M. Grigiante

Vapor-Phase Helmholtz Equation for HFC-227ea from Speed-of-Sound Measurements

This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of ∼900 cm3 at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.

A predictive density model in a corresponding states format. Application to pure and mixed refrigerants

A three parameters density model based on Corresponding States (CS) technique is proposed as a means of predicting the density of pure fluids and their mixtures on the entire PρT (PρTx) surface. The studied fluids belong to two conformal families of the new refrigerant fluids generation: the halogenated alkanes (HA) and the hydrofluoroethers (HFE). The new model is based on an original scaling factor parameter that is determined only on a saturated liquid density experimental value. Using two accurate dedicated equations of state (EoS) as references, the same structure of the Teja CS model is maintained, substituting the classical acentric factor with the new defined scaling parameter. Through this model, the density of the refrigerant fluids considered can be calculated on the whole surface with an accuracy level similar to that of the dedicated equations. The model is validated against experimental data for HFC refrigerants including fluoropropanes, fluorobutanes and fluoroethers. A comparison is also proposed with available density models regarded of high accuracy level.

A corresponding states predictive model for the saturated liquid density of halogenated alkanes and of fluorinated propanes and ethers

Abstract A three-parameter corresponding states (CS) model is proposed here for the prediction of the saturated liquid density of pure fluids pertaining to the two conformal families of halogenated alkanes and hydrofluoroethers (HFE), most of which are either already used or proposed for use as refrigerants. Two fluids from each family were chosen for their acentric factor value and the availability of dedicated saturated liquid density equations and at first, on the basis of the three-parameter CS model by Teja et al., the saturated liquid density of a given fluid was obtained in reduced variables. Assuming experimental saturated liquid density data for several components of each of the two families of fluids, an improvement was then introduced, substituting the acentric factor with a new constant scaling factor. As a final result, the proposed liquid model has a predictive nature. The prediction accuracy reached by this new method is similar to that of the dedicated equations, where available, for all the fluids in a family. The result is particularly satisfactory for application requirements in refrigeration.

Vapor phase acoustic measurements for R125 and development of a Helmholtz free energy equation

Abstract This paper presents speed of sound measurements on pentafluoroethane (R125) in the vapor phase. The measurements were performed in a stainless steel spherical resonator of ∼900xa0cm 3 at temperatures in the range 260–360xa0K and pressures up to 500xa0kPa. Acoustic virial coefficients and ideal gas heat capacities are deduced directly from the data. The whole set of speed of sound measurements and the ideal gas heat capacities are then correlated in the forms u 2 ( T , p ) and c p 0 ( T ), respectively. Analytical expressions for the temperature dependencies of the thermodynamic virial coefficients, based on a hard-core square-well potential, are then assumed and the model is fitted to the acoustic data, obtaining a virial equation of state for the vapor phase. A highly accurate Helmholtz equation of state a ( ρ , T ) is established on the basis of the measured data, representing the ( pρT ) surface of the vapor phase in the same temperature and pressure ranges. The ideal gas Helmholtz equation a 0 ( ρ , T ) is obtained from the former c p 0 ( T ) correlation. Given the high accuracy of the equation form, only very precise experimental data, such as acoustic measurements, are suitable for fitting the a R ( ρ , T ) equation parameters. Both the thermodynamic models are validated on available density data. The good level of consistency reached by the Helmholtz equation, shows its form to be very reliable.

Modelling enthalpy and entropy of pure and mixed refrigerants with an innovative corresponding states method

In this work an original improvement of the Corresponding States technique is developed and a new model, based on a three parameters CS format, is proposed to predict the enthalpy and the entropy of the new generation halogenated alkanes fluids together with some alkanes. Limiting the analysis of the selected fluids to a specific thermodynamic property behaviour, an appropriate conformality approach can be deduced, which allows to set up a predictive model of high accuracy level on a wide range of the enthalpy and entropy surfaces. The fundamentals of the model are innovative scaling parameters deduced from the enthalpy of vaporization and from two dedicated equations, belonging to the selected family of fluids. This allows to set up innovative models following a CS format. Through the introduction of advanced mixing rules, the models can be simply extended to calculate the corresponding properties for mixtures. The proposed models allow also the calculation of VLE for systems of rather regular behaviour. The required inputs for a pure target fluid are an ideal gas isobaric heat capacity correlation, a single value of saturated liquid density and of vaporization enthalpy; if the last one is lacking, a single value of vapor pressure can be alternatively supplied. For non azeotropic mixtures the enthalpy and entropy models are predictive, whereas in case of azeotropy VLE calculations are possibly only applying regressed interaction coefficients. Due to the lack of accurate experimental enthalpy data and to the particular nature of the entropy function, the validation of the models is proposed against fundamental dedicated EoS available, both for pure and mixtures, for a significant number of the studied family of fluids. The predictive character of the proposed approach as well as the high performances reached, make these models particularly suitable for the new families of fluids regarding advanced technological applications.

A new three-parameter corresponding states model for pure halocarbons viscosity prediction

Predictive and semipredictive models for viscosity calculation are currently needed and highly appreciated. Models developed for halogenated refrigerants (HR) and based on Corresponding States (CS) are leading to a prediction accuracy comparable to that of specifically developed models. In the present work, using recently published, highly accurate viscosity dedicated equations, it has been verified that viscosity conforms to a two-parameter CS model is then developed, based on Teja and coworkers three-parameter CS structure. Two fluids of the same family are taken for reference, and the reduced viscosity of a third fluid is obtained in reduced P,T variables. At first the Pitzer acentric factor is proposed as a third parameter, then it is substituted with a temperature-dependent function fitted on saturated viscosity data. The prediction accuracy of the model is comparable to that of the reference fluid equations and, considering its predictive nature, it is a satisfactory tool for the needs of technical applications.

Prediction of halocarbon mixture thermodynamics using an innovative gE-EoS mixing rule in a three-parameter CS framework

Abstract Historical models with g E -EoS mixing rules, which combine a cubic equation of state (EoS) requiring only the three parameters T c , P c and ω as individual inputs with a g E model for the liquid phase, are only applied to the saturation surfaces. A limitation of this rule is basically the number of parameters of the one-fluid EoS considered, which cannot exceed 2 or 3. By integrating an improved Teja corresponding states EoS (T), which requires the same individual parameters as a cubic equation, in a g E -EoS mixing rule framework, a new technique is obtained with two modes, one correlative and one predictive. In the correlative mode, the liquid phase γ is generated from input VLE data using the improved T model and the historical Wong–Sandler–Teja mixing rules for the pseudocritical functions, except for T cmix . In the predictive mode, the same general procedure is followed, but with the liquid phase γ coming from a UNIFAC g L E model, which makes the mixing rule predictive. The T cmix values are locally generated from these new rules and are correlated as an individual function, which in both cases presents a very smooth trend for the systems studied. The two proposed rules are applied to systems of halogenated alkanes, which are known to be polar and deviating, and are compared with the dedicated EoS available for these mixtures. The results for both modes show an interesting level of accuracy in representing the whole thermodynamic behaviour of a mixture.