Universal parameters of the extended corresponding states (ECS) model for hydrofluoroolefin refrigerants

doi:10.1016/j.ijrefrig.2021.08.013

International Journal of Refrigeration

Volume 131, November 2021, Pages 33-40

https://doi.org/10.1016/j.ijrefrig.2021.08.013 Get rights and content

Highlights

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New universal parameters of the ECS model are presented for HFO refrigerants.
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They are based on the saturation properties of well-studied eight refrigerants.
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Typical deviations are within 1% for vapor pressures and within 3% for saturated liquid densities.
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They are sufficient accuracies for the preliminary evaluation of novel refrigerants.

Abstract

New universal parameters of the extended corresponding states (ECS) model are presented for hydrofluoroolefin (HFO) refrigerants. The ECS model employing the universal parameters successfully represents the saturation properties. For well-studied HFO refrigerants, which were used to determine the universal parameters, typical deviations between estimations with the ECS model and calculated values with accurate equations of state are within 1 % for vapor pressures and within 3% for saturated liquid densities at reduced temperatures from 0.6 to 0.9. Similar deviations are expected for other HFO refrigerants if reliable experimental values for the critical parameters and acentric factors are available. If these values are less reliable, larger deviations could be observed, up to 3 % and 8 % for vapor pressures and saturated liquid densities, respectively. The ECS model presented here is readily implemented and provides reasonable accuracies; therefore, it is suitable for the preliminary evaluation of novel refrigerants.

Introduction

In terms of environmental protection, low-GWP refrigerants, including hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs), have been given much attention as alternative candidates to hydrofluorocarbons (HFCs), which have been widely used in HVAC/R industries. Over the last decade, thermodynamic property measurement and modeling have been extensively conducted for potential candidates, and reliable equations of state (EOS) were developed for eight HFO and HCFO refrigerants. They are available on REFPROP (Lemmon et al., 2018) and are commonly used in the refrigeration industry. Bobbo et al. (2018) reviewed available literature data for 17 potential candidates including the eight refrigerants for which accurate equations of state were already available on REFPROP. This review revealed that some candidates were still being studied, and no property model for them was published. Besides, within the next decade, other new candidates will be suggested for cryogenic refrigeration cycles because HFO refrigerants that have been ever proposed are mainly for the use of residential air-conditioners, chillers, and high-temperature heat pumps. The property information on these new candidates is normally scarce.

Generally, it takes several years with much effort to develop an accurate equation of state for a fluid. As for screening purposes, on the other hand, one needs quick estimations of thermodynamic properties of potential fluids. Therefore, simpler models have been proposed which readily calculates the properties with reasonable accuracies.

The corresponding states principle indicates that fluids at the same reduced temperature and reduced density nearly have the same compressibility factor. In order to obtain better agreement with experimental data, the extended corresponding states (ECS) model improves this simple principle, employing the acentric factor and some adjustable parameters. The ECS model has often been used to estimate properties of fluids with limited experimental data. It is also possible by using cubic equations of state such as the Peng-Robinson (PR) EOS, but thermodynamic properties calculated from the cubic equations are known to have a significant error for the liquid phase. On the contrary, if experimental data for the saturation properties are available, adjustable parameters of the ECS model can be more fitted to the properties of a fluid of interest. The ECS model was originally developed by Leland and Chappler (1968) for hydrocarbons, and subsequently Ely (1990) and Huber and Ely (1994) extended it to various fluids, including cryogens and refrigerants. Recently it was applied to 19 HFC refrigerants by Estela-Uribe (2014). The ECS model is sometimes used as a preliminary model until a more accurate and wide-ranging equation of state becomes available.

The ECS model can also be applied to the calculations of transport properties. Baltatu et al. (1996) proposed a predictive model based on the ECS model for the viscosity of hydrocarbon liquids. Klein et al. (1997) employed an improved ECS model for estimation of viscosity of pure refrigerants and mixtures. McLinden et al. (2000) presented a modified ECS model for the thermal conductivity of refrigerants and refrigerant mixtures. Huber et al. (2003) correlated the thermal conductivities and viscosities of 17 pure refrigerants with the ECS model using R134a as a reference fluid. Islam et al. (2016) reported the estimations with the ECS model for the thermal conductivity and viscosity of R1234ze(Z). It is beneficial that the ECS model can be implemented on REFPROP; users can readily employ it without any programming.

In this work, HFO and HCFO refrigerants are classified into two groups. Group 1 is the set of refrigerants for which reliable thermodynamic equations of state have been developed based on the sufficient amount of experimental data. Group 2 contains other candidates for which no equation of state has ever been reported. This work determined new universal values of the ECS model parameters optimized for the Group 1 refrigerants. The ECS model coupled with the new universal parameters successfully represents the saturation properties of the Group 1 refrigerants. Deviation plots of calculated vapor pressures and saturated liquid densities are presented. Moreover, the ECS model employing the universal parameters were applied to the Group 2 refrigerants, which were not considered in the optimization of the parameters. Typical deviations in the estimations of the saturation properties of the Group 2 refrigerants are discussed.

Section snippets

Overview

Details in the ECS model is discussed in literature, e.g., Huber and Ely (1994) and Sengers et al. (2000). The outline of the model is presented here.

The ECS model associates the temperature and density of a reference fluid, $T_{ref}$ and $ρ_{ref}$ , with the temperature and density of a fluid of interest (target fluid), $T_{j}$ and $ρ_{j}$ , according to the following relations: $T_{ref} = T_{j} / f_{j} (T_{j})$ and $ρ_{ref} = ρ_{j} h_{j} (T_{j}),$ where $f_{j}$ and $h_{j}$ are the scaling factors. They are defined as $f_{j} (T_{j}) = \frac{T_{c, j}}{T_{c, ref}} θ_{j} (T_{j})$ and $h_{j} (T_{j}) = \frac{ρ_{c, j}}{ρ_{c, ref}} ϕ_{j} (T_{j})$

Universal parameters for HFO refrigerants

The universal parameters optimized for the Group 1 refrigerants are given in Table 2. The parameters $α_{1}$ and $α_{2}$ for R134a as the reference fluid are similar to those determined by Huber and Ely (1994). Those for R1234ze(E) as the reference fluid are also similar, since the two reference fluids are close in acentric factor ( $ω_{R 134 a} = 0.32684$ , $ω_{R 1234 ze (E)} = 0.313$ ). The universal parameters for density, $β_{1}$ and $β_{2}$ , are similar for the two reference fluids; however, the parameter $β_{1}$ is positive, whereas

Conclusions

New universal parameters of the ECS model were determined from the saturation properties of well-studied eight HFO refrigerants (Group 1). R134a and R1234ze(E) were used as the reference fluid. The ECS model employing these universal parameters successfully represents the vapor pressures and saturated liquid densities of the Group 1 refrigerants. If R134a is used as the reference fluid, typical deviations from calculated values with accurate equations of state are within 1 % for vapor pressures

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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View full text

Universal parameters of the extended corresponding states (ECS) model for hydrofluoroolefin refrigerantsParamètres universels du modèle des états correspondants étendu (ECS) pour les frigorigènes hydrofluorooléfines

Highlights

Abstract

Introduction

Section snippets

Overview

Universal parameters for HFO refrigerants

Conclusions

Declaration of Competing Interest

Int. J. Refrig.

Int. J. Refrig.

Int. J. Refrig.

Int. J. Refrig.

Int. J. Refrig.

Int. J. Refrig.

Int. J. Refrig.

Fluid Phase Equilib

Int. J. Refrig.

Fundamental equations of state for cis-1,3,3,3-tetrafluoropropene [R-1234ze(Z)] and 3,3,3-trifluoropropene (R-1243zf)

J. Chem. Eng. Data

A Helmholtz energy equation of state for cis-1-chloro-2,3,3,3-tetrafluoropropene (R-1224yd(Z))

Viscosity of defined and undefined hydrocarbon liquids calculated using an extended corresponding-states model

Int. J. Thermophys.

Compressed liquid density and vapor phase PvT measurements of cis-1,2,3,3,3-pentafluoroprop-1-ene (R1225ye(Z))

J. Chem. Eng. Data

A predictive, exact shape factor extended corresponding states model for mixtures

Adv. Cryog. Eng.

A predictive extended corresponding states model for pure and mixed refrigerants

Helmholtz energy and extended corresponding states model for the prediction of thermodynamic properties of refrigerants

Fluid Phase Equil

Saturated pressure measurements of cis-pentafluoroprop-1-ene (R1225ye(Z))

Int. J. Refrig.

Determination of saturated densities, critical temperature and critical density for new refrigerant HFO1132(E)

Thermodynamic properties of R134a (1,1,1,2-tetrafluoroethane)

Model for the viscosity and thermal conductivity of refrigerants, including a new correlation for the viscosity of R134a

Ind. Eng. Chem. Res.

Application of the extended corresponding states model for prediction of the viscosity and thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z))

Sci. Technol. Built En.