Isothermal Vapor–Liquid Equilibria of the Absorption Working Pairs

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Isothermal Vapor−Liquid Equilibria of the Absorption Working Pairs (R1234yf + NMP, R1234yf + DMETrEG) at Temperatures from 293.15 K to 353.15 K Yibo Fang, Wenjie Guan, Kangli Bao, Yanzhi Wang, Xiaohong Han,* and Guangming Chen Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China ABSTRACT: The vapor−liquid equilibria (VLE) data of R1234yf + NMP and R1234yf + DMETrEG were measured at the temperature range of 293.15−353.15 K in a dual cycle experimental apparatus. The thermodynamic consistency of the VLE data was checked with an area test. The VLE data were correlated by the nonrandom two-liquid model, and the results showed that they had a good agreement. The average relative deviation of pressure for R1234yf + DMETrEG was within 1.37% and its maximum was 3.51%; the average relative deviation of pressure for R1234yf + NMP was within 1.43% and its maximum was 3.65%. The results still showed that there was a large positive deviation between the binary system R1234yf + NMP and Raoul’s law, and the system R1234yf + DMETrEG exhibited a slight positive deviation to the ideal solution.

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INTRODUCTION Under the background of energy saving and environmental protection, the absorption system attracts more and more attention as it can use a heat source (e.g., solar energy, a fossilfueled flame, waste heat from factories, or district heating systems).1,2 In absorption systems, the characteristics of the absorption working pairs (the working fluids are usually called the absorption working pairs, which are usually binary or ternary solutions) are inextricably linked to the performance of the absorption system. It is beneficial for the matched working fluid to improve the cycle performance of the absorption system, increase the cofficients of performance (COP), reduce the circulation ratio, and reduce energy consumption, etc. Therefore, it is of particular importance for the selection and thermodynamical research of the working pairs to improve the performance of the absorption cycle. Among the research, the vapor−liquid equilibria (VLE) characteristic of the working pair is the basis for the performance of the absorption cycle. In the development of the absorption working pairs, there are different types of working pairs, and they can usually be divided into water absorption working pairs, ammonia absorption working pairs, alcohol absorption working pairs, and halogenated hydrocarbon (including chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), and hydrofluorocarbons (HFCs)) absorption working pairs. Among the different kinds of absorption working pairs, as the HFCs absorption working pairs have good thermal performance and environmental performance, and they can be used in a wide range of temperatures in absorption refrigeration, they have attracted more and more attention. The vapor−liquid equilibria of HFCs absorption working pairs (HFCs + organic solvents) have been studied by many © XXXX American Chemical Society

researchers. For example, the experimental data of VLE for 1,1,1,2-tetrafluoroethane (R134a) + N,N-dimethylformamide (DMF), difluoromethane (R32) + DMF, and trifluoromethane (R23) + DMF were meausred by Han et al., and a new mixing rule was proposed for the VLE of the mixtures with the big molecular structure differences.3−5 The VLE of 1,1-difluoroethane (R152a) + DMF, R152a + diethylene glycol dimethyl ether (DMEDEG), R32 + N,N-dimethylacetamide (DMAC), and R32 + DMEDEG at temperatures of 293.15−353.15 K were measured by Li et al.6,7 The VLE of fluoroethane (R161) + DMAC, R161 + N-methyl-2-pyrrolidone (NMP), and R134a + DMAC in the temperature range of 293.15−353.15 K were studied by Jing et al.8 Zhang et al.9 measured the VLE and correlated the data of 1,1,1,3,3-pentafluoropropane (R245fa) + DMAC, 1,1,1,3,3,3-hexafluoropropane (R236fa) + DMAC, and R236fa + DMEDEG in the temperature range of 293.15− 353.15 K, and the negative deviations relative to Raoult’s law for the three working pairs were in the order of R236fa + DMEDEG > R236fa + DMAC > R245fa + DMAC. Meanwhile, there was other literature which focused on related research, and the typical research results of VLE for the HFCs absorption working pairs were summarized in Table 1. Among the other studies, the VLE research on R134a with different absorbents was developed most within a wide temperature range. The working pairs of R161, R32, and R245fa with a variety of absorbents, have been studied well within a wide temperature range, respectively. However, the VLE investigation on the working pairs (2,3,3,3-tetrafluoropropene (R1234yf) + absorbReceived: September 15, 2017 Accepted: March 27, 2018

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DOI: 10.1021/acs.jced.7b00821 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Research Progress of VLE for Working Pairs of HFCs + Absorbents refrigeranta

absorbentb

temp range/K

pressure range/kPa

sources

R134a R134a R134a R134a R134a R134a R134a R134a R134a R134a R134a R134a

DMAC DMEDEG DMEMEG DMETEG DMETrEG DMETrEG DMETrEG DMETrEG DMETrEG DMF DMF HEXG TETG TGDE DMAC DMEDEG DMF DMF DMAC DMEDEG DMETrEG DMF NMP DMF DMAC DMEDEG DMAC DMEDEG DMF NMP DMAC DMEDEG DMF

293.15−353.15 303.30−353.33 283.15−353.15 258.15−298.15 303.30−353.33 283.15−353.15 258.15−298.15 282.55−322.82 268.15−353.15 263.15−363.15 303.30−353.33 268.15−353.15

68.6−2300.4 181.7−2411.3 45−2629 101.33 232.2−2453.0 24.9−2203.3 101.33 276.7−1304.9 90−960 30.1−2715.8 152.5−2605.9 90−960

8 10 11 12 10 13 12 14 16 3 15 16

293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−343.15 293.15−353.15 293.15−353.15 283.15−363.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 283.15−363.15

110.3−1828.9 110.8−2217.4 108.4−2030.0 108.4−2030.0 140.2−2460.3 78.6−2490.5 143.2−2679.4 104.2−2631.5 84.4−2610.5 202.5−3462.2 42.9−739.9 32.1−780.9 24.7−602.9 11.3−640.8 14.7−512.2 19.7−500.5 185.2−5278.0 142.8−4323.0 124.3−2713.1

17 6 17 7 8 18 19 18 8 14 9 9 9 20 21 20 6 6 4

R152a R152a R152a R152a R161 R161 R161 R161 R161 R23 R236fa R236fa R245fa R245fa R245fa R245fa R32 R32 R32

a 1,1,1,2-Tetrafluoroethane (R134a); 1,1-difluoroethane (R152a); fluoroethane (R161); trifluoromethane (R23); 1,1,1,3,3,3-hexafluoropropane (R236fa); 1,1,1,3,3-pentafluoropropane (R245fa); difluoromethane (R32). bN,N-Dimethylacetamide (DMAC); diethylene glycol dimethyl ether (DMEDEG); ethylene glycol dimethyl ether (DMEMEG); triethylene glycol dimethyl ether (DMETrEG); N,N-dimethylformamide (DMF); hexylene glycol (HEXG); N-methyl-2-pyrrolidone (NMP); tetraethylene glycol (TETG); tetraethylene glycol dimethyl ether (TGDE).

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ents) and (dimethylmethane (R290) + absorbents) has rarely been reported. As a very promising alternative refrigerant, R1234yf attracts more and more attention with zero ODP (ozone depletion potential) and a 100-year GWP (global warming potential) lower than 1. The heat transfer performance, saturated vapor pressure, and viscosity of R1234yf have been reported,22−24 but the research on the potential applications in absorption refrigeration systems has not been reported. As absorbents DMETrEG (triethylene glycol dimethyl ether) and NMP have a high boiling point, weak toxicity, and good ability to dissolve many refrigerants, such as R134a, R161, and R32. Therefore, R1234yf + NMP and R1234yf + DMETrEG were considered as potential working pairs to be used in the absorption system. On the basis of these, the experimental study on the VLE of R1234yf + DMETrEG and R1234yf + NMP in the temperature range 293.15−353.15 K needed to be carried out by using a dual-cycle experimental device. The nonrandom two-liquid (NRTL) model was used to correlate the VLE data, and the results were further discussed carefully. This research lays a good foundation for the future application of R1234yf in the absorption system.

EXPERIMENTAL SECTION

Materials. R1234yf was supplied by Zhejiang Lantian Environmental Protection Co., Ltd. (FLTCO) with a minimum purity of 99.5%. DMETrEG and NMP were purchased from Aladdin with a minimum purity of 99.0% and 99.9%, respectively. The basic description of the materials used was shown in Table 2. All samples were used without any further purification. Experimental Apparatus. The VLE data of R1234yf + DMETrEG and R1234yf + NMP were obtained by a dual cycle apparatus. The apparatus consists of the stainless steel equilibrium cell, the thermostatic bath, the temperature and pressure measuring systems and the other parts, as shown in Figure 1. This apparatus is similar to the system published in the literature.3−5,19 A slight difference is that a bypass existed before the liquid phase enters the GC, which is helpful to obtain the best chromatographic peak. The circulation loop with a liquid phase pump (model GAH-T23, PVS.B, USA) and a vapor phase pump (self-designed) is equipped for achieving the phase equilibrium faster. The thermostatic bath temperature is measured by a platinum resistance thermometer (model WZPB-I, Kunming Temperature Instrument Co., Ltd.,

B

DOI: 10.1021/acs.jced.7b00821 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Basic Properties for R1234yf, DMETrEG, and NMP25−27

0.001 K. (2) Thermostat bath temperature fluctuations: it is found through the experimental measurement that the thermostat bath temperature fluctuation is less than 0.01 K/h, so uT,2 = 0.01 K. (3) Error from the digital multimeter resolution, uT,3 = 0.005 K for Keithley 2002 digital multimeter. Therefore, the total temperature measurement uncertainty is 3

uT =

∑ uT2 ,i

= 0.011 K (1)

i=1

Uncertainty of Composition Measurement. Composition measurement uncertainty consists of two parts: (1) measurement accuracy of GC1690 is 0.3%, so ux,1 = 0.003; (2) repeatability error of component measurement, in the measurement process, usually the error among the multiple sampling is within 1%, so ux,2 = 0.01. The total composition measurement uncertainty is 2

ux =

Figure 1. Schematic diagram of the experimental apparatus.

∑ ux2,i

= 0.01 (2)

i=1

China) with a precision of ±0.001 K. The pressure inside the cell is measured by pressure sensor (model PMP4010, Druck, England, pressure range: 0−3.5 MPa) with an accuracy of ±0.04% FS (full scale). Temperatures and pressures are logged by a Keithley 2002 data acquisition/switch unit. The liquid sample is collected via the six-port sampling port. The liquid samples are analyzed by gas chromatograph (GC) equipped with a flame ionization detector (FID) (model GC1690, Hangzhou Kexiao Company, China). Uncertainty Analysis. The uncertainty analysis is similiar to that in our past work,19 and the uncertainties of temperature (T), pressure (p), and composition (x) are given as follows. Uncertainty of Temperature Measurement. Temperature measurement uncertainty consists of the three parts: (1) Error from the platinum resistance thermometer: as the accuracy of WZPB-1 platinum resistance thermometer is 0.001 K, so uT,1 =

Standard Uncertainty of Vapor Pressure. Pressure measurement uncertainty consists of the two parts: (1) Error from the pressure transducer: it can be calculated according to full scale and accuracy of the PMP4010 pressure sensor, up,1 = 1.4 kPa. (2) Error from the digital multimeter resolution: up,2 = 0.002 kPa for Keithley 2002 digital multimeter. The total pressure measurement uncertainty is 2

up =

∑ up2,i i=1

= 1.4 kPa (3)

According to Moffat,28 the standard uncertainty of vapor pressure Up is from the pressure measurement uncertainty up, temperature measurement uncertainty uT, and composistion measurement uncertainty ux. C

DOI: 10.1021/acs.jced.7b00821 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. VLE data of the binary mixture R1234yf (1) + NMP (2) and R1234yf (1) + DMETrEG (2) in the temperature range from 293.15 K to 353.15 K R1234yf (1) + NMP (2)

R1234yf (1) + DMETrEG (2)

T/Ka

x1a

pexp/kPaa

pcal/kPa

γ1,cal

δp/%b

x1a

p/kPaa

pcal/kPa

γ1,cal

δp/%b

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

0.0579 0.1089 0.1542 0.2199 0.3481 0.4917 0.6224 0.7740 0.8332 0.0540 0.1021 0.1434 0.2100 0.3403 0.4693 0.6172 0.7499 0.8240 0.0528 0.0976 0.1325 0.2029 0.3347 0.4557 0.6022 0.7062 0.8175 0.8940 0.0485 0.0896 0.1300 0.1919 0.3073 0.4481 0.5894 0.6861 0.8012 0.8938

82.5 140.6 185.4 247.8 316.6 375.5 435.4 484.3 516.1 102.6 176.5 234.8 317.8 409.8 490.6 572.9 637.8 675.2 124.4 214.9 289.1 396.4 518.3 627.9 726.9 802.8 867.7 924.7 147.5 256.0 348.0 482.7 639.9 785.9 907.0 1000.7 1088.4 1169.2

82.3 141.9 187.4 242.8 323.6 387.0 433.4 485.9 509.2 101.1 176.0 232.1 308.7 420.1 498.5 569.6 630.6 668.2 126.9 217.4 280.1 387.6 536.4 634.7 728.3 790.7 862.3 920.0 147.8 254.7 347.8 470.4 646.1 798.7 916.5 991.5 1085.5 1174.1

2.454 2.244 2.089 1.894 1.589 1.342 1.185 1.066 1.036 2.459 2.258 2.114 1.914 1.601 1.373 1.188 1.080 1.040 2.451 2.263 2.141 1.926 1.608 1.390 1.202 1.109 1.042 1.014 2.459 2.283 2.140 1.950 1.661 1.399 1.214 1.124 1.050 1.014

−0.25 0.93 1.05 −1.98 2.20 3.06 −0.46 0.33 −1.34 −1.49 −0.29 −1.15 −2.85 2.50 1.61 −0.58 −1.13 −1.03 1.96 1.18 −3.10 −2.21 3.51 1.08 0.19 −1.51 −0.61 −0.51 0.24 −0.53 −0.06 −2.54 0.97 1.64 1.05 −0.92 −0.26 0.42

0.0460 0.0888 0.1245 0.1897 0.2921 0.4038 0.5713 0.6829 0.7996 0.8979 0.0412 0.0757 0.1169 0.1731 0.2744 0.3671 0.5496 0.6738 0.7990

171.2 299.0 409.9 576.7 765.6 957.4 1124.4 1238.3 1353.5 1456.3 192.8 341.7 473.2 674.0 909.4 1102.6 1371.7 1507.6 1661.0

174.1 297.6 416.3 579.3 779.9 945.2 1130.5 1240.3 1361.7 1481.7 191.5 331.6 482.1 661.7 919.2 1101.4 1369.2 1522.5 1686.2

2.459 2.294 2.149 1.949 1.690 1.469 1.233 1.126 1.050 1.013 2.472 2.315 2.166 1.989 1.725 1.531 1.256 1.132 1.050

1.70 −0.45 1.56 0.45 1.87 −1.27 0.54 0.16 0.60 1.75 −0.65 −2.93 1.88 −1.83 1.08 −0.11 −0.19 0.99 1.52

0.1099 0.2044 0.3016 0.4079 0.4830 0.5774 0.6860 0.7786 0.8742 0.1025 0.1936 0.2820 0.3516 0.4715 0.5593 0.6760 0.7689 0.8668 0.0997 0.1808 0.2627 0.3468 0.4648 0.5513 0.6278 0.6633 0.7417 0.8602 0.0925 0.1711 0.2529 0.3243 0.4357 0.5404 0.6015 0.6470 0.7133 0.7321 0.8544 0.0846 0.1620 0.2408 0.3125 0.4076 0.5050 0.6023 0.6847 0.7221 0.8489 0.0806 0.1537 0.2246 0.2982 0.3852 0.4813 0.5413 0.6664 0.7135

78.5 139.7 198.6 260.0 311.0 369.5 428.8 485.9 536.6 99.3 173.8 247.2 311.6 397.0 480.3 556.3 633.4 699.7 121.0 213.6 306.6 389.2 500.1 606.1 659.0 708.6 793.2 891.8 143.6 255.4 370.1 473.8 603.9 747.1 812.5 883.5 946.1 978.3 1124.8 166.1 299.5 436.9 562.3 714.9 898.0 1009.4 1151.6 1210.1 1400.3 190.2 343.5 504.9 652.4 829.5 1052.5 1120.3 1396.4 1459.6

78.8 142.3 203.8 267.0 309.7 361.4 419.1 468.2 519.7 96.6 177.5 251.9 308.0 399.5 463.9 546.4 612.0 682.1 120.8 214.1 304.1 392.2 509.5 592.4 663.0 696.1 768.5 878.8 141.6 256.5 371.2 467.5 610.5 739.6 812.5 867.0 944.7 967.4 1114.4 160.8 302.2 440.8 562.5 717.6 871.5 1018.2 1142.7 1199.0 1392.6 186.9 350.8 505.0 659.9 837.0 1027.5 1140.4 1379.0 1466.2

1.238 1.199 1.161 1.122 1.096 1.068 1.040 1.021 1.007 1.238 1.201 1.166 1.140 1.099 1.072 1.042 1.022 1.008 1.235 1.203 1.171 1.140 1.100 1.074 1.053 1.044 1.027 1.009 1.235 1.204 1.173 1.147 1.109 1.076 1.059 1.048 1.033 1.029 1.009 1.235 1.205 1.175 1.149 1.117 1.086 1.058 1.039 1.031 1.010 1.233 1.206 1.179 1.153 1.123 1.092 1.074 1.042 1.032

0.35 1.86 2.58 2.68 −0.43 −2.19 −2.27 −3.65 −3.13 −2.80 2.14 1.90 −1.18 0.63 −3.42 −1.78 −3.38 −2.53 −0.17 0.21 −0.82 0.77 1.87 −2.26 0.62 −1.76 −3.12 −1.46 −1.39 0.43 0.29 −1.34 1.08 −1.01 −0.01 −1.86 −0.15 −1.11 −0.93 −3.17 0.92 0.89 0.05 0.37 −2.95 0.87 −0.77 −0.92 −0.55 −1.78 2.11 0.03 1.15 0.90 −2.38 1.79 −1.24 0.45

D

DOI: 10.1021/acs.jced.7b00821 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. continued R1234yf (1) + NMP (2)

R1234yf (1) + DMETrEG (2)

T/Ka

x1a

pexp/kPaa

pcal/kPa

γ1,cal

δp/%b

x1a

p/kPaa

pcal/kPa

γ1,cal

δp/%b

343.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

0.8911 0.0398 0.0720 0.1082 0.1710 0.2473 0.3492 0.5070 0.6582 0.8086 0.8900

1786.7 219.3 385.8 538.6 774.9 1039.0 1248.9 1545.1 1797.0 2060.9 2202.6

1827.7 221.5 379.6 541.9 787.7 1035.3 1292.7 1593.8 1833.2 2078.1 2238.7

1.015 2.467 2.319 2.186 1.988 1.784 1.562 1.308 1.145 1.045 1.015

2.29 1.03 −1.60 0.63 1.66 −0.35 3.50 3.15 2.02 0.88 1.64

0.8472 0.0750 0.1409 0.2163 0.2776 0.3688 0.4652 0.5136 0.6497 0.6935 0.8485

1719.9 210.0 383.9 574.9 744.5 942.7 1175.2 1292.9 1662.5 1747.6 2087.3

1723.7 208.4 386.9 585.7 743.8 970.7 1204.4 1319.6 1642.8 1744.2 2114.1

1.010 1.232 1.208 1.180 1.158 1.127 1.096 1.082 1.046 1.036 1.010

0.22 −0.77 0.79 1.88 −0.09 2.98 2.48 2.07 −1.18 −0.20 1.28

Standard uncertainties u were u(T) = 0.011 K, u(x1) = 0.003, ur(p) = 0.039 (for R1234yf + DMETrEG) or 0.049 (for R1234yf + NMP). bδp(%) = (pcal − pexp)/pexp × 100. a

3

Up =

⎛ ∂p ⎞2 uX ⎟ ⎝ ∂Xi i⎠

where γ1 was the activity coefficient of component 1, x1 and x2 were the mole fractions of the component 1 and 2, respectively, and G12 and G21 were defined as

∑⎜ i=1

(4)

where Xi includes all the variables in the derivation of vapor pressure, that is, the temperature T, mass fraction x, and vapor pressure p. Eventually, the relative standard uncertainty of vapor pressure Up/p is ≤ 0.049 for the system of R1234yf + NMP, and Up/p is ≤ 0.039 for system of R1234yf + DMETrEG. The Experimental Procedure. The experimental procedure can be described as follows: (1) After the clean and leaktest, the experimental system was evacuated with a vacuum pump, and then a desired amount of absorbent was charged into equilibrium cell. (2) The thermostatic bath was heated to 333.15 K, and the cell was evacuated with the vacuum pump again to keep the system in the high vacuum state. (3) The thermostatic bath was cooled down to 283.15 K, and a desired amout of R1234yf was charged into the cell. (4) The vapor pump and liquid pump were turned on and the bath temperature was set to the experimental value. (5) The temperatures and pressures were recorded, and the samples of liquid phase were measured by GC. (6) The temperature was reset, and Step (4) was repeated until the required temperatures were set completely. (7) The ratio of the refrigerant to the absorbent was changed and the process was repeated from Step (1).

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(6)

G21 = exp( −ατ21)

(7)

where α, τ12, and τ21 were the equation parameters of eqs 5 to 7. To consider the temperature dependence of the parameters τ12 and τ21 in the NRTL model, the following formulas, each containing two parameters, were adopted by eqs 8 to 9 τ12 = A 0 + A1 ln T

(8)

τ21 = B0 + B1 ln T

(9)

where A0, A1, B1, B2 were the nondimensional parameters, and T was the temperature, K. The values of the parameters α (in eqs 6 and 7), A0, A1, B1, B2 (in eqs 8 and 9) should be obtained by fitting the experimental data. A computer program was developed applying the least-squares method to minimize the objective function (OBF), which can be expressed as 1 OBF = N

⎛ p − p ⎞2 exp cal ⎟ ∑ ⎜⎜ pexp ⎟⎠ i=1 ⎝ N

(10)

where N was the number of experimental points, pexp was the experimental pressure, kPa, and pcal was the calculated pressure, kPa. Thermodynamic Consistency Tests. The thermodynamic consistency test of the experimental data was carried out by the area test. Generally, it was considered that the experimental data passed thermodynamic consistency tests when D < 0.02.30 D can be calculated by eq 11.

RESULTS AND DISCUSSION

Experimental Data. Following the above-described experimental procedure, the VLE data for the working pairs R1234yf + NMP and R1234yf + DMETrEG at temperature between 293.15 K and 353.15 K were obtained. They were listed in Table 3. Analysis Method. In this work, the boiling point of the refrigerant was much lower than that of the absorbents, thus there was almost free of absorbents in the vapor phase. The NRTL model29 was used to correlate the experimental data. It could be expressed as follows 2 ⎡ ⎤ τ21G21 τ12G12 ⎥ ln γ1 = x 22⎢ + 2 2 (x 2 + x1G12) ⎦ ⎣ (x1 + x 2G21)

G12 = exp( −ατ12)

1

∫0 ln(γ1/γ2) dx1 S+ − S− = D= + 1 S + S− ∫0 |ln(γ1/γ2)| dx1

(11)

where S+ was the area above the ln(γ1/γ2) = 0 line and underneath the curve on the plot of ln(γ1/γ2) versus x1, and S− was the area underneath the ln(γ1/γ2) = 0 line and above the curve on the plot of ln(γ1/γ2) versus x1. It was found that the D values of R1234yf + NMP and R1234yf + DMETrEG both were