Vapor Phase PνTx Measurements of Binary Blends of 2,3,3,3

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Vapor Phase PνTx Measurements of Binary Blends of 2,3,3,3-Tetrafluoroprop-1-ene + Isobutane and trans-1, 3,3,3-Tetrafluoroprop-1-ene + Isobutane J. Steven Brown,*,† Gianluca Coccia,‡ Sebastiano Tomassetti,‡ Mariano Pierantozzi,§ and Giovanni Di Nicola‡ †

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 § Dscuola di Ateneo Architettura e Design, Università degli studi di Camerino, Ascoli Piceno, 62032, Italy ‡

ABSTRACT: The paper presents 96 PνTx vapor phase data values for binary blends of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and isobutane (R600a) and 102 PνTx vapor phase data values for binary blends of trans1,3,3,3-tetrafluoroprop-1-ene (R1234ze(E)) and R600a. The R1234yf/ R600a blends were measured for five isochores (0.0751, 0.0944, 0.1280, 0.1666, 0.1701) m3·kg−1 for (303 < T < 383) K for six R600a mole fractions (0.234, 0.400, 0.472, 0.606, 0.772, 0.850) mol·mol−1. The R1234ze(E)/ R600a blends were measured for four isochores (0.0852, 0.0894, 0.1006, 0.1064) m3·kg−1 for (303 < T < 383) K for six R600a mole fractions (0.290, 0.428, 0.516, 0.612, 0.685, 0.755) mol·mol−1. The data were fitted with a fundamental Helmoltz equation of state (EoS), a Peng−Robinson EoS, and a truncated virial EoS.

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INTRODUCTION This paper extends the low-global warming potential (GWP) refrigerant blend investigations1−4 of the authors to include blends of R600a (isobutane) and two fluorinated propene isomers: R1234yf (2,3,3,3-tetrafluoroprop-1-ene) and R1234ze(E) (1,3,3,3-tetrafluoroprop-1-ene), both of which have been commercialized in the past 10−15 years, primarily driven by regulation and legislation regarding low-GWP working fluids.5−10 While R600a, R1234yf, and R1234ze(E) all possess ultralow GWP values (i.e., GWP < 30),11 it is becoming increasingly necessary to blend working fluids to achieve the right combination of environmental characteristics, thermodynamic and transport properties, flammability, toxicity, cost, lubricant compatibility, etc. This is particularly true as the number of low-GWP single-component working fluids appropriate for many applications, including air-conditioning and refrigeration, is limited.12 For example, the blending of hydrocarbons with unsaturated halocarbons in many applications can potentially lower cost, while potentially improving lubricant solubility and heat exchanger performance. An additional motive for undertaking the current study is simply to expand the scientific knowledge of low-GWP blends consisting of a variety of working fluids. Thus, this paper contributes to the knowledge base of hydrocarbon/fluorinated propene isomer blends by presenting vapor phase PνTx data for binary blends of R1234yf/R600a and R1234ze(E)/R600a, together with several simple fitting models (ideal gas equation of state (EoS), fundamental Helmoltz © 2017 American Chemical Society

(FEQ) EoS, Peng−Robinson (P-R) EoS, and a truncated virial EoS).

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EXPERIMENTAL SECTION Materials. Table 1 lists information for the R600a (isobutane, CH(CH3)3, CAS number 75-28-5), R1234yf (2,3,3,3-tetrafluoroprop-1-ene, CF3CF = CH2, CAS number 754-12-1), and R1234ze(E) (trans-1,3,3,3-tetrafluoroprop-1ene, CF3CH = CHF, CAS number 29118-24-9) samples. The R1234yf and R1234ze(E) samples were subjected to several cycles of freezing, evacuation, thawing, and ultrasonic stirring to remove noncondensable gases. Experimental Apparatus and Procedure. The core of the experimental setup consisted of a constant-volume sphere and two temperature baths: one of which operated over a temperature range of (210 to 290) K while the other operated over a temperature range of (290 to 380) K. Since details of the experimental apparatus,1−4 experimental procedure,1−4 and experimental uncertainties13−15 have been previously reported, only a brief summary is provided here. The blends were prepared following a gravimetric methodology. First, the constant-volume sphere and associated tubing were placed under vacuum, after which the specified amounts of the working fluids were charged into the test sphere. Received: June 19, 2017 Accepted: August 22, 2017 Published: August 31, 2017 3577

DOI: 10.1021/acs.jced.7b00564 J. Chem. Eng. Data 2017, 62, 3577−3584

Journal of Chemical & Engineering Data

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Table 1. R600a, R1234yf, and R1234ze(E) Sample Descriptions chemical name R600a

a

source

initial mole fraction purity

purification method

0.999

none

R1234yfa

Matheson Gas Products Arkema, France

0.9995

R1234ze(E)b

Honeywell

0.995

several cycles of freezing, evacuation, melting, andultrasonic agitation several cycles of freezing, evacuation, melting, andultrasonic agitation

final mole fraction purity

analysis method

0.9997

GC

0.999

GC

2,3,3,3-Tetrafluoroprop-1-ene. btrans-1,3,3,3-Tetrafluoroprop-1-ene.

Table 2. PνTx Data in the Vapor Phase for R1234yf/R600a Binary Blendsa T

P

ν

T

P

ν

K

kPa

m3·kg−1

K

kPa

m3·kg−1

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

xR600a = 0.234 246.7 251.2 255.6 260.1 264.6 269.0 273.4 277.8 282.2 286.6 291.0 295.4 299.8 304.1 308.5 313.0 317.4 xR600a = 0.400 269.3 274.3 279.2 284.2 289.2 294.1 299.0 303.9 308.8 313.5 318.3 323.2 328.1 332.9 337.7 342.6 347.4 xR600a = 0.472 163.5 166.4 169.2 172.1 174.7 177.5 180.3 183.1 185.9 188.7 191.5

0.0939 0.0940 0.0940 0.0940 0.0940 0.0940 0.0941 0.0941 0.0941 0.0941 0.0941 0.0942 0.0942 0.0942 0.0942 0.0942 0.0943

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15

0.0942 0.0942 0.0943 0.0943 0.0943 0.0943 0.0944 0.0944 0.0944 0.0944 0.0944 0.0945 0.0945 0.0945 0.0945 0.0945 0.0946

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15

xR600a = 0.606 180.2 183.3 186.5 189.7 192.9 196.0 199.2 202.3 205.5 208.6 211.8 214.9 218.0 221.1 224.3 227.5 230.6 xR600a = 0.772 260.6 265.4 270.2 275.1 279.9 284.6 289.4 294.2 298.9 303.6 308.1 312.6

0.1698 0.1699 0.1699 0.1700 0.1700 0.1700 0.1701 0.1701 0.1701 0.1702 0.1702

308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15

xR600a = 0.850 426.8 435.6 444.2 452.8 461.2 469.7 477.9 486.3 494.6 502.9 511.2

Table 2. continued

0.1663 0.1664 0.1664 0.1665 0.1665 0.1665 0.1666 0.1666 0.1666 0.1667 0.1667 0.1667 0.1668 0.1668 0.1669 0.1669 0.1669

T

P

ν

T

P

ν

K

kPa

m3·kg−1

K

kPa

m3·kg−1

358.15 363.15 368.15 373.15 378.15 383.15

xR600a = 0.472 194.3 197.1 200.1 202.9 205.7 208.5

0.1703 0.1703 0.1703 0.1704 0.1704 0.1704

363.15 368.15 373.15 378.15 383.15

xR600a = 0.850 519.5 527.7 535.9 544.1 552.4

0.0799 0.0799 0.0799 0.0799 0.0799

a

Standard uncertainties are u(T) = 0.03 K, u(P) = 1 kPa, u(ν) = 0.266 dm3·kg−1, and u(xR600a) = 0.002 mol·mol−1.

0.1279 0.1279 0.1279 0.1279 0.1280 0.1280 0.1280 0.1281 0.1281 0.1281 0.1281 0.1282

Figure 1. Vapor phase PνTx data (Table 2) for binary blends of R1234yf/R600a: +, xR600a = 0.234 and ν = 0.0941 m3·kg−1; ▲, xR600a = 0.400 and ν = 0.0944 m3·kg−1; λ, xR600a = 0.472 and ν = 0.1701 m3·kg−1; ○, xR600a = 0.606 and ν = 0.1666 m3·kg−1; ×, x600a = 0.772 and ν = 0.1280 m3·kg−1; △, xR600a = 0.850 and ν = 0.0751 m3·kg−1.

The masses of the working fluids discharged from their respective containers were measured using an analytical balance with an uncertainty of 0.3 mg. The total sample mass was determined by subtracting the estimated sample mass remaining in the tubing, that was estimated to be between (0.01 and 0.06) g depending on the charging temperature, pressure, and molar mass of fluid, from the total discharged mass. Finally, the expanded uncertainty in mass was estimated to be lower than ±0.9 mg. The expanded uncertainties with coverage factors k = 2 (95% level of confidence) for the temperature measurements (Hart Scientific 5680-25 ohm platinum resistance thermometer), pressure measurements (Ruska 7000 pressure transducer), and volume measurements (total volume of constant-volume sphere, tubing, and pressure transducer cavity is 273.5 cm3 at 298 K) were 0.03 K, 1 kPa, and 0.3 cm3, respectively. The expanded uncertainty of the pressure measurements take into account fluctuations in the bath temperature.

0.0797 0.0797 0.0797 0.0797 0.0797 0.0798 0.0798 0.0798 0.0798 0.0798 0.0798 3578

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Table 3. PνTx Data in the Vapor Phase for R1234ze(E)/ R600a Binary Blendsa T K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15

ν

P kPa xR600a = 0.290 267.9 273.0 277.9 282.8 287.8 292.7 297.6 302.5 307.4 312.2 317.1 321.9 326.8 331.6 336.5 341.4 346.2 xR600a = 0.428 305.5 311.3 317.1 322.8 328.5 334.2 339.9 345.6 351.2 356.9 362.6 368.2 373.9 379.5 385.1 390.7 396.3 xR600a = 0.516 259.6 264.5 269.2 274.0 278.8 283.5 288.2 292.9 297.6 302.3 307.0 311.7 316.4 321.1 325.7 330.4 335.1

m ·kg 3

T −1

K

0.0895 0.0895 0.0896 0.0896 0.0896 0.0896 0.0896 0.0897 0.0897 0.0897 0.0897 0.0897 0.0898 0.0898 0.0898 0.0898 0.0898

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15

0.0844 0.0844 0.0844 0.0845 0.0845 0.0845 0.0845 0.0845 0.0846 0.0846 0.0846 0.0846 0.0846 0.0846 0.0847 0.0847 0.0847

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15

0.1062 0.1062 0.1062 0.1063 0.1063 0.1063 0.1063 0.1064 0.1064 0.1064 0.1064 0.1064 0.1065 0.1065 0.1065 0.1065 0.1066

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15

P

ν

kPa

m ·kg−1

xR600a = 0.612 321.0 327.2 333.4 339.5 345.6 351.7 357.8 363.8 369.8 375.8 381.8 387.8 393.7 399.7 405.6 411.7 417.6 xR600a = 0.685 304.9 310.7 316.5 322.2 328.0 333.7 339.5 345.1 350.8 356.5 362.1 367.7 373.3 379.0 384.7 390.3 395.9 xR600a = 0.755 367.4 374.9 382.2 389.5 396.8 404.0 411.2 418.3 425.4 432.4 439.4 446.5 453.5 460.5 467.6 474.5 481.6

3

0.0890 0.0890 0.0891 0.0891 0.0891 0.0891 0.0891 0.0892 0.0892 0.0892 0.0892 0.0892 0.0892 0.0893 0.0893 0.0893 0.0893

Figure 2. Vapor phase PνTx data (Table 3) for binary blends of R1234ze(E)/R600a: ○, xR600a = 0.290 and ν = 0.0897 m3·kg−1; +, xR600a = 0.428 and ν = 0.0846 m3·kg−1; ●, xR600a = 0.516 and ν = 0.1064 m3·kg−1; ▲, xR600a = 0.612 and ν = 0.0892 m3·kg−1; ×, xR600a = 0.685 and ν = 0.1006 m3·kg−1; △, xR600a = 0.775 and ν = 0.0858 m3·kg−1.

the volume estimation and the mass measurement. From the uncertainties reported below, the expanded specific volume uncertainties were calculated for the studied isochores (blends) from the following equation:

0.1004 0.1004 0.1005 0.1005 0.1005 0.1005 0.1005 0.1006 0.1006 0.1006 0.1006 0.1007 0.1007 0.1007 0.1007 0.1007 0.1008

⎡⎛ u(ν) ⎞2 ⎛ u(m)ν ⎞2 ⎤ ⎟ +⎜ ⎟⎥ u(ν)2 = ν 2⎢⎜ ⎝ V ⎠ ⎥⎦ ⎢⎣⎝ V ⎠

(1)

where the u(ν) is the expanded specific volume uncertainty in dm3·kg−1, ν is the sample specific volume in dm3·kg−1, V is the total volume of the constant-volume sphere, tubing, and pressure transducer cavity and u(m) is twice the expanded uncertainty in mass in kg. From eq 1, the expanded specific volume uncertainties with coverage factors k = 2 (95% level of confidence) for binary blends of R1234yf/R600a and R1234ze(E)/R600a ranged from (0.097 to 0.266) dm3·kg−1 and from (0.104 to 0.138) dm3·kg−1, respectively. The molar fraction uncertainty depends on the mass of the blend sample charged into the test sphere, on the specific volume of the blend sample and on the molar fraction itself. The uncertainties associated with the molar fraction were calculated for the studied molar fractions from the following equations:

0.0856 0.0856 0.0857 0.0857 0.0857 0.0857 0.0857 0.0857 0.0858 0.0858 0.0858 0.0858 0.0858 0.0859 0.0859 0.0859 0.0859

2 ⎤ ⎛ νu(m) ⎞2 ⎡⎛ 1⎞ ⎟ ⎢⎜1 + ⎟ + (1 + α)2 ⎥ u(x R600a)2 = ⎜ ⎝ V ⎠ ⎣⎝ α⎠ ⎦

( )x α= MR600a M2−3

(2)

R600a

(1 − x R600a)

(3)

where u(xR600a) is the expanded molar fraction uncertainty of isobutane in mol·mol−1, MR600a is the molar mass of isobutane, M2−3 represents the molar masses of R1234yf and R1234ze(E) and xR600a is the molar fraction of isobutane. From eq 2, the expanded uncertainties with coverage factors k = 2 (95% level of confidence) for the six isobutane molar fractions of R1234yf/ R600a blends and R1234ze(E)/R600a blends ranged from (0.001 to 0.002) mol·mol−1 and from (0.001 to 0.002) mol·mol−1, respectively. The primary steps prior to taking pressure and temperature measurements were (1) allowing the bath temperature to achieve the test temperature, (2) activating a circulating pump

a Standard uncertainties are u(T) = 0.03 K, u(P) = 1 kPa, u(ν) = 0.138 dm3·kg−1, and u(xR600a) = 0.002 mol·mol−1

The uncertainty associated with the specific volume, which is calculated as the ratio of the actual volume of the sample space to the mass of the sample, is dependent on the uncertainties in 3579

DOI: 10.1021/acs.jced.7b00564 J. Chem. Eng. Data 2017, 62, 3577−3584

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The vapor pressures, liquid densities, and vapor phase PvT behaviors of the pure components R1234yf and R1234ze(E) have been previously measured using this apparatus.16−19

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RESULTS AND DISCUSSION Experimental Data. Table 2 and Figure 1 present 96 PνTx vapor phase data values for binary blends of R1234yf/R600a and Table 3 and Figure 2 present 102 PνTx vapor phase data values for binary blends of R1234ze(E)/R600a. The R1234yf/ R600a data were measured for five isochores (0.0751, 0.0944, 0.1280, 0.1666, 0.1701) m3·kg−1 for (303 < T < 383) K for six R600a mole fractions (0.234, 0.400, 0.472, 0.606, 0.772, 0.850) mol·mol−1, and the R1234ze(E)/R600a data were measured for four isochores (0.0852, 0.0894, 0.1006, 0.1064) m3·kg−1 for (303 < T < 383) K for six R600a mole fractions (0.290, 0.428, 0.516, 0.612, 0.685, 0.755) mol·mol−1. Ideal Gas Model. As a first step, the experimental data were fitted using the Ideal Gas Law. The resulting fits do not wellrepresent the experimental data. The mean relative deviation

Figure 3. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between Helmholtz free energy EoS for R1234yf21 and R600a22 coupled with a modified van der Waals one-fluid linear mixing model23 with optimized constants Kt = 1.03 and Kν = 1.39 and the data of Table 2 (Pexp): +, xR600a = 0.234 and ν = 0.0941 m3·kg−1; ▲, xR600a = 0.400 and ν = 0.0944 m3·kg−1; ●, xR600a = 0.472 and ν = 0.1701 m3·kg−1; ○, xR600a = 0.606 and ν = 0.1666 m3·kg−1; ×, x600a = 0.772 and ν = 0.1280 m3·kg−1; △, xR600a = 0.850 and ν = 0.0751 m3·kg−1.

⎛ n ΔP ⎜⎜∑ i = ⎝ i = 1 Pi

Pcalc, i − Pexp, i ⎞ ⎟⎟ Pexp, i ⎠

n

∑ i=1

and the mean absolute relative deviation ⎛ n ΔP i ⎜∑ = ⎜ P i ⎝ i=1

Pcalc, i − Pexp, i ⎞ ⎟ ⎟ Pexp, i ⎠

n

∑ i=1

between the Ideal Gas Law (Pcalc) and experimental data for blends of R1234yf/R600a (Table 2; Pexp) are (6.32)% and (6.32)%, respectively; whereas, the mean relative deviations and the mean absolute relative deviations between the Ideal Gas Law (Pcalc) and experimental data for blends of R1234ze(E)/ R600a (Table 3; Pexp) are (7.41)% and (7.41)%, respectively. The ideal gas model was included to show the behavior of the simplest model, and thus demonstrate its inability to adequately model the experimental data. Fundamental Helmholtz Free Energy Equation of State. Figure 3 presents relative deviations between the REFPROP20 Helmholtz free energy (FEQ) EoS for R1234yf21 and R600a22 coupled with a modified van der Waals one-fluid linear mixing model23 with constants Kt = 1.03 and Kν = 1.39 and experimental data for blends of R1234yf/R600a (Table 2), for which the constants were determined by minimizing the mean absolute relative deviation. The resulting mean relative deviation and the mean absolute relative deviation are 0.064% and 0.649%, respectively. Figure 4 presents similar results for blends of R1234ze(E)/R600a (Table 3), where the FEQ EoS for R1234ze(E)24 is from REFPROP.20 The optimized constants for the modified van der Waals one-fluid linear mixing model23 are Kt = 0.97 and Kν = 1.39. The resulting mean

Figure 4. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between Helmholtz free energy EoS for R1234ze(E)24 and R600a22 coupled with a modified van der Waals one-fluid linear mixing model23 with optimized constants Kt = 0.97 and Kν = 1.39 and the data of Table 2 (Pexp): ○, xR600a = 0.290 and ν = 0.0897 m3·kg−1; +, xR600a = 0.428 and ν = 0.0846 m3·kg−1; ●, xR600a = 0.516 and ν = 0.1064 m3·kg−1; ▲, xR600a = 0.612 and ν = 0.0892 m3·kg−1; ×, xR600a = 0.685 and ν = 0.1006 m3·kg−1; △, xR600a = 0.775 and ν = 0.0858 m3·kg−1.

for approximately 15 min, and (3) allowing the test sample to stabilize for approximately 20 min. Once a measurement had been taken, the bath temperature was adjusted to the next desired test temperature and the procedure was repeated.

Table 4. Binary Interaction Parameters (k12) for One-Fluid Mixing Model Coupled with Peng−Robinson Equation of State R1234yf/R600a

R1234ze(E)/R600a

xR600a

ν/m3·kg−1

k12 PR1

k12 PR2

xR600a

ν/m3·kg−1

k12 PR1

k12 PR2

0.234 0.400 0.472 0.606 0.772 0.850

0.0941 0.0944 0.1701 0.1666 0.1280 0.0752

−0.3161 −0.3161 −0.3161 −0.3161 −0.3161 −0.3161

−0.8675 −0.5122 0.0659 −0.2504 0.0463 −0.3790

0.290 0.428 0.516 0.612 0.685 0.775

0.0897 0.0846 0.1064 0.0892 0.1006 0.0858

−0.2215 −0.2215 −0.2215 −0.2215 −0.2215 −0.2215

−0.2387 −0.1298 −0.1810 −0.4081 −0.1242 −0.2473

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relative deviation and the mean absolute relative deviation are (0.070)% and (0.338)%, respectively. Peng−Robinson Equation of State. The experimental data for the two blends were fitted using a Peng−Robinson (PR) EoS25 coupled with a one-fluid linear van der Waals mixing model.26 The first model (PR1) consists of the binary interaction parameter (k12) having been determined by minimizing

the mean absolute relative deviation of the entire data set; whereas, the second model (PR2) consists of the binary interaction parameters (k12) having been determined by minimizing the mean absolute relative deviations for each isochore. Table 4 provides the resulting binary interaction parameters for both models for both blends. Figure 5 presents relative deviations between the second model (PR2) and the experimental data for blends of R1234yf/R600a (Table 2). The resulting mean relative deviation and mean absolute relative deviation are (−0.022)% and (0.101)%, respectively. Figure 6 presents similar results for blends of R1234ze(E)/R600a (Table 3). The resulting mean relative deviation and mean absolute relative deviation are (−0.017)% and (0.053)%, respectively. Virial Equation of State. The data of Tables 2 and 3 were fitted to a truncated Virial EoS described by the following equation: P=

⎞ B blend C RT ⎛ ⎜1 + ⎟ + blend 2 ν ⎝ ν ν ⎠

(4) −1

−1

where P is in kPa, R is in kJ·kmol ·K , ν and Bblend are in m3·kmol−1, and Cblend is in m6·kmol−2. Following our earlier work,4 the constants Bblend and Cblend were assumed to have the functional forms given by

Figure 5. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between P-R EoS (Pcalc) for R1234yf/R600a coupled with a van der Waals one-fluid linear mixing model25 with binary interaction parameters optimized (Table 4) for each isochore (PR2) and the data of Table 2 (Pexp): +, xR600a = 0.234 and ν = 0.0941 m3·kg−1; ▲, xR600a = 0.400 and ν = 0.0944 m3·kg−1; ●, xR600a = 0.472 and ν = 0.1701 m3·kg−1; ○, xR600a = 0.606 and ν = 0.1666 m3·kg−1; ×, x600a = 0.772 and ν = 0.1280 m3·kg−1; △, xR600a = 0.850 and ν = 0.0751 m3·kg−1.

B blend = B1 ln T +

B2 + B3x R600a 2 + B4 x R600a + B5 T

(5)

C blend = C1 ln T +

C2 + C3x R600a 2 + C4x R600a + C5 T

(6)

where T is in K and x is in kmol·kmol−1. Table 5 provides the constants B1...B5 and C1...C5, which were determined by minimizing the mean absolute relative deviations between eq 4 and the data of Tables 2 and 3. Figure 7 displays Bblend and Cblend for blends of R1234yf/R600a (Figure 7a,b) and for blends of R1234ze(E)/R600a (Figure 7c,d). Figures 8 and 9 show relative deviations between the virial EoS and experimental data for blends of R1234yf/R600a (Table 2) and for blends of R1234ze(E)/R600a (Table 3), respectively. The mean relative deviations and the mean absolute relative deviations for blends of R1234yf/R600a are (−0.003)% and (0.037)%, respectively, and for blends of R1234ze(E)/R600a they are (0.001)% and (0.016)%, respectively. Summary of Model Results. Tables 6 and 7 present summary results for various fitting models. Table 6 shows percentages of measured data falling within specified bounds for blends of R1234yf/R600a and for blends of R1234ze(E)/ R600a. The models PR2 and virial perform the best among the models, with 100% of the PR2 data having relative deviations within ±0.5% and 100% of the virial data having relative deviations within ±0.25% for both blends. The ideal gas model does not well-represent any of the data, while the other two models predict 95% of the data for both blends within ±1.5%,

Figure 6. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between P-R EoS (Pcalc) for R1234ze(E)/R600a coupled with a van der Waals one-fluid linear mixing model25 with binary interaction parameters optimized (Table 4) for each isochore (PR2) and the data of Table 3 (Pexp): ○, xR600a = 0.290 and ν = 0.0897 m3·kg−1; +, xR600a = 0.428 and ν = 0.0846 m3·kg−1; ●, xR600a = 0.516 and ν = 0.1064 m3·kg−1; ▲, xR600a = 0.612 and ν = 0.0892 m3·kg−1; ×, xR600a = 0.685 and ν = 0.1006 m3·kg−1; △, xR600a = 0.775 and ν = 0.0858 m3·kg−1.

Table 5. Coefficients for Bblend [eq 5] and for Cblend [eq 6] B1

B2

B3

B4

B5

R1234yf/R600a R1234ze(E)/R600a

−0.81425 1.2044 C1

−490.49 142.11 C2

8.1658 −9.9051 C3

−11.116 14.035 C4

9.3180 −12.407 C5

R1234yf/R600a R1234ze(E)/R600a

−2.5532 −16.436

−1429.7 −5865.6

−82.357 99.518

3581

112.44 −133.96

−17.479 154.43

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Figure 7. (a) Bblend [eq 5] for binary blends of R1234yf/R600a as a function of mole fraction of R600a and temperature (each symbol represents one of the 17 measured isotherms ranging from 303.2 to 383.2 K). (b) Cblend [eq 6] for binary blends of R1234yf/R600a as a function of mole fraction of R600a and temperature (each symbol represents one of the 17 measured isotherms ranging from 303.2 to 383.2 K). (c) Bblend [eq 5] for binary blends of R1234ze(E)/R600a as a function of mole fraction of R600a and temperature (each symbol represents one of the 17 measured isotherms ranging from 303.2 to 383.2 K). (d) Cblend [eq 6] for binary blends of R1234ze(E)/R600a as a function of mole fraction of R600a and temperature (each symbol represents one of the 17 measured isotherms ranging from 303.2 to 383.2 K).

Figure 8. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between virial EoS (Pcalc) of eq 4 and the data of Table 2 (Pexp) for binary blends of R1234yf/R600a: +, xR600a = 0.234 and ν = 0.0941 m3·kg−1; ▲, xR600a = 0.400 and ν = 0.0944 m3·kg−1; ●, xR600a = 0.472 and ν = 0.1701 m3·kg−1; ○, xR600a = 0.606 and ν = 0.1666 m3·kg−1; ×, x600a = 0.772 and ν = 0.1280 m3·kg−1; △, xR600a = 0.850 and ν = 0.0751 m3·kg−1.

Figure 9. Relative deviations (ΔP/P = (Pcalc − Pexp)/Pexp) between virial EoS (Pcalc) of eq 4 and the data of Table 3 (Pexp) for binary blends of R1234ze(E)/R600a: ○, xR600a = 0.290 and ν = 0.0897 m3·kg−1; +, xR600a = 0.428 and ν = 0.0846 m3·kg−1; ●, xR600a = 0.516 and ν = 0.1064 m3·kg−1; ▲, xR600a = 0.612 and ν = 0.0892 m3·kg−1; ×, xR600a = 0.685 and ν = 0.1006 m3·kg−1; △, xR600a = 0.775 and ν = 0.0858 m3·kg−1.

which is acceptable for many engineering calculations. Table 7 shows the mean absolute relative deviations for each of the models for blends of R1234yf/R600a and for blends of R1234ze(E)/R600a. Again, PR2 and virial are the best performers with mean absolute relative deviations for PR2 of

(0.101)% and (0.053)% for blends of R1234yf/R600a and R1234ze(E)/R600a, respectively, and with mean absolute relative deviations for virial of (0.037)% and (0.016)% for blends of R1234yf/R600a and R1234ze(E)/R600a, respectively. 3582

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Table 6. Percentage of Measured Data Falling within Specified Bounds for Binary Blends of R1234yf/R600a and R1234ze(E)/ R600a for Several Equations of Statea R1234yf/R600a

R1234ze(E)/R600a

bounds

ideal gas

PR1

PR2

FEQ

virial

ideal gas

PR1

PR2

FEQ

virial

±0.025% ±0.05% ±0.25% ±0.50% ±1.00% ±1.50% ±2.50%

0.0 0.0 0.0 0.0 0.0 0.0 0.0

2.1 5.2 32.3 36.5 82.3 100.0 100.0

22.9 42.7 86.5 100.0 100.0 100.0 100.0

3.2 4.2 22.9 41.7 75.0 96.9 100.0

35.4 76.0 100.0 100.0 100.0 100.0 100.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

10.8 17.6 57.8 83.3 100.0 100.0 100.0

33.3 60.8 97.1 100.0 100.0 100.0 100.0

3.9 9.8 49.0 78.4 95.1 100.0 100.0

77.5 97.1 100.0 100.0 100.0 100.0 100.0

a PR1 is the Peng−Robinson EoS with a mean interaction parameter for R1234yf/R600a of −0.316 and for R1234ze(E)/R600a of −0.222, PR2 is the Peng−Robinson EoS with binary interaction parameters optimized for each isochore, FEQ is the fundamental Helmholtz EoS contained in REFPROP,20 and virial is the truncated virial EoS described in eq 4.

Table 7. Mean Absolute Relative Deviations between Models and Measured Data for Blends of R1234yf/R600a and R1234ze(E)/R600aa R1234yf/R600a

R1234ze(E)/R600a

ideal gas

PR1

PR2

FEQ

virial

ideal gas

PR1

PR2

FEQ

virial

6.32

0.601

0.101

0.649

0.037

7.41

0.250

0.053

0.338

0.016

PR1 is the Peng−Robinson EoS with a mean interaction parameter for R1234yf/R600a of −0.316 and for R1234ze(E)/R600a of −0.222, PR2 is the Peng−Robinson EoS with binary interaction parameters optimized for each isochore, FEQ is the fundamental Helmholtz EoS contained in REFPROP,20 and virial is the truncated virial EoS described in eq 4. a

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CONCLUSIONS There is considerable scientific and commercial interest in low global warming potential working fluids for a wide-range of applications. As the number of design constraints continues to increase and become increasingly more stringent, it is becoming more and more difficult to identify single-component solutions to meet all application needs. Therefore, it is becoming increasingly more important to be able to identify blends of working fluids that can be tailored to meet the various imposed design constraints. This paper takes a step in this direction by presenting vapor phase PνTx measurements for two low global warming potential binary blends. The blends consist of a hydrocarbon (isobutane) and one of two unsaturated halocarbon working fluids, both of which have seen considerable commercialization effort expended over the past 15 or so years. Despite the flammability of isobutane, it was selected as one of the components since it can potentially lower cost, increase lubricant solubility, and improve heat exchanger performance.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Tel.: + 001 202 3195247. Fax +001 202 3194499. E-mail: [email protected]. ORCID

J. Steven Brown: 0000-0003-4914-7778 Funding

This work was supported by MIUR of Italy within the framework of PRIN2015 project “Clean Heating and Cooling Technologies for an Energy Efficient Smart Grid”. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Arkema France for donating the R1234yf sample and Honeywell for donating the R1234ze(E) sample. 3583

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