consequently judged as suspicious.     

Refrigerant conversion of auto-refrigerating cascade (ARC) systems

This paper describes converting Auto-Refrigerating Cascade (ARC) ultra-low temperature systems from a multicomponent zeotropic working fluid containing CFS to a CFC-free mixture. The differences between azeotropes, mixtures and blends with minimal glides used in conventional refrigeration systems and the steep glide (wide span) zeotropes required for ARC system operation are compared. The design tools used include the Carnahan-Starling-DeSantis and the Peng-Robinson equations of state and relationships of components based upon Raoult's law. Some comparisons of prep and post-conversion operating data are presented. A brief history of ARC cycle cooling systemsis included.     

Statistical mechanical description of supercritical fluid extraction and retrograde condensation

The phenomena of supercritical fluid extraction (SFE) and its reverse effect, which is known as retrograde condensation (RC), have found new and important applications in industrial separation of chemical compounds and recovery and processing of natural products and fossil fuels. Full-scale industrial utilization of SFE/RC processes requires knowledge about thermodynamic and transport characteristics of the asymmetric mixtures involved and the development of predictive modeling and correlation techniques for performance of the SFE/RC system under consideration. In this report, through the application of statistical mechanical techniques, the reasons for the lack of accuracy of existing predictive approaches are described and they are improved. It is demonstrated that these techniques also allow us to study the effect of mixed supercritical solvents on the solubility of heavy solutes (solids) at different compositions of the solvents, pressures, and temperatures. Fluid phase equilibrium algorithms based on the conformal solution van der Waals mixing rules and different equations of state are presented for the prediction of solubilities of heavy liquid in supercritical gases. It is shown that the Peng-Robinson equation of state based on conformal solution theory can predict solubilites of heavy liquid in supercritical gases more accurately than the van der Waals and Redlich-Kwong equations of state.     

The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures

This paper reports on the development and application of a thermodynamic model based on the second-order Modified Huron Vidal equation of state (MHV-2) to predict the properties of ternary mixtures of the refrigerants R32, R125, and R134a. The mixing rules of this equation of state have been used to incorporate directly an activity-coefficient model for the excess Gibbs free energy. The parameters for the activity-coefficient model have been derived from experimental VLE data for binary mixtures. This methodology has enabled the production of a thermodynamically consistent model which can be used to predict the phase equilibria of R32/R125/R134a mixtures. The input data used in the model are presented in the paper and the predictions of the model are compared with available experimental data. The model has been used to predict the behavior of ternary refrigerant blends of R32/R125/R134a in fractionation scenarios, such as liquid charging and vapor leakage, which are of direct interest to the refrigeration industry. Details of these applications and comparisons with experimental data are discussed, along with other general uses of the thermodynamic model.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, USA.