Experimental Measurement of Vapor Pressures and Densities at

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Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State Moussa Dicko,† Ghemina Belaribi-Boukais,§ Christophe Coquelet,*,†,‡ Alain Valtz,† Farid Brahim Belaribi,§ Paramespri Naidoo,‡ and Deresh Ramjugernath‡ †

Mines ParisTech, Centre Energetique et Procedes, CEP/TEP 35 Rue Saint Honore, 77305 Fontainebleau, France Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Durban, 4041, South Africa § Laboratoire de Thermodynamique et Modelisation Moleculaire, Universite des Sciences et de la Technologie Houari Boumediene (USTHB), BP 32 El Alia 16111 Bab Ezzouar, Alger, Algerie ‡

bS Supporting Information ABSTRACT: Hydrofluoroalkenes, like hexafluoropropylene, can be considered as new working fluids for refrigeration systems and consequently volumetric and critical property data are required. In this study, a vibrating tube densitometer technique was used to determine densities at nine different temperatures between (263 and 358) K, and pressures between (0.04 and 15) MPa. The experimental uncertainties are (0.0003 and (0.0006 MPa for pressure, ( 0.02 K for temperature, ( 0.5% (relative) for vapor densities, and (0.05% for liquid densities. A different equipment based on static method is used for the determination of pure component vapor pressures for temperatures between (231 and 359) K. The experimental uncertainties are (0.0005 MPa for pressure and (0.02 K for the temperature. Critical properties have been determined by direct measurement and also from utilization of experimental densities considering the asymptotic scaling law behavior. The Patel
Teja and crossover Patel
Teja equations of state are used to correlate the data.

’ INTRODUCTION Because of their fairly high global warming potential (GWP), hydrofluorocarbons (HFCs) will probably soon be phased out. Historically, they were used because of their zero ozone depletion potential (ODP). Prior to their use, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) were used, but research indicated that they led to damage of the Earth’s ozone layer, and they were ultimately banned. HFCs, which do not contain chlorine, pose no threat to the ozone layer, but because of their high stability, they have a high GWP (for example, the GWP of R134a is 13001 on a time scale of 100 years and with CO2 as reference fluid). This has forced the refrigeration industry (domestic, cars, and heat pumps) to consider and find alternate HFCs, which have a much lower GWP. One solution could be the utilization of hydrofluoroalkenes, like hexafluoropropene (HFP, R1216, CAS Number 116-15-4) or hexafluoropropene oxide (HFPO, CAS Number 428-59-1). The GWP of HFP is 0.25,2 which is negligible in comparison with the GWP of R134a. Thermodynamic properties of pure HFP such as vapor pressure and volumetric properties at saturation or outside saturation, have been studied in a previous paper.3 The critical properties of this fluid have also been determined. Hexafluoropropylene oxide (HFPO) is a versatile fluorointermediate that can be used in the synthesis of fluoromonomers, fluoropolymers and to add fluorine functionality to a variety of organic precursors. R1216 is the key chemical precursor to HFPO, which is synthesized in an oxidation process. R1216 is used in the manufacture of fluoropolymers and in other specialty agrochemical and pharmaceutical applications. r 2011 American Chemical Society

In this paper, a complete study of volumetric properties of pure HFPO using the vibrating tube densitometer technique4 is presented. Pure component vapor pressures were also measured and critical properties determined from these density measurements. A multitude of equations of state have been developed to represent fluids properties (cubic EoS’s, molecular-based EoS’s, etc.). Unfortunately, it has been proven that such classical EoS’s, which follow a mean field approach fail to represent physical properties in the vicinity of the critical point. Moreover, it is wellknown that in this area the representation of thermodynamic properties must rely on scale invariance. Therefore, in this work, a crossover treatment has been applied to a cubic EoS. The Landau-crossover method, successfully employed by Sengers and co-workers and also by Kiselev in a simplified way,5 has been chosen. The method consists in rewriting the free energy with the inclusion of a crossover function. It is then possible to switch between the mean field zone and the critical area. Following the procedure of Kiselev,6 modified by Dicko and Coquelet,7 the classical Patel
Teja8 EoS (PT EoS) has been transformed into a crossover Patel
Teja EoS (CR-PT EoS). Both EoS’s have been used to correlate the data.

Received: November 22, 2010 Accepted: February 25, 2011 Revised: February 25, 2011 Published: March 09, 2011 4761

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’ EXPERIMENTAL SECTION Vapor Pressure Apparatus. A classical static sapphire tube cell was used for the determination of pure HFPO vapor pressures. It is similar to the cell used by Coquelet et al.3 for the determination of pure HFP vapor pressure. Temperatures are measured by two Pt100 probes connected to a HP34970A data acquisition unit. Pressures were measured using a pressure transducer (model Druck PTX611) with a pressure range of (0
4) MPa. Vibrating Tube Densitometer Apparatus. The apparatus and the procedure have been presented in detail in a previous publication,3 and a detailed description of a typical vibrating tube density measurement apparatus was given in the original publication (Bouchot and Richon4). The density of a mixture is determined by measuring the period of vibration as a function of temperature and pressure. The apparatus of this work uses an Anton Paar DMA 512 vibrating tube. The uncertainty of the vibrating period values is (10
8 s. Temperatures are measured by two Pt100 probes connected to the HP34970A data acquisition unit. Pressures are measured using two pressure transducers (model: Druck PTX611) with two complementary ranges: (0
3) and (0
20) MPa. Materials. HFPO (CAS 428-59-1) was supplied by NECSA (South African Nuclear Energy Corporation) with a certified purity greater than 99.99% volume fraction. Gas chromatographic analysis of the sample indicated a single component peak and therefore qualitatively verified the purity. R134a (CAS 811-97-2) was supplied by ARKEMA with a certified purity greater than 99.95% volume fraction. Experimental Procedure. Details concerning the experimental procedure are fully described in a previous paper.3 The forced path mechanical calibration model (FPMC method) proposed by Bouchot and Richon9 is used to convert periods into density values. FPMC parameters were calculated from (PVT) data of a reference fluid (R134a), whose thermodynamic properties are well described by the equation of state of Tillner-Roth and Baehr.10 Estimation of Uncertainties. Because of the uncertainties of the mechanical parameters used in the FPMC model, the total uncertainty on density data are estimated to be (0.5% for the vapor phase and (0.05% for the liquid phase. Total temperature uncertainties are estimated to be (0.02 K. Total uncertainties on pressure measurements after calibration are ((0.0003 and (0.0006) MPa, respectively, for sensor ranges: (0
3) and (0
20) MPa. Concerning the vapor pressure measurements, the uncertainties are within (0.0005 MPa. The uncertainties on temperatures measurements are within (0.02 K.

’ EXPERIMENTAL RESULTS Vapor Pressure. Table 1 shows the results for pure HFPO vapor pressures. The temperature range for measurements was from (231.39 to 359.20) K. The values of critical temperature TC and pressure PC were determined by experimental means. The critical point was observed with the disappearance of the vapor
liquid interface and critical opalescence in the cell. From this observation, it was determined that TC = (359.3 ( 0.1) K and PC = (2.930 ( 0.001) MPa. The measured vapor pressure data were used to fit the parameters of the Frost
Kalkwarf11 equation (see eq 1).
P=Pa ¼ exp A þ

B þ C lnðT=KÞ þ D  10
17  ðT=KÞE ðT=KÞ



ð1Þ

Table 1. Pure Component Experimental Vapor Pressure for HFPO T/K

P/MPa

T/K

P/MPa

231.39

0.0536

305.22

0.8283

235.37 239.35

0.0643 0.0786

309.22 313.22

0.9226 1.0250

243.34

0.0943

317.23

1.1349

247.31

0.1124

321.22

1.2539

251.27

0.1339

325.23

1.3821

255.32

0.1565

329.23

1.5202

259.32

0.1880

333.24

1.6677

263.32

0.2155

337.24

1.8254

267.30 271.30

0.2501 0.2890

339.26 343.25

1.9094 2.0826

273.22

0.3117

347.24

2.2739

277.20

0.3552

351.25

2.4781

281.19

0.4071

355.26

2.6956

285.20

0.4619

358.26

2.8702

289.20

0.5227

358.96

2.9137

293.22

0.5895

358.99

2.9164

297.23 301.23

0.6626 0.7418

359.08 359.20

2.9197 2.9286

where P is the pressure, T is the temperature, and A, B, C, D, and E are adjustable parameters with the values of 53.1702,
3799.8834,
4.7530, 12.3069, and 6, respectively. Average absolute relative deviation is less than 0.34% and the bias is
0.25% (see Figure 1). There exists no literature data concerning this fluid to the knowledge of the authors. Densities. The Tables S1 and S2 (in Supporting Information) present our experimental results for temperatures between (263 and 362) K. Table 2 shows the densities determined at saturation in the (0
2.9) MPa pressure range. The vapor pressure measurements are used to calculate the saturation pressure at the temperature of densities measurement. Then, the experimental densities are fitted by a polynomial to interpolate the densities at equilibrium pressure. As presented in a previous paper (Coquelet et al.3), the densities at saturation were used to determine the critical coordinates of the pure component. Two laws were used for the determination of critical temperature TC and critical density FC. Equation 1 at TC was then used to determine PC. The first law is the following asymptotic scaling-law expression of the difference of densities between the liquid and the vapor phase (eq 2): FL
FV ¼ AðTC
TÞβ

ð2Þ

where β is a critical exponent (0.325). It is also assumed that the densities on the vapor
liquid coexistence curve obey the law of rectilinear diameters (eq 3) given as FL þ FV ¼ BðTC
TÞ þ FC 2

ð3Þ

where FL (kg 3 m
3) and FV (kg 3 m
3) are liquid and vapor densities, respectively. A (kg 3 m
3 3 K
β) and B (kg 3 m
3 3 K) are adjustable parameters. Their numerical values are presented in Table 3, along with critical properties of HFPO. 4762

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Figure 1. Deviation between calculated vapor pressure and experimental one with the Frost
Kalkwarf equation.

Table 2. Vapor and Liquid Densities at Saturation vapor phase FV/kg 3 m
3

liquid phase FL/kg 3 m
3

T/K

P/MPa

263.27 273.21

0.2172 0.3110

17.6 25.2

1485.8 1452.2

283.17

0.4332

35.00

1412.7

293.22

0.5900

48.2

1365.6

303.15

0.7833

64.1

1311.7

323.22

1.3155

112.2

1187.4

343.26

2.0869

202.2

992.5

353.06

2.5758

297.1

914.9

357.92

2.8511

401.4

770.6

Data Consistency in the Critical Region. The asymptotic behavior of the difference of densities between the liquid and the vapor phase can be used to verify the consistency of our experimental data. Indeed, one can deduce from eq 2 the following equation:

lnðFL
FV Þ ¼ β lnðT
TC Þ þ constant

Figures 2 and 3 show the P
F and T
F diagrams, including the critical point. Using eqs 2 and 3, one can obtain eqs 4 and 5 for the determination of vapor and liquid densities at saturation as follows: FL ¼ BðT
TC Þ þ FC þ

AðTC
TÞβ 2

ð4Þ

FV ¼ BðT
TC Þ þ FC


AðTC
TÞβ 2

ð5Þ

Using eqs 4 and 5, the average absolute relative deviations on density for the vapor and liquid phases are 2% and 0.8%, respectively. The deviation for the vapor density is more significant because of its low order of magnitude. The obtained critical parameters TC (359.26 K) and PC (2.9312 MPa) are found to be in very good agreement with those determined by vapor pressure measurements TC (359.3 K) and PC (2.93 MPa). Information obtained from Dupont de Nemours Safety sheet12 lists TC = 359.15 K and PC = 2.896 MPa. The values of TC and PC obtained in our study are in very good agreement with those listed in the Dupont de Nemours Safety sheet.

ð6Þ

Therefore, a linear behavior is expected if the logarithm of the difference of densities on the coexistence curve against the logarithm of the departure from the critical temperature is represented. The plot, starting from T = 303 K, can be seen in Figure 4. The linear regression proves that the critical exponent β is recovered (0.3253) and that the data are thermodynamically consistent. Modeling. In a previous paper,3 we used the Peng
Robinson equation of state (PR EoS)13 with the Mathias
Copeman (MC)14 alpha function to correlate the vapor pressure and the densities of HFP. As expected, the PR EoS was not accurate enough to represent the densities of the liquid phase at saturation. The calculations revealed the difficulty to represent accurately the thermodynamic properties in the vicinity of the critical point. To achieve this representation, a specific model relying on renormalizationgroup theory is required. The new Landau-crossover approach developed by Dicko and Coquelet7 has been used for this purpose. Other crossover EoS can be found in the literature (Cf White’s recursive procedure15). That is why, in this work, it is specified “Landau-crossover”. All details concerning the chosen model are explained in a previous paper.7 The method is applied to a generalized EoS in a form proposed by Zielke and Lempe16 P ¼

RT aðTÞ
v
b ðv þ cÞðv þ dÞ

ð7Þ

where P is the pressure, v the molar volume, R the gas constant, and T the temperature. The two parameters, c and d, can be expressed in terms of the parameters b and c* of the original form 4763

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Table 3. Classical and Crossover Parameters for HFPO and HFP experimental critical coordinates

CR-PT EoS parameters

component

TC/K

PC/MPa

FC/kg 3 m
3

ω

Z0c

GN

d1

HFPO

359.3

2.931

584.18

0.3338

0.319

1.14

1.12

HFP

358.9

3.136

579.03

0.3529

0.314

1.15

1.06

eqs 4 and 5 parameters A

B

335.12

1.80

Figure 2. HFPO P-F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using eqs 4 and 5.

Figure 3. HFPO T-F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using eqs 4 and 5.

of the cubic EoS. a(T) depends on the choice of the alpha function. Here, the generalized form of Patel and Teja8 is

selected. The eq 8, where ω is the Pitzer acentric factor, gives its expression. The determination of the critical parameters Ωa, 4764

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Figure 4. Calculation of β critical exponent. Δ, calculated points with experimental values; black line, linear regression.

Figure 5. HFPO T
F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using CR-PT EoS; dashed line, calculated using PT EoS. 4765

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Figure 6. HFPO P-F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using CR-PT EoS; Dashed line, calculated using PT EoS.

Figure 7. HFP T-F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using CR-PT EoS; dashed line, calculated using PT EoS.

Ωb, and Ωc, which are linked to a, b, and c* in eq 9 is obtained by solving the eq 7 developed in terms of critical compressibility at the critical point. RðTÞ ¼ 0:452413 þ 1:30982  ω
0:296937  ω2

ð8Þ

aðTÞ ¼

Ωa

RTC 2 RTC  RTC RðTÞb ¼ Ωb c ¼ ΩC PC 2 PC PC

ð9Þ

The crossover theory is independent of the choice of the classical EoS. In our previous publication,7 the Redlich
Kwong
Soave equation of state (RKS EoS)17,18 was selected. In 4766

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Figure 8. HFP P-F diagram. Δ, Experimental densities;  , critical point; black line, calculated densities using CR-PT EoS; dashed line, calculated using PT EoS.

Table 4. Calculated Absolute Average Deviation AADa for VLE Densities and Vapor Pressures in the (263
358) K Temperature Range component

AAD for FL PT

AAD for FL CR-PT

AAD for FV

AAD for FV

AAD for Pvap PT

AAD for Pvap CR-PT

[source]

(%)

(%)

PT /%

CR-PT /%

(%)

(%)

HFPO [this work] HFP [31] a

7.9 12

1

6

6.2

3.9

3.7

1.7

2.8

2.7

1.3

1.2

AAD = 1/(Nexp)Σ|(Fexp
Fcalc)/(Fexp)| or AAD = 1/(Nexp)Σ|(Pexp
Pcalc)/(Pexp)|.

this work, the PT EoS8 has been preferred, since three parameters cubic EoS are more flexible. Indeed, the RKS EoS cannot render the experimental data even with a crossover treatment. Finally, for the crossover Patel
Teja EoS (CR-PT EoS), vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u
! u   2 bþc b þ c t þ cb þ ð10Þ c¼ 2 2 and

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u
! b þ c u b þ c 2 t 
c bþ d¼ 2 2

ð11Þ

Moreover, applying the critical conditions leads to the following relationships between the dimensionless parameters Ωa, Ωb, and Ωc and the critical compressibility factor Z0c. Ωc ¼ 1
3Z0c

ð12Þ

Ωa ¼ 3Z0c 2 þ 3ð1
2Z0c ÞΩb þ Ωb 2 þ Ωc

ð13Þ

Ωb is the smallest positive root of the equation Ωb 3 þ ð2
3Z0c ÞΩb 2 þ 3Z0c 2 Ωb
Z0c 3 ¼ 0

Experimental densities have been used to determine the parameter d1 (reduced rectilinear diameter) for HFPO and HFP. The Ginzburg number GN and Z0c have been fitted simultaneously on experimental data. Classical and crossover parameters are presented in Table 3. As can be seen in Figures 5
8, the model represents very well the experimental data. The absolute average deviations have been calculated and are reported in Table 4. The calculated vapor pressures and densities are similar for the original PT EoS and the CR-PT EoS. However, great improvement can be noticed for the liquid densities calculation.

ð14Þ

’ CONCLUSION A vibrating tube densitometer was used to determine the density of pure hexafluoropropylene oxide. Using these data, new values of critical properties were determined and validated through visual measurement on a static cell. The obtained data are consistent with the expected asymptotic behavior near the critical point. A crossover PT EoS has been successfully used to correlate the data. The crossover EoS keeps the performance of the original PT Eos for vapor properties and improves the representation of liquid densities. 4767

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’ ASSOCIATED CONTENT

bS

Supporting Information. Experimental results are given in Tables S1 and S2. This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Telephone: þ33 164694962. Fax þ33 164694968.

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