Isothermal Vapor–Liquid Equilibrium of the Ternary Mixture of 1,1,1,2

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Isothermal Vapor−Liquid Equilibrium of the Ternary Mixture of 1,1,1,2-Tetrafluoroethane + 2,3,3,3-Tetrafluoroprop-1-ene + Dimethyl Ether at Temperatures from 253.15 K to 323.15 K Xiaohong Han,*,† Zanjun Gao,† Jun Lei,‡ Bo Yang,‡ Yang Zhao,‡ and Guangming Chen† †

Institute of Refrigeration and Cryogenics, Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Zhejiang University, Hangzhou 310027, P. R. China ‡ Zhejiang Quhua Fluorine Chemistry Co., Ltd., Quzhou 324004, P. R. China ABSTRACT: Isothermal vapor−liquid equilibrium (VLE) data for the ternary mixture of 1,1,1,2-tetrafluoroethane (HFC-134a) + 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + dimethyl ether (DME) were measured at temperatures from 253.15 K to 323.15 K using a recirculation apparatus. The experimental data were correlated by the PR (Peng−Robinson) equation of state with the LCVM (linear combination of Vidal and Michelsen) mixing rule and the NRTL (nonrandom two liquid) model. The average absolute vapor composition deviations are 0.007 (for HFC-134a) and 0.012 (for HFO-1234yf), and the largest absolute deviation of the vapor compositions are 0.022 (for HFC-134a) and 0.031 (for HFO-1234yf); the average relative pressure deviation is within 1.2 % and its largest relative pressure deviation is 3.7 %. The correlation results are in good agreement with the experiment results. With the regressed parameters obtained by the ternary mixture (HFC-134a + HFO-1234yf + DME), the VLE of two binary mixtures (HFC-134a + HFO-1234yf and HFC-134a + DME) were predicted by the PR + LCVM + NRTL model. The predicted results were compared with the experimental data of other researchers. The results showed that the regressed parameters obtained by the ternary mixture (HFC-134a + HFO-1234yf + DME) in this work could be used to predict VLE behavior of the binary mixtures. The results also indicated that there is no azeotrope in the ternary mixture.

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INTRODUCTION HFCs (hydrofluorocarbons) and their mixtures are the most promising alternative refrigerants of HCFCs (hydrochlorofluorocarbons) and CFCs (chlorofluorocarbon). Owing to the high GWP (global warming potential) of the active HFCs, especially the refrigerants which have a GWP above 150 are banned in automobile air conditioning in the European Union.1 Thus, it is important to find a new refrigerant which has zero ODP (ozone depression potential) and low GWP. As a new promising refrigerant, 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf, ODP = 0, GWP = 4)2 has drawn much attention in the refrigeration and air-condition industry.3−5 In recent years, many thermophysical properties of HFO-1234yf have been determined, such as p−V−T behavior,6,7 thermal conductivity,8 saturated pressure,7,9,10 specific heat capacities,11,12 densities,11,13−15 and viscosities.16 However, because of the small latent heat and mild flammability of HFO-1234yf, it is believed that the mixtures of HFO-1234yf and other refrigerants may be a good choice. Therefore, many mixtures of HFO-1234yf combined with HFCs or natural refrigerants have been studied, such as HFO-1234yf +HC-600a,17 HFO-1234yf + HFC-227ea,18 HFO-1234yf + HFC-143a,19 HFO-1234yf + HFC-152a20 and HFO-1234yf + CO2,21 HFO-1234yf + HFC-32, HFO-1234yf + HFC-125, HFO-1234yf + HFC-134a.22 © XXXX American Chemical Society

Though HFO-1234yf has excellent environmental properties, as compared to HFC-134a (1,1,1,2-tetrafluoroethane, ODP = 0, GWP = 1430),23 the coefficient of performance and capacity of HFO-1234yf were slightly lower than those of HFC-134a in mobile air-conditioners.4,24,25 DME (dimethyl ether, ODP = 0, GWP = 1)23 has the similar performance to those of HFC134a,26 and the latent heat of DME is much higher than that of HFO-1234yf. Therefore, when HFO-1234yf is mixed with DME, it is possible to lower the mass flow rates, the pressure drops in heat exchangers and connection pipes, and there is a further increase in the coefficients of performance. However, HFO1234yf and DME are somewhat flammable in use. To prevent the flammability of HFO-1234yf and DME, HFC-134a is chosen as a component of the mixed refrigerant. Thus, the vapor−liquid equilibrium behavior for the mixed refrigerant (HFC-134a + HFO-1234yf + DME) is necessary to be evaluated before the actual application. On the basis of the above description, isothermal vapor−liquid equilibrium data of the ternary mixture (HFC-134a + HFO-1234yf + DME) were measured at T = (253.15−323.15) K with a recirculation apparatus in this work. Received: December 26, 2014 Accepted: June 16, 2015

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DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Physical Characteristics of HFC-134a, HFO-1234yf, and DME4,23,32 refrigerants physical characteristics chemical formula CAS no. boiling point at 101.3 kPa molecular weight lower flammability level ODP (R11 = 1) GWP (CO2 = 1, 100 yrs) critical temp critical pressure acentric factor total latent heat at 0 °C

units

°C %

K MPa kJ/kg

HFC-134a

HFO-1234yf

DME

CH2FCF3 811-97-2 −26.07 102.03 nonflammable 0 1430 374.21 4.0593 0.32684 163.29

CH2CFCF3 754-12-1 −29.45 114.04 6.2 0 4 367.85 3.3822 0.276 198.60

CH3OCH3 115-10-6 −24.78 46.068 3.3 0 1 400.38 5.3368 0.196 435.01

Figure 1. Flow diagram of the apparatus: 1, thermostatic bath; 2, equilibrium cell; 3, vapor circulation pump; 4, liquid circulation pump; 5, vapor sample valve; 6, liquid sample valve; 7, gas chromatograph; 8, computer; 9, digital multimeter; 10, pressure sensor; 11, vacuum pump; 12, thermometer; 13, heater; 14, thermometer; 15, stirrer; 16, evaporator 17, refrigeration system; 18, temperature controller.

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by online. The sampling injection volume is about 20 μL for the vapor phase and 5 μL for the liquid phase. The cell is put in a thermostatic bath which is equipped with a blender. The temperature controller is used to control the temperature of the system by adjusting the heating capacity of the heater. In this experiment, the temperature fluctuation is less than ± 5 mK/30 min. The equilibrium temperature is measured by a 4-wired platinum resistance thermometer (WZPB-I, China) with an accuracy of ± 10 mK. The platinum resistance thermometer is placed at same height of the cell. The pressure of the system is measured by a pressure transducer (PMP4010, 0 to 3.5 MPa, 0.04 % F.S.). The pressure transducer was calibrated by the oilpiston-type dead-weight pressure gauge before the experiments. All the data are collected by a Keithley 2002 data acquisition/ switch unit. In consideration of the uncertainties from the platinum resistance thermometer, pressure transducer, and the digital multimeter, the whole standard temperature uncertainty for the system is less than 10 mK, and the whole standard pressure uncertainty for the system is less than 1.4 kPa. The concentration of the components is measured by a gas chromatography (GC 1690, China), which is equipped with a flame ionization detector (FID). The GC is calibrated with pure components of the known purity and with mixtures of the known composition that are available gravimetrically. Considering the margin of error and reproducibility of GC, the standard uncertainty for both the liquid and vapor phases is 0.003 in mole fraction. The chromatographic column used is TM-PLOT Q (40 μm, 30 m × 0.53 mm i.d.).

EXPERIMENTAL SECTION

Samples. HFC-134a, HFO-1234yf, and DME were provided by Zhejiang Quhua Fluorine Chemistry Co., Ltd. with a minimum mass fraction purity of 99.96 %, 99.99 %, and 99.5 %, respectively; the detailed information on these refrigerants is shown in Table 1. No further purification was done on these chemicals before use. Experimental Apparatus. In this investigation, vapor− liquid equilibrium data (p−T−x−y) were obtained by an experimental apparatus with a dual recirculating still. A brief description of the experimental setup is given in Figure 1, similar to the works published in the literature.27,28 A stainless steel cylinder which is equipped with two sight glasses at both ends is used as the equilibrium cell. The volume of the equilibrium cell is about 90 mL. The equilibrium cell was immersed in an 18 L stainless thermostatic bath insulated with polyurethane foams. In the middle situation of the thermostatic bath, there are two observed windows which are fixed. Thus, when the equilibrium cell is put in the corresponding situations to the two windows of the thermostatic bath, the samples in the equilibrium cell are observed clearly. A fabricated in-house gas phase circulation pump is used to recirculate the vapor from the top of the cell to the bottom. The liquid phase is recirculated by a liquid pump (GAH-T23, PVS, B, MicroPump) from the bottom to the top of the cell. A vapor (liquid) six-way valve is equipped between the outlet of the vapor (liquid) pump and the cell, and the valve is connected to a gas chromatograph (GC). By controlling the sixway valve, the vapor/liquid sample can be injected into the GC B

DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimental and Calculated Results by the PR + LCVM + NRTL Models for the Mixture (HFC-134a (1) + HFO-1234yf (2) + DME (3))

a

T/Ka

p/kPaa

pcal/kPa

100((p − pcal)/p)

x1a

x2a

y1a

y2a

y1,cal

y2,cal

y1 − y1,cal

y2 − y2,cal

253.15 253.15 253.15 253.15 253.15 263.15 263.15 263.15 263.15 263.15 273.15 273.15 273.15 273.15 273.15 283.15 283.15 283.15 283.15 283.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15

167.3 151.9 149.1 166.5 152.5 237.6 217.5 212.3 236.5 220.0 328.1 305.4 297.7 330.2 309.9 447.5 420.6 409.8 449.8 426.8 598.7 568.4 551.6 582.0 575.8 772.5 742.0 730.4 761.9 747.9 966.3 1015.6 1042.7 954.7 928.6 992.7 967.6 1301.9 1230.3 1276.2

166.0 151.9 143.6 164.2 157.1 238.3 217.9 206.2 235.3 224.2 334.7 302.2 290.9 329.4 313.7 441.2 425.2 409.4 438.7 430.1 592.3 564.9 545.2 586.7 572.6 776.7 738.5 715.3 770.7 750.8 947.7 1024.7 1024.7 954.0 921.0 1016.0 987.3 1303.9 1218.2 1299.7

0.7 0.0 3.7 1.4 −3.0 −0.3 −0.2 2.9 0.5 −1.9 −2.0 1.0 2.3 0.3 −1.2 1.4 −1.1 0.1 2.5 −0.8 1.1 0.6 1.2 −0.8 0.6 −0.5 0.5 2.1 −1.2 −0.4 1.9 −0.9 1.7 0.1 0.8 −2.3 −2.0 −0.2 1.0 −1.8

0.0655 0.3503 0.3322 0.0811 0.0997 0.0647 0.3539 0.3352 0.0816 0.0996 0.0641 0.3559 0.3350 0.0773 0.0927 0.0641 0.3559 0.3369 0.0715 0.0918 0.0648 0.3589 0.3403 0.0700 0.0923 0.0621 0.3635 0.3514 0.0713 0.1016 0.3039 0.0610 0.2036 0.3636 0.3696 0.0709 0.0995 0.2082 0.3668 0.0797

0.8217 0.2795 0.1932 0.7374 0.5616 0.8277 0.2850 0.1927 0.7447 0.5629 0.8288 0.2814 0.1960 0.7522 0.5699 0.8295 0.2892 0.1982 0.7562 0.5795 0.8336 0.2953 0.2032 0.7635 0.5851 0.8326 0.2969 0.2057 0.7762 0.6000 0.3138 0.8426 0.6036 0.2885 0.2178 0.7832 0.6166 0.6006 0.2975 0.7907

0.0694 0.3530 0.3273 0.0846 0.0961 0.0694 0.3582 0.3345 0.0845 0.0973 0.0706 0.3601 0.3409 0.0899 0.0905 0.0696 0.3617 0.3447 0.0756 0.0917 0.0678 0.3625 0.3509 0.0733 0.0931 0.0697 0.3517 0.3564 0.0838 0.1043 0.2995 0.0726 0.2207 0.3567 0.3672 0.0814 0.1045 0.2216 0.3678 0.0890

0.8496 0.3608 0.2640 0.7881 0.6240 0.8474 0.3520 0.2582 0.7852 0.6227 0.8488 0.3474 0.2545 0.7758 0.6356 0.8548 0.3401 0.2514 0.7888 0.6368 0.8577 0.3391 0.2509 0.7993 0.6376 0.8460 0.3515 0.2425 0.7973 0.6370 0.3707 0.8537 0.6493 0.3625 0.2729 0.8010 0.6670 0.6298 0.3568 0.8057

0.0540 0.3649 0.3454 0.0753 0.1028 0.0536 0.3727 0.3506 0.0760 0.1027 0.0655 0.3655 0.3485 0.0788 0.0943 0.0768 0.3647 0.3454 0.0829 0.0997 0.0759 0.3657 0.3474 0.0802 0.1005 0.0692 0.3740 0.3612 0.0786 0.1085 0.3077 0.0744 0.2210 0.3699 0.3742 0.0837 0.1080 0.2291 0.3786 0.0960

0.8362 0.3566 0.2667 0.7737 0.6317 0.8460 0.3517 0.2551 0.7815 0.6293 0.8489 0.3329 0.2411 0.7853 0.6253 0.8257 0.3369 0.2445 0.7608 0.6058 0.8349 0.3387 0.2442 0.7732 0.6124 0.8400 0.3334 0.2396 0.7891 0.6271 0.3730 0.8440 0.6266 0.3485 0.2766 0.7923 0.6468 0.6229 0.3492 0.7991

0.015 −0.012 −0.018 0.009 −0.007 0.016 −0.015 −0.016 0.009 −0.005 0.005 −0.005 −0.008 0.011 −0.004 −0.007 −0.003 −0.001 −0.007 −0.008 −0.008 −0.003 0.004 −0.007 −0.007 0.001 −0.022 −0.005 0.005 −0.004 −0.008 −0.002 0.000 −0.013 −0.007 −0.002 −0.004 −0.008 −0.011 −0.007

0.013 0.004 −0.003 0.014 −0.008 0.001 0.000 0.003 0.004 −0.007 0.000 0.015 0.013 −0.010 0.010 0.029 0.003 0.007 0.028 0.031 0.023 0.000 0.007 0.026 0.025 0.006 0.018 0.003 0.008 0.010 −0.002 0.010 0.023 0.014 −0.004 0.009 0.020 0.007 0.008 0.007

Standard uncertainties u are u(T) = 0.01K, u (p) = 1.4 kPa, u(x1) = 0.003, u(y1) = 0.003, u(y2) = 0.003.

Table 3. Correlated Results of Vapor−Liquid Equilibrium Using the PR + LCVM + NRTL Model for (HFC-134a (1) + HFO1234yf (2) + DME (3)) from T = (253.15 to 323.15) K T/Ka

Np

τ12

τ13

τ21

τ23

τ31

τ32

δpb

δy1c

δy2d

253.15 263.15 273.15 283.15 293.15 303.15 313.15 323.15

5 5 5 5 5 5 7 3

9.4024 9.0580 0.1298 1.1674 0.7461 0.6817 0.5029 0.1840

0.2215 0.3425 17.0365 −0.4953 −0.4713 0.1641 −0.4803 −0.2792

0.0259 −0.2058 0.0093 −0.4255 −0.3653 −0.3315 0.0017 0.2862

13.8317 14.5951 17.0494 −0.0091 0.0223 0.0459 0.0594 −0.1473

−0.2063 −0.3990 −0.2300 0.4593 0.3475 −0.3944 −0.0766 −0.3105

−0.0867 −0.1456 −0.0212 0.1889 0.1255 −0.0510 −0.0611 0.0149

1.8 1.2 1.4 1.2 0.9 0.9 1.4 1.0

0.012 0.012 0.007 0.005 0.002 0.007 0.005 0.008

0.009 0.003 0.010 0.020 0.017 0.009 0.012 0.007

c Standard uncertainties u are u(T) = 0.01 K. bδp is relative pressure average deviation, and it is defined as δp = (1/Np)ΣiNp = 1|((p − pcal)/p)|. δy1 is d Np the average deviation of the 1st component and it is defined as δy1 = (1/Np)Σi = 1|y1 − y1,cal|. δy2 is the average deviation of the 2nd component and it is defined as δy2 = (1/Np)Σi Np = 1|y2 − y2,cal|. a

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DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Experimental Procedure. The experimental procedure can be described as follows: (1) The cell was evacuated to remove all the inert gases, and HFC-134a was charged into the cell and evacuated again to clean the cell. (2) The thermostatic bath was cooled down to about 5 °C, the desired amount of DME, HFO1234yf, and HFC-134a were put into the cell in order. (3) Set the temperature by the temperature controller to the experimental temperature. The vapor and liquid in the equilibrium cell were circulated continuously by vapor-phase circulating pump and liquid phase circulating pump to ensure the homogeneous mixing. When the temperature fluctuation is less than 5 mK/30 min, the pressure fluctuation is within 300 Pa/30 min, the equilibrium state was established. It was believed that 2 h or more was sufficient to establish a thermal equilibrium state between the cell and thermostatic bath. (4) Record the temperature and pressure at each equilibrium state, and the samples of liquid and vapor phase were online measured by GC, respectively. The composition for vapor and liquid phases of the sample in the equilibrium cell was measured three times at each equilibrium state; the average values for vapor and liquid compositions were obtained, respectively. (5) Change the experimental temperature, and repeat from step 3. (6) Change concentrations of the refrigerants, then repeat from step 1.

Figure 4. VLE data of HFC-134a (1) + DME (2) at 293.18 K and 303.17 K. Experimental data are from the literature.33 A solid line was predicted by PR + LCVM + NRTL (The parameters are obtained from the ternary mixture HFC-134a (1) + HFO-1234yf (2) + DME (3)).

from (253.15 to 323.15) K. The experimental results are given in Table 2. Homemade software was used to correlate the experimental VLE data. The used model is the combination of PR (Peng−Robinson equation of state),29 LCVM (linear combination of Vidal and Michelsen mixing rules),30 and NRTL (nonrandom two liquid model).31 The PR EoS used here can be expressed as follows:

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EXPERIMENTAL RESULTS AND DISCUSSION The isothermal VLE data of the ternary mixture HFC-134a + HFO-1234yf + DME were measured in the temperature range

RT a − V−b V (V + b) + b(V − b)

p=

a = 0.45724α

(1)

R2Tc2 pc

(2)

α = (1 + (0.37464 + 1.54226ω − 0.26992ω 2) 2

(1 − (T /Tc)0.5 ))

b = 0.07780

(3)

RTc pc

(4)

where p is the pressure; V is the molar volume; T is the absolute temperature; pc is the critical pressure; Tc is the critical temperature; ω is the acentric factor; R is the general gas constant; and a and b are equation of state dependent parameters, respectively. The parameters of HFC-134a, HFO-1234yf, and DME are from REFPROP 9.032 and shown in Table 1. The LCVM model is expressed as

Figure 2. Absolute deviations of vapor mole fraction for the ternary mixture HFC-134a (1) + HFO-1234yf (2) + DME (3).

E,M ⎛ λ am 1 − λ ⎞g =⎜ + ⎟ bmRT AMHV1 ⎠ RT ⎝ AHV

+

bm =

∑ xibi i

1−λ AMHV1

⎛ bm ⎞ ⎟+ ⎝ bi ⎠

∑ xi ln⎜ i

∑ xi i

ai biRT

(5)

(6)

where g is Gibbs free energy and λ = 0.36, AHV = −0.623, AMHV1 = −0.52 for PR equation of state, superscripts E, HV, and MHV1, are the excess property, Huron−Vidal mixing rule, and the first modified Huron−Vidal mixing rule, respectively. x stands for liquid mole fraction, subscript i is the ith component. The NRTL model for mixture can be represented as

Figure 3. Relative deviations of vapor pressure for the ternary mixture HFC-134a (1) + HFO-1234yf (2) + DME (3).

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DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Predicted Results and Experimental Results33 of VLE Data of HFC-134a (1) + DME (2) at 293.18 K and 303.17 K

a

Ta/K

pa/kPa

pcal/kPa

100((p − pcal)/p)

x1a

y1a

y1,cal

y1 − y1,cal

293.18 293.18 293.18 293.18 293.18 293.18 293.18 293.18 293.18 293.18 293.18

502.0 496.5 494.9 491.2 489.3 488.1 487.6 495.2 507.6 525.7 548.4

0.0559 0.0949 0.1206 0.1704 0.2205 0.2666 0.3261 0.4531 0.5863 0.7712 0.8951

671.4 665.1 659.6 658.3 677.1 699.0 719.9 737.6 746.2 750.9

−0.5 −1.4 −1.6 −2.3 −2.7 −3.1 −3.4 −2.6 −1.6 −1.4 −0.3 1.9 −0.3 −0.8 −1.3 −1.8 −1.0 −0.3 0.2 0.7 0.6 0.7 0.7

0.0677 0.1176 0.1373 0.1844 0.2324 0.2744 0.3246 0.4349 0.5499 0.7301 0.8683

303.17 303.17 303.17 303.17 303.17 303.17 303.17 303.17 303.17 303.17

504.5 503.4 503.0 502.6 502.6 503.0 504.0 508.3 515.6 532.8 550.2 AARD % 673.2 670.3 667.9 669.9 683.7 700.8 718.2 732.6 742.1 745.9 AARD %

0.0574 0.1162 0.1912 0.3822 0.5610 0.6868 0.7845 0.8531 0.8950 0.9109

0.0498 0.1088 0.1796 0.3954 0.5989 0.7292 0.8204 0.8814 0.9161 0.9293

0.0646 0.1143 0.1344 0.1832 0.2341 0.2793 0.3340 0.4550 0.5797 0.7645 0.8922 AAD 0.0535 0.1108 0.1873 0.3942 0.5918 0.7246 0.8205 0.8828 0.9186 0.9317 AAD

−0.009 −0.019 −0.014 −0.013 −0.014 −0.013 −0.008 −0.002 0.007 0.007 0.003 0.010 −0.004 −0.002 −0.008 0.001 0.007 0.005 0.000 −0.001 −0.003 −0.002 0.003

Standard uncertainties u are u (T) = 0.02 K, u (p) = 0.1 kPa, u (x1) = 0.01, u (y1) = 0.01.33

Figure 5. VLE data of HFC-134a (1) + HFO-1234yf (2) at 273.15 K and 293.15 K. Experimental data are from the literature.22 The solid line was predicted by PR+LCVM+NRTL (The parameters are obtained from the ternary mixture HFC-134a (1) + HFO-1234yf (2) + DME (3)).

gE = RT

∑ xi ∑ i

j

xj exp( −αjiτji) ∑k xk exp( −αkiτki)

Figure 6. VLE of HFC-134a (1) + HFO-1234yf (2) + DME (3) with the PR + LCVM + NRTL model at 273.15 K.

τji (7)

Table 5. Predicted Results and Experimental Results22 of VLE Data of HFC-134a (1) + HFO-1234yf (2) at 273.15 K and 293.15 K

a

Ta/K

pa/kPa

pcal/kPa

100((p − pcal)/p)

x1a

y1a

y1,cal

y1 − y1,cal

273.15 273.15 273.15

311.7 323.0 321.8

0.7460 0.2831 0.5195

599.4 610.2 612.6

2.7 2.4 3.2 2.8 −1.8 −2.2 −2.5 2.1

0.7703 0.2714 0.5278

293.15 293.15 293.15

303.3 315.2 311.4 AARD % 610.0 623.4 627.7 AARD %

0.7703 0.2714 0.5278

0.7343 0.2793 0.5098

0.7464 0.2680 0.5092 AAD 0.7374 0.2902 0.5169 AAD

0.000 0.015 0.010 0.009 −0.003 −0.011 −0.007 0.007

Standard uncertainties u are u (T) = 0.015 K, u (p) = 0.7 kPa, u (x1) = 0.01, u (y1) = 0.001.22 E

DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Tables 2 showed the correlated results obtained by PR + LCVM + NRTL. The values of the parameters τ12, τ13, τ21, τ23, τ31, and τ32 are shown in Table 3. From the results in Table 2, the correlated results (with PR+LCVM+NRTL) agreed well with the experimental data within a big range of temperatures and pressures. The average absolute vapor composition deviations are within 0.007 (for HFC-134a), 0.012 (for HFO-1234yf), and its largest absolute deviations of the vapor composition are 0.022 (for HFC-134a) and 0.031 (for HFO-1234yf); the average relative pressure deviation is within 1.2 %, and its largest relative pressure deviation is 3.7 %, also seen in Figures 2 and3. Using the parameters which were regressed by the experimental data of the ternary mixture of HFC-134a + HFO1234yf + DME, the VLE data of two binary mixtures (HFC-134a + DME at 293.18 K and 303.17 K and HFC-134a + HFO-1234yf at 273.15 K and 293.15 K) were predicted. The predicted results and experimental results33 for the VLE of HFC-134a (1) + DME (2) are shown in Figure 4 and Table 4. The average absolute relative pressure deviations are 1.9 % (at 293.18 K) and 0.7 % (at 303.17 K), the average absolute vapor composition deviations are 0.010 (at 293.18 K) and 0.003 (at 303.17 K). All the results show that the PR + LCVM + NRTL model with the parameters obtained by the ternary mixture (HFC-134a + HFO-1234yf + DME) in this paper has a good prediction for the binary mixture HFC-134a + DME. Figure 5 and Table 5 show the predicted results and the experimental results22 for VLE of HFC-134a (1) + HFO-1234yf (2). The average absolute relative pressure deviations are 2.8 % (at 273.15 K) and 2.1 % (at 293.15 K); the average absolute vapor composition deviations are 0.009 (at 273.15 K) and 0.007 (at 293.15 K). All the results show that the PR + LCVM + NRTL model with the parameters obtained by the ternary mixture (HFC-134a + HFO-1234yf + DME) have a good prediction for the binary mixture HFC-134a + HFO-1234yf. Figures 6 to 8 give VLE of the ternary mixture HFC-134a (1) + HFO-1234yf (2) + DME (3) at 273.15 K, 293.15 K, and 313.15 K. From Figures 4 to 8, all the results imply that there is no azeotrope in the ternary mixture of HFC-134a (1) + HFO1234yf (2) + DME (3).

Figure 7. VLE of HFC-134a (1) + HFO-1234yf (2) + DME (3) with the PR + LCVM +NRTL model at 293.15 K.

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Figure 8. VLE of HFC-134a (1) + HFO-1234yf (2) + DME (3) with the PR + LCVM +NRTL model at 313.15 K.

ln γi =

∑j τji exp( −αjiτji)xj ∑k xk exp( −αkiτki)

⎡

+

∑⎢ j

CONCLUSION In this paper, the isothermal vapor−liquid equilibrium data of the ternary mixture (HFC-134a + HFO-1234yf + DME) were measured at T = (253.15−323.15) K. The experimental data were correlated by the PR + LCVM + NRTL model, and the regressed parameters were given in the paper. The VLE data of the two binary mixtures (HFC-134a + DME, HFC-134a + HFO1234yf) were predicted by the PR + LCVM + NRTL model with the regressed parameters. The experimental data of HFC-134a + DME and HFC-134a + HFO-1234yf were compared with predicted results. All results show that there is good agreement between the calculated results and experimental data, and no azeotrope exists in the ternary mixture (HFC-134a + HFO1234yf + DME).

xj exp( −αijτij)

⎢⎣ ∑k xk exp( −αkjτkj)

⎛ ∑ x τ exp( −αkjτkj) ⎞⎤ ⎜⎜τij − k k kj ⎟⎥ ∑k xk exp( −αkjτkj) ⎟⎠⎥⎦ ⎝

(8)

where τii = 0, αij = αji. αij, τij, and τji are the adjustable parameters, γ is the activity coefficient. In this work, αij is taken equal to 0.3. The method used to minimize the objective function (OF) is simplex algorithm, and the OF can be expressed as

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⎛ p − p ⎞2 exp cal ⎟ 2 OF = ∑ ⎜⎜ ⎟ + (y1,exp − y1,cal )i p i=1 ⎝ ⎠i exp Np

+ (y2,exp −

y2,cal )i2

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +86 571 8795 3944. Fax: +86 571 8795 3944.

(9)

Funding

where Np stands for the number of the experimental data, y stands for the vapor mole fraction, subscripts exp and cal are experimental results and calculated results, respectively.

This work has been supported by the Nation Natural Science Foundation of China (No.51176166). F

DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to the technicians from Zhejiang Quhua Fluorine Chemistry Co., Ltd., for dealing with the composition measurement in the experimental study.

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DOI: 10.1021/je501167d J. Chem. Eng. Data XXXX, XXX, XXX−XXX