PvT Measurements of trans-1,3,3,3-Tetrafluoroprop-1-ene + Methane

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PvT Measurements of trans-1,3,3,3-Tetrafluoroprop-1-ene + Methane and trans-1,3,3,3-Tetrafluoroprop-1-ene + Nitrogen Binary Pairs J. Steven Brown,† Francesco Corvaro,‡ Giovanni Di Nicola,*,‡ Giuliano Giuliani,‡ and Marco Pacetti‡ †

Department of Mechanical Engineering, The Catholic University of America, Washington, D.C. 20064, United States Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, via Brecce Bianche 12, 60131 Ancona, Italy

‡

ABSTRACT: Presented in this work are 102 vapor phase PvT measurements for blends of trans-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(E)) + methane and 85 vapor phase PvT measurements for blends of R1234ze(E) + nitrogen. The R1234ze(E) + methane data consist of eight data sets measured along five isochores (0.12, 0.09, 0.06, 0.04, and 0.03) m3·kg−1 for (267 < T < 413) K. The blends consisted of four methane mole fractions (0.25, 0.31, 0.50, and 0.75) mol·mol−1. The R1234ze(E) + nitrogen data consist of six data sets measured along three isochores (0.07, 0.11, and 0.14) m3·kg−1 for (263 < T < 413) K. The blends consisted of three nitrogen mole fractions (0.25, 0.50, and 0.75) mol·mol−1.

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and (2) R1234ze(E) + carbon dioxide.16 Note: all four of these fluorinated propylene isomers have GWP values less than one.17 The current work forms part of the ongoing investigations by the authors to seek low-GWP refrigerant blends appropriate for low-temperature industrial refrigeration applications. In particular, this work presents PvT measurements in the vapor phase for binary blends of R1234ze(E) with two “natural” refrigerants: methane and nitrogen. Note the GWP of methane is 202 and diatomic nitrogen is not a global warming gas. While these blends are unusual in that they consist of fluids with widely different normal boiling point temperatures, namely, (254.2, 111.67, and 77.4) K for R1234ze(E), methane, and nitrogen, respectively, there is interest in investigating them by some compressor manufacturers for potential compressor applications, particularly with regard to discharge temperatures. Regardless, there also is scientific interest in investigating lowGWP blends comprising a wide number of and types of refrigerants.

INTRODUCTION Recently much effort has been focused on identifying and commercializing working fluids (refrigerants, aerosols, foam blowing agents, and fire suppressants, etc.) possessing low global warming potentials (GWP). While there is no universal definition of “low-GWP”,1 it is clear that industry, governments, and the public-at-large desire values that are considerably lower than typical GWP values of hydrofluorocarbon (HFC) working fluids; e.g., the refrigerants R32 and R134a have GWP values of 675 and 1430,2 respectively. (Note: all GWP values presented in this work are for a 100 year time frame relative to carbon dioxide.) For example, the European Union promulgated its Mobile Directive,3 which specifies that refrigerants possessing GWP values greater than 150 cannot be used in new vehicle models beginning Jan. 1, 2017. Partly as a response to this directive, considerable effort has been expended on commercializing R1234yf (2,3,3,3-tetrafluoroprop-1-ene; CF3CFCH2; CAS No. 754-12-1) for automotive applications.4 However, in addition to R1234yf, several other halogenated propylene isomers and their blends have been, and are being, investigated as low-GWP working fluids for a wide range of applications. While not intending to provide a complete bibliography of all studies related to halogenated propylene isomers, the authors in previous reports have been among those who have studied fluorinated propylene isomers. In particular, the authors measured PvT properties of R1234yf,5−8 R1234ze(E) (trans1,3,3,3-tetrafluoroprop-1-ene; CF3CHCHF; CAS No. 2911824-9),9,10 R1243zf (3,3,3-trifluoroprop-1-ene; CF3CHCH2; CAS No. 677-21-4),11,12 and R1234ze(Z) (cis-1,3,3,3-tetrafluoroprop-1-ene; CF3CHCHF; CAS No. 29118-25-0),13,14 and the PvTx properties of two binary blends containing fluorinated propylene isomers: (1) R1234yf + carbon dioxide15 © 2014 American Chemical Society

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EXPERIMENTAL SECTION Materials. Table 1 specifies the R1234ze(E), methane (CH4, CAS No. 74-82-8), and nitrogen (N2, CAS No. 7727-379) samples. Note any remaining noncondensable gases in the R1234ze(E) sample were removed through several iterations of freezing, evacuation, thawing, and ultrasonic stirring. Experimental Apparatus and Procedure. The experimental setup consisted of an isochoric stainless steel sphere, Received: July 17, 2014 Accepted: September 23, 2014 Published: October 3, 2014 3798

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used to measure the bath temperature. A Ruska 7000 pressure transducer/readout with a total uncertainty of 0.003 % of full scale (6000 kPa) was used to measure the sample pressure. Note that temperature fluctuations in the bath can also affect the total pressure uncertainty; however, the total pressure uncertainty was found always to be less than 1 kPa. The blends were prepared using the gravimetric method. To minimize the uncertainties in the mass measurements, the pure fluids were first charged into bottles of known tare weights. The combined masses of the bottles and samples were then measured using an analytical balance with an uncertainty of 0.3 mg. After placing the cell and connections under vacuum, the bottles were connected to the sphere, after which the bottles were once again weighed. Moreover, the masses remaining in the tubing were estimated and subtracted from the discharged masses. These corrected values represent the total sample mass. Based on the uncertainties in the mass measurement and total volume measurement, the expanded uncertainty of the molar fraction (z) is estimated to be less than 0.001 mol·mol−1 and the expanded uncertainty of the specific volume is estimated to be less than 0.005 m3·kg−1. After reaching the desired temperature, a mixing pump was switched on for approximately 15 min. Then the sample was allowed to stabilize for approximately 20 min before measure-

Table 1. Methane, Nitrogen, and R1234ze(E) Sample Descriptions

a

chem name

source

initial mole fraction purity

purif method

final mole fraction purity

methane nitrogen R1234ze(E)a

Sol SpA Sol SpA Honeywell

0.9999 0.9999 0.995

none none none

0.9999 0.9999 0.995

trans-1,3,3,3-Tetrafluoropropene.

instrumentation for measuring temperature, pressure, and mass, a proportional-integral-derivative (PID) controller, a data acquisition system, and two controllable thermostatic baths. The experimental apparatus and procedure already have been described;15,16 therefore, only a brief overview will be provided here. The test cell and pressure transducer were submerged in one of two thermostatic baths depending on the operating temperature range. The lower range was approximately from (210 to 290) K, and the higher range was approximately from (290 to 360) K. The total volume of the test cell, associated piping, and the cavity of the pressure transducer were estimated to be (273.5 ± 0.3) cm3 at room temperature. A 25 Ω platinum resistance thermometer (Hart Scientific 5680) with a total uncertainty of approximately 0.03 K was

Table 2. PvT Data in the Vapor Phase for R1234ze(E) + Methane Binary Blendsa T

P

v

T

P

v

T

P

v

T

P

v

K

kPa

(m3·kg−1)

K

kPa

(m3·kg−1)

K

kPa

(m3·kg−1)

K

kPa

(m3·kg−1)

zCH4 = 0.496

zCH4 = 0.310 273.14 283.07 293.03 303.16 313.15 323.17 333.27 343.18 353.17 363.15 373.20 383.28 393.13 403.18 413.34

216.8 225.4 233.9 242.4 251.0 259.0 267.5 275.8 284.2 292.6 301.0 309.5 317.8 326.4 334.9 zCH4 = 0.513

0.120 0.120 0.120 0.120 0.121 0.121 0.121 0.121 0.121 0.121 0.121 0.121 0.121 0.121 0.121

288.33 293.33 303.16 313.24 323.19 333.20 343.23 353.24 363.25 373.23 383.33 393.32 403.27 413.30

273.11 283.38 293.06 303.23 313.19 323.19 333.25 343.16 353.22 363.24 373.10 383.30 393.22 403.17 413.18

305.7 319.0 330.6 342.7 354.4 366.1 378.1 389.7 401.5 413.1 424.6 437.0 448.6 460.3 472.0

0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.114 0.114 0.114 0.114 0.114 0.114

283.29 293.17 303.16 313.20 323.29 333.25 343.23 353.23 363.28 373.27 383.31 393.33 403.26 413.29

665.7 681.4 711.2 738.5 765.2 792.0 818.7 845.0 871.2 897.8 924.1 950.3 976.2 1002.5

0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.052

263.12 273.19 283.30 293.03 303.22 313.23 323.35 333.20 343.25 353.15 363.21 373.27 383.25 393.14 403.21 413.23

zCH4 = 0.748 1326.6 1381.0 1435.1 1488.8 1542.4 1595.7 1648.5 1701.4 1754.1 1806.6 1859.5 1911.9 1963.8 2016.0

zCH4 = 0.261

zCH4 = 0.747

0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041 0.041

293.26 303.15 323.17 343.11 373.23 413.38

541.7 565.7 588.9 611.2 634.1 657.6 680.5 702.6 725.3 747.4 770.2 792.6 815.0 837.2 860.0 881.9 zCH4 = 0.251

0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092

456.1 474.1 510.4 546.9 600.7 671.6

0.056 0.056 0.056 0.056 0.056 0.056

313.15 323.21 333.25 343.12 353.23 363.16 373.10 383.18 393.06 403.12 413.15

995.8 1040.8 1083.7 1126.5 1167.7 1209.5 1251.1 1291.3 1327.0 1366.9 1405.5

0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026 0.026

zCH4 = 0.513 313.22 323.27 333.18 343.34 353.34 363.19 373.11 383.17 393.10 403.03 412.96

1512.1 1573.2 1636.8 1700.6 1759.0 1820.5 1881.5 1940.6 2000.7 2059.7 2117.2

0.024 0.024 0.024 0.024 0.024 0.024 0.024 0.025 0.025 0.025 0.025

a

Standard uncertainties are u(T) = 0.03 K, u(P) = 1 kPa, u(v) = 0.005 m3·kg−1, and u(z) = 0.001 mol·mol−1 3799

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ments were taken. After making the measurement, the thermostatic bath temperature was changed to the next desired level.

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RESULTS AND DISCUSSION PvT Data in the Vapor Phase for R1234ze(E) + Methane. This work reports 102 experimental vapor phase PvT data for binary blends of R1234ze(E) + methane. The data are provided in Table 2 and Figure 1.

Figure 2. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the Ideal Gas Law (Pcalc) and the data of Table 2 (Pexp): ▲, zCH4 = 0.310 and v = 0.121 m3·kg−1; Δ, zCH4 = 0.513 and v = 0.113 m3·kg−1; •, zCH4 = 0.747 and v = 0.092 m3·kg−1; ○, zCH4 = 0.251 and v = 0.056 m3·kg−1; ■, zCH4 = 0.496 and v = 0.051 m3·kg−1; □, zCH4 = 0.748 and v = 0.041 m3·kg−1; = 0.261 and v = 0.026 m3·kg−1; ∇, zCH4 = 0.513 and v = 0.024 m ·kg .

▼, zCH 4 3

−1

Figure 1. PvT data in the vapor phase for R1234ze(E) + methane binary blends; ▲, zCH4 = 0.310 and v = 0.121 m3·kg−1; Δ, zCH4 = 0.513 and v = 0.113 m3·kg−1; •, zCH4 = 0.747 and v = 0.092 m3·kg−1; O, zCH4 = 0.251 and v = 0.056 m3·kg−1; ■, zCH4 = 0.496 and v = 0.051 m3·kg−1; □, zCH 4

= 0.748 and v = 0.041 m3·kg−1; ▼, zCH4 = 0.261 and v = 0.026

m3·kg−1; ∇, zCH4 = 0.513 and v = 0.024 m3·kg−1.

The eight R1234ze(E) + methane data sets were measured along five isochores (0.12, 0.09, 0.06, 0.04, and 0.03) m3·kg−1 for (267 < T < 413) K. The blends consisted of four methane mole fractions (0.25, 0.31, 0.50, and 0.75) mol·mol−1. Figure 2 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) between the Ideal Gas Law (Pcalc) and the data of Table 2 (Pexp), with ΔP/P = (−0.25 to 13.79) % and with a mean absolute deviation (|100ΔP/P |) of 3.74. Note this model is referred to as IG. The percentage deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the default high-accuracy equations of state (EoS) represented in terms of the reduced molar Helmholtz free energy for R1234ze(E)18 and methane19 contained in REFPROP20 coupled with a modified van der Waals onefluid linear mixing model21 where the two constants Kt and Kv are both set equal to unity (Pcalc) and the data of Table 2 (Pexp) are ΔP/P = (−1.47 to 0.91) % with a mean absolute deviation (|100ΔP/P |) of 6.59. Note this model is referred to as REF. In a further note, ref 21. provides a modified ref 22 mixing rule by introducing a constant Kt for the reduced critical temperature and Kv for the reduced critical volume. Figure 3 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) for the REF model where the two constants Kt and Kv both now have been set equal to 0.91 (Pcalc) and the data of Table 2 (Pexp), with ΔP/P = (−1.09 to 1.80) % and with a mean absolute deviation (|100ΔP/P |) of 0.45. Note the two constants Kt and Kv were selected to minimize the mean absolute deviation. This new model is referred to as REF2.

Figure 3. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the default high-accuracy EoS represented in terms of the reduced molar Helmholtz free energy for R1234ze(E)18 and methane19 contained in REFPROP20 coupled with a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.91 (Pcalc) and the data of Table 2 (Pexp): ▲, zCH4 = 0.310 and v = 0.121 m3·kg−1; Δ, zCH4 = 0.513 and v = 0.113 m3·kg−1; •, zCH4 = 0.747 and v = 0.092 m3·kg−1; ○, zCH4 = 0.251 and v = 0.056 m3·kg−1; ■, zCH4 = 0.496 and v = 0.051 m3·kg−1; □, zCH4 = 0.748 and v = 0.041 m3·kg−1; = 0.261 and v = 0.026 m3·kg−1; ∇, zCH4 = 0.513 and v = 0.024 m ·kg .

▼, zCH 4 3

−1

The percentage deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between Peng−Robinson (P-R) EoS (P calc ) for both R1234ze(E) and methane developed by the authors and a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to unity (Pcalc) and the data of Table 2 (Pexp) are ΔP/P = (−2.29 to 0.30) % with a mean absolute deviation (|100ΔP/P |) of 1.09. Note this model is referred to as PR. 3800

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Figure 4 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) for the PR model where the two constants Kt and Kv both

Table 4. PvT Data in the Vapor Phase for R1234ze(E) + Nitrogen Binary Blendsa T

P

v

T

P

v

K

kPa

(m3·kg−1)

K

kPa

(m3·kg−1)

zN2 = 0.254 303.18 313.14 323.13 333.34 343.12 353.08 363.06 373.00 383.26 393.14 403.14 413.13

Figure 4. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between P-R EoS (Pcalc) for both R1234ze(E) and methane developed by the authors and a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.86 (Pcalc) and the data of Table 2 (Pexp): ▲, zCH4 = 0.310 and v = 0.121 m3·kg−1; Δ, zCH4 = 0.513 and v = 0.113 m3·kg−1; •, zCH4 = 0.747 and v = 0.092 m3·kg−1; m3·kg−1; □, zCH4 = 0.748 and v = 0.041 m3·kg−1; ▼, zCH4 = 0.261 and v = 0.026 m3·kg−1; ∇, zCH4 = 0.513 and v = 0.024 m3·kg−1.

now have been set equal to 0.86 (Pcalc) and the data of Table 2 (Pexp), with ΔP/P = (−1.24 to 1.67) % and with a mean absolute deviation (|100ΔP/P |) of 0.51. Note the two constants Kt and Kv were selected to minimize the mean absolute deviation. This new model is referred to as PR2. Table 3 shows the percentage of deviations falling within the specified bounds for the R1234ze(E) + methane blends. The Table 3. Percentage of Data Points Falling within Specified Bounds for the R1234ze(E) + Methane Blends IG

PR

REF

PR2

REF2

6.9 11.8 21.6

24.5 47.1 68.6

33.3 76.5 100.0

52.9 89.2 99.0

57.8 93.1 99.0

273.19 283.12 293.11 303.16 313.17 323.17 333.17 343.11 353.10 363.12 373.09 383.05 393.06 403.05 413.10

464.3 485.7 506.5 525.9 545.2 564.0 582.8 601.4 619.5 638.7 657.0 675.5 694.0 712.5 731.0 zN2 = 0.750

0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

381.3 396.1 410.2 423.9 438.2 451.9 465.8 479.5 494.4 508.1 521.2 535.2

0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069

263.05 273.12 283.10 293.13 303.17 313.18 323.16 333.19 343.14 353.13 363.25 373.07 383.09 393.06 403.04 413.06

383.1 398.4 413.5 428.7 443.8 458.8 473.2 488.7 503.4 518.1 533.3 547.3 562.6 577.5 592.5 607.4 zN2 = 0.746

0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114 0.114

0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.111 0.111 0.111 0.111 0.111 0.111 0.111

263.16 273.13 283.10 293.09 303.35 313.20 323.17 333.17 343.13 353.13 363.10 373.16 383.08 393.13 403.10 413.04

622.6 648.5 673.7 699.0 724.8 749.1 773.9 799.4 823.9 848.5 872.9 897.7 922.8 947.3 971.7 995.8

0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069

zN2 = 0.495 283.07 293.08 303.05 313.18 323.17 333.18 343.12 353.11 363.10 373.09 383.09 393.08 402.99 413.00

model ± 0.5 ± 1.0 ± 1.5

0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.137 0.137

zN2 = 0.250 303.19 313.17 323.15 333.16 343.14 353.05 363.10 373.10 383.06 393.05 403.04 413.01

○, zCH4 = 0.251 and v = 0.056 m3·kg−1; ■, zCH4 = 0.496 and v = 0.051

bounds/%

196.3 203.2 209.9 216.7 223.3 229.5 236.3 242.6 249.6 256.3 262.9 269.4

zN2 = 0.500

IG model lacks accurate robust predictive capability. While all four PR and REF models well-predict the data, the PR2 and REF2 models are the most accurateboth predict more than approximately 50% of the data to within ± 0.5 %, approximately 90 % of the data to within ± 1.0 %, and approximately 99 % of the data to within ± 1.5 %. PvT Data in the Vapor Phase for R1234ze(E) + Nitrogen. This work reports 85 experimental vapor phase PvT data for binary blends of R1234ze(E) + nitrogen. The data are provided in Table 4 and Figure 5. The six R1234ze(E) + nitrogen data sets were measured along three isochores (0.07, 0.11, and 0.14) m3·kg−1 for (263 < T < 413) K. The blends consisted of three nitrogen mole fractions (0.25, 0.50, and 0.75) mol·mol−1. Figure 6 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) between the Ideal Gas Law (Pcalc) and the data of Table 4

291.8 302.8 313.9 324.5 335.3 346.1 356.8 367.5 378.2 389.2 399.9 410.6 421.1 432.1

a

Standard uncertainties are u(T) = 0.03 K, u(P) = 1 kPa, u(v) = 0.005 m3·kg−1, and u(z) = 0.001 mol·mol−1.

(Pexp), with ΔP/P = (−0.29 to 4.96) % and with a mean absolute deviation (|100ΔP/P |) of 1.33. Note this model is referred to as IG. 3801

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Figure 5. PvT data in the vapor phase for R1234ze(E) + nitrogen binary blends: ▲, zN2 = 0.254 and v = 0.136 m3·kg−1; Δ, zN2 = 0.250 and v = 0.069 m3·kg−1; •, zN2 = 0.495 and v = 0.111 m3·kg−1; ○, zN2 = 0.500 and v = 0.066 m3·kg−1; ■, zN2 = 0.750 and v = 0.114 m3·kg−1; □, zN2 = 0.746 and v = 0.069 m3·kg−1.

Figure 7. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the default high-accuracy EoS represented in terms of the reduced molar Helmholtz free energy for R1234ze(E)18 and methane19 contained in REFPROP20 coupled with a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.91 (Pcalc) and the data of Table 2 (Pexp): ▲, zN2 = 0.254 and v = 0.136 m3·kg−1; Δ, zN2 = 0.250 and v = 0.069 m3·kg−1; •, zN2 = 0.495 and v = 0.111 m3·kg−1; ○, zN2 = 0.500 and v = 0.066 m3·kg−1; ■, zN2 = 0.750 and v = 0.114 m3·kg−1; □, zN2 = 0.746 and v = 0.069 m3·kg−1.

The percentage deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between P-R EoS (Pcalc) for both R1234ze(E) and nitrogen developed by the authors and a modified van der Waals onefluid linear mixing model21 where the two constants Kt and Kv are both set equal to unity (Pcalc) and the data of Table 4 (Pexp) are ΔP/P = (−1.66 to 0.78) % with a mean absolute deviation (|100ΔP/P|) of 0.54. Note this model is referred to as PR. Figure 8 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) for the PR model where the two constants Kt and Kv both now have been set equal to 0.86 (Pcalc) and the data of Table 4

Figure 6. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the Ideal Gas Law (Pcalc) and the data of Table 2 (Pexp): ▲, zN2 = 0.254 and v = 0.136 m3·kg−1; Δ, zN2 = 0.250 and v = 0.069 m3·kg−1; •, zN2 = 0.495 and v = 0.111 m3·kg−1; ○, zN2 = 0.500 and v = 0.066 m3·kg−1; ■, zN2 = 0.750 and v = 0.114 m3·kg−1; □, zN2 = 0.746 and v = 0.069 m3·kg−1.

The percentage deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between the default high-accuracy EoS represented in terms of the reduced molar Helmholtz free energy for R1234ze(E)18 and nitrogen22 contained in REFPROP20 coupled with a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to unity (Pcalc) and the data of Table 4 (Pexp) are ΔP/P = (−1.41 to 1.21) % with a mean absolute deviation (|100ΔP/P|) of 0.38. Note this model is referred to as REF. Figure 7 shows percentage deviations (ΔP/P = (Pcalc − Pexp)/ Pexp) for the REF model where the two constants Kt and Kv both now have been set equal to 0.91 (Pcalc) and the data of Table 4 (Pexp), with ΔP/P = (−1.21 to 1.74) % and with a mean absolute deviation (|100ΔP/P|) of 0.35. Note the two constants Kt and Kv were selected to minimize the mean absolute deviation. This new model is referred to as REF2.

Figure 8. Deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between P-R EoS (Pcalc) for both R1234ze(E) and methane developed by the authors and a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.86 (Pcalc) and the data of Table 2 (Pexp): ▲, zN2 = 0.254 and v = 0.136 m3·kg−1; Δ, zN2 = 0.250 and v = 0.069 m3·kg−1; •, zN2 = 0.495 and v = 0.111 m3·kg−1; ○, zN2 = 0.500 and v = 0.066 m3·kg−1; ■, zN2 = 0.750 and v = 0.114 m3· kg−1; □, zN2 = 0.746 and v = 0.069 m3·kg−1. 3802

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(Pexp), with ΔP/P = (−1.32 to 1.63) % and with a mean absolute deviation (|100ΔP/P |) of 0.36. Note the two constants Kt and Kv were selected to minimize the mean absolute deviation. This new model is referred to as PR2. Table 5 shows the percentage of deviations falling within the specified bounds for the R1234ze(E) + nitrogen blends. The IG

*Tel.: +39 071 2204277. Fax: +39 071 2202324. E-mail: g. [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We thank Honeywell for donating the R1234ze(E) sample.

model IG

PR

REF

PR2

REF2

± 0.5 ± 1.0 ± 1.5

22.4 43.5 62.4

61.2 94.1 98.8

74.1 91.7 100.0

76.5 94.1 99.8

80.0 92.9 98.8

AUTHOR INFORMATION

Corresponding Author

Table 5. Percentage of Data Points Falling within Specified Bounds for the R1234ze(E) + Nitrogen Blends bounds/%

Article

REFERENCES

(1) Brown, J. S. Fourth ASHRAE/NIST Refrigerants Conference: “Moving Towards Sustainability”. HVACR Res. 2013, 19, 101−102. (2) IPCC; Solomon, S.; Qin, D.; Manning, M.; Chen, Z.; Marquis, M.; Averyt, K. B.; Tignor, M.; Miller, H. L. Climate Change 2007: The Physical Science Basis, IPCC Fourth Assessment Report: Working Group I Report; Cambridge University Press: New York, 2007. (3) Directive 2006/40/EC of The European Parliament and of the Council of 17 May 2006 Relating to Emissions from Air-Conditioning Systems in Motor Vehicles & Amending Council Directive 70/156/ EC. Off. J. Eur. Union 2006, 161, 12−18. (4) Brown, J. S. Introduction to hydrofluoro-olefin alternatives for high global warming potential hydrofluorocarbon refrigerants. HVACR Res. 2013, 19, 693−704. (5) Di Nicola, G.; Polonara, F.; Santori, G. Saturated pressure measurements of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf). J. Chem. Eng. Data 2010, 55, 201−204. (6) Di Nicola, C.; Di Nicola, G.; Pacetti, M.; Polonara, F.; Santori, G. P−V−T behavior of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) in the vapor phase from (243 to 373) K. J. Chem. Eng. Data 2010, 55, 3302−3306. (7) Fedele, L.; Bobbo, S.; Groppo, F.; Brown, J. S.; Zilio, C. Saturated pressure measurements of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) for reduced temperatures ranging from 0.67 to 0.93. J. Chem. Eng. Data 2011, 56, 2608−2612. (8) Fedele, L.; Brown, J. S.; Colla, L.; Ferron, A.; Bobbo, S.; Zilio, C. Compressed liquid density measurements for 2,3,3,3-tetrafluoroprop1-ene (R1234yf). J. Chem. Eng. Data 2012, 57, 482−489. (9) Di Nicola, G.; Brown, J. S.; Fedele, L.; Bobbo, S.; Zilio, C. Saturated pressure measurements of trans-1,3,3,3-tetrafluoroprop-1ene (R1234ze(E)) for reduced temperatures ranging from 0.58 to 0.92. J. Chem. Eng. Data 2012, 57, 2197−2202. (10) Brown, J. S.; Di Nicola, G.; Zilio, C.; Fedele, L.; Bobbo, S.; Polonara, F. Subcooled liquid density measurements and PvT measurements in the vapor phase for trans-1,3,3,3-tetrafluoroprop-1ene (R1234ze(E). J. Chem. Eng. Data 2012, 57, 3710−3720. (11) Brown, J. S.; Di Nicola, G.; Fedele, L.; Bobbo, S.; Zilio, C. Saturated pressure measurements of 3,3,3-trifluoroprop-1-ene (R1243zf) for reduced temperatures ranging from 0.62 to 0.98. Fluid Phase Equilib. 2013, 351, 48−52. (12) Di Nicola, G.; Brown, J. S.; Fedele, L.; Securo, M.; Bobbo, S.; Zilio, C. Subcooled liquid density measurements and PvT measurements in the vapor phase for 3,3,3-trifluoroprop-1-ene (R1243zf). Int. J. Refrig. 2013, 36, 2209−2215. (13) Fedele, L.; Di Nicola, G.; Brown, J. S.; Bobbo, S.; Zilio, C. Measurements and correlations of cis-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(Z)) saturation pressure. Int. J. Therm. 2014, 35, 1−12. (14) Fedele, L.; Brown, J. S.; Di Nicola, G.; Bobbo, S.; Scattolini, M. Measurements and correlations of cis-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(Z)) subcooled liquid density and vapor phase PvT. Int. J. Therm. 2014, in press. (15) Di Nicola, G.; Di Nicola, C.; Arteconi, A.; Stryjek, R. PVTx measurements of the carbon dioxide + 2,3,3,3-Tetrafluoroprop-1-ene binary system. J. Chem. Eng. Data 2012, 57, 450−455. (16) Di Nicola, G.; Passerini, G.; Polonara, F.; Stryjek, R. PVTx measurements of the carbon dioxide + trans-1,3,3,3-Tetrafluoroprop1-ene binary system. Fluid Phase Equilib. 2013, 360, 124−128.

model is more accurate in its predictive capability for this blend than for the R1234ze(E) + methane blend. While all four PR and REF models well-predict the data, the PR2 and REF2 models are the most accurateboth predict more than approximately 75 % of the data to within ± 0.5 %, approximately 93 % of the data to within ± 1.0 %, and approximately 99 % of the data to within ± 1.5 %.

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CONCLUSION Eight data sets consisting of 102 PvT measurements in the vapor phase for binary blends of R1234ze(E) + methane were measured along five isochores (0.12, 0.09, 0.06, 0.04, and 0.03) m3·kg−1 for (267 < T < 413) K. The blends consisted of four methane mole fractions (0.25, 0.31, 0.50, and 0.75) mol·mol−1. Six data sets consisting of 85 PvT measurements in the vapor phase for binary blends of R1234ze(E) + nitrogen were measured along three isochores (0.07, 0.11, and 0.14) m3·kg−1 for (263 < T < 413) K. The blends consisted of three nitrogen mole fractions (0.25, 0.50, and 0.75) mol·mol−1. The data for both R1234ze(E) + methane blends and R1234ze(E) + nitrogen blends are well-predicted with both: (1) the default high-accuracy equations of state (EoS) represented in terms of the reduced molar Helmholtz free energy for R1234ze(E)18 and methane19 or R1234ze(E)18 and nitrogen22 contained in REFPROP20 coupled with a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.91 and (2) the simpler Peng−Robinson EoS developed by the authors for R1234ze(E) and methane or R1234ze(E) and nitrogen coupled with a modified van der Waals one-fluid linear mixing model21 where the two constants Kt and Kv are both set equal to 0.86. Note the widely different normal boiling point temperatures between the fluids in the binary pairs could be one of the reasons for deviation from ideal mixing. Both modeling approaches can predict (1) more than approximately 50 % of the R1234ze(E) + methane data to within ± 0.5 %, approximately 90 % of the R1234ze(E) + methane data to within ± 1.0 %, and approximately 99 % of the R1234ze(E) + methane data to within ± 1.5 % and (2) more than approximately 75 % of the R1234ze(E) + nitrogen data to within ± 0.5 %, approximately 93 % of the R1234ze(E) + nitrogen data to within ± 1.0 %, and approximately 99 % of the R1234ze(E) + nitrogen data to within ± 1.5 %. 3803

dx.doi.org/10.1021/je500669y | J. Chem. Eng. Data 2014, 59, 3798−3804

Journal of Chemical & Engineering Data

Article

(17) Hodnebrog, O.; Etminan, M.; Fuglestvedt, J. S.; Marston, G.; Myhre, G.; Nielsen, C. J.; Shine, K. P.; Wallington, T. J. Global warming potentials and radiative efficiencies of halocarbons and related compounds: A comprehensive review. Rev. Geophys. 2013, 51, 300−378. (18) McLinden, M. O.; Thol, M.; Lemmon E. W. Thermodynamic properties of trans-1,3,3,3-tetrafluoropropene [R1234ze(E)]: Measurements of density and vapor pressure and a comprehensive equation of state. Proceedings of the 2010 International Refrigeration and Air Conditioning Conference at Purdue, West Lafayette, IN, USA, Jul. 12− 15, 2010; Paper 2189. (19) Setzmann, U.; Wagner, W. A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 1991, 20, 1061−1151. (20) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23, Reference Fluid Thermodynamic and Transport Properties (REFPROP), version 9.1; National Institute of Standards and Technology: Gaithersburg, MD, USA, 2010 (R1234ze.fld file updated Mar. 19, 2013). (21) McLinden, M. O.; Klein, S. A. A next generation refrigerant properties database. Proceedings of the 1996 International Refrigeration and Air Conditioning Conference at Purdue, West Lafayette, IN, USA, Jul. 23−26, 1996; Ray W. Herrick Laboratories, Purdue University: West Lafayette, IN, USA, 1996; pp 409−414. (22) Plocker, U.; Kamp, H.; Prausnitz, J. Calculation of high-pressure vapor-liquid equilibria from a corresponding-states correlation with emphasis on asymmetric mixtures. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 324−332. (23) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W.; Yokozeki, A. A reference equation of state for the thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa. J. Phys. Chem. Ref. Data 2000, 29, 1361−1433.

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