Experimental Study on the Saturated Liquid Density and Bubble Point

Article pubs.acs.org/jced

Experimental Study on the Saturated Liquid Density and Bubble Point Pressure for R1234ze(E) + R290 Haiyang Zhang,†,‡ Quan Zhong,†,‡ Maoqiong Gong,*,† Huiya Li,*,† Xueqiang Dong,† Jun Shen,† and Jianfeng Wu† †

Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100039, China

‡

ABSTRACT: Saturated liquid densities and bubble point pressures of trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) + propane (R290) binary mixture were measured at temperatures from (253.141 to 293.284) K and mole fractions of R1234ze(E) from (0.1746 to 0.8803) using a compact single-sinker densimeter. The standard uncertainties were estimated to be less than 5 mK for temperature, 600 Pa for pressure, 0.003 for mole fraction, and 0.01% for density. The experimental saturated liquid densities were reproduced by the VDNS and our modified Rackett density equations, while the experimental bubble point pressures were represented with the Patel−Teja (PT) equation of state. Good agreement between values of calculation and experiment were found for both saturated liquid densities and bubble point pressures. In addition, saturated vapor and liquid densities of azeotropy point at temperatures T = (258.150, 263.150, 273.150 and 283.150) K were determined.

1. INTRODUCTION

In this work, we present saturated liquid densities and bubble point pressures for R1234ze(E) + R290 binary mixture. These measurements were performed by a compact single-sinker densimeter at temperatures from (253.141 to 293.284) K with mole fractions from (0.1746 to 0.8803). The experimental data were correlated with density equations and Patel−Teja (PT) equation of state (EOS).

Ozone depletion and the greenhouse effect are two key environmental problems. According to the Montreal Protocol and the Kyoto Protocol, traditional chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), and hydrofluorocarbons (HFCs) refrigerants have already been or will be replaced by refrigerants with zero ozone depletion potential (ODP) and low global warming potential (GWP), such as hydrocarbons (HCs), ammonia (NH3), carbon dioxide (CO2), and hydrofluoroolefins (HFOs).1 Owing to the better performance relative to the pure refrigerant, mixed refrigerants especially the azeotropic mixtures are considered to be much promising alternative refrigerants.2−8 Reliable vapor−liquid equilibrium (VLE) data and pressure−density−temperature−mole fraction (pρTx) data of mixed refrigerants are essential for evaluating its performance in the refrigeration cycle. Many studies for VLE,9−13 pρTx properties,14−18 bubble point pressure, and saturated liquid density measurements19−23 can be found in the open literature. The azeotropic mixture of R1234ze(E) + R290 is one promising alternative refrigerant, as the flammability of R290 could be reduced by adding R1234ze(E).24 Many thermophysical properties of R1234ze(E) such as vapor pressures,25−29 saturated densities, 25,28,30,31 and pρT or pvT properties25−28,32−36 have been published. The VLE and gaseous pρTx properties of R1234ze(E) + R290 have been measured experimentally36,37 and simulated by COSMO-RS model based on quantum chemistry.38 However, the saturated liquid densities for R1234ze(E) + R290 binary mixture are still absent in the open literature. © 2016 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Material. The experimental sample of R1234ze(E) was supplied by Honeywell, whereas the R290 sample was provided by Beijing AP BAIF Gases Industry Co. Ltd. The suppliers claimed a mass fraction purity of higher than 99.5% for R1234ze(E), and a mole fraction purity of higher than 99.9% for R290. The samples were used without further purification except for being cooled in liquid nitrogen and evacuated by a vacuum pump to remove possible air impurities. Detailed information on the two samples is shown in Table 1. 2.2. Experimental Apparatus and Uncertainty. The experimental apparatus has been described in our previous work,39 and the working principle has been presented in detail in another paper.40 It is only briefly described here. As shown in Figure 1, the densimeter mainly consists of the following parts: magnetic suspension balance, thermostat system, (temperature, pressure, and composition) measuring systems, sample filling system, vacuum and auxiliary systems. Figure 2 is the schematic drawing of the thermostat system around the measuring cell. Received: April 20, 2016 Accepted: July 13, 2016 Published: July 26, 2016 3241

DOI: 10.1021/acs.jced.6b00327 J. Chem. Eng. Data 2016, 61, 3241−3249

Journal of Chemical & Engineering Data

Article

Table 1. Information of the Two Samples Used in the Present Work41 M

Tc

pc

ρc

chemical name

CAS no.

stated purity

g·mol−1

K

MPa

kg·m−3

R1234ze(E)a R290b

29118-24-9 74-98-6

>99.5% >99.9%

114.0416 44.09562

382.51 369.89

3.632c 4.2512

486c 220.48

ω

Zc

0.313 0.1521

0.2680c 0.2765

a

trans-1,3,3,3-Tetrafluoropropene, supplied by Honeywell with a mass fraction purity. bPropane, supplied by Beijing AP BAIF Gases Industry Co. Ltd. with a mole fraction purity. cTaken from ref 30.

Figure 1. Schematic drawing of the whole apparatus based on the single-sinker densimeter: 1. vacuum vessel; 2. thermostat bath; 3. position sensor; 4. 25 Ω platinum resistance thermometer; 5. measuring cell; 6. sinker; 7. permanent magnet; 8. electromagnet; 9. valve; 10. 100 Ω platinum resistance thermometer; 11. heater; 12. thermostat bath; 13. stir impeller; 14. density measuring control system; 15. temperature, pressure, and composition collector; 16. temperature control system; 17. analytical balance; 18. motor; 19. refrigerator; 20. vacuum pump; 21. heat exchanger; 22. liquid accumulator; 23. valve.

ments of R134a + R29018 and R1234ze(E) + R29036 binary mixtures have been performed successfully. The working principle of the densimeter is based on the wellknown Archimedes’ buoyancy principle ρfluid =

mS − W VS(T , p)

(1)

where ms is the true mass of the sinker in vacuum, W is the apparent mass of the sinker when immersing in the fluid and Vs(T, p) is volume of the sinker under the state point (T, p, x1) conditions. The force transmission error was analyzed for the density measurement and the finally computational formula was presented in our previous work.39 The temperature was measured and collected by a 25 Ω standard platinum resistance thermometer (SPRT) and a Guildline 6622A/T series automatic resistance bridge (ARB), respectively. The SPRT and ARB have been calibrated in National Institute of Metrology, P. R. China. The overall standard uncertainty of temperature was estimated to be less than 5 mK. It includes the contributions from Pt25 SPRT, ARB, and temperature during measurement process with values of 4 mK, 0.02 ppm, and less than 3 mK, respectively.

Figure 2. Schematic drawing of the thermostat system around the measuring cell.

The liquid accumulator has been specially designed for measuring VLE. When measuring the saturated liquid density, the sinker and permanent magnet must be submerged completely in the liquid phase by filling up the liquid accumulator partially. The internal volume of the measuring cell, connecting pipe, and liquid accumulator is about 156 mL. About 10% of the volume is occupied by the vapor phase. The densimeter covers a density range from (0 to 2000) kg·m−3 with temperatures from (210 to 300) K and pressures up to 6.0 MPa. Up to now, gaseous36 and saturated31 pρT measurements of pure R290 and pure R1234ze(E), gaseous pρTx measure-

u(T ) =

42 + (2 × 10−8 × T × 103)2 + 32 ≈ 5 mK (2)

The compositions of the liquid phase were analyzed by a Shimadzu GC2014 GC equipped with a thermal conductivity detector (TCD). The GC was calibrated by the mixtures, which were preprepared gravimetrically using a Sartorius Cubis 3242



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Table 2. Saturated Liquid Densities and Bubble Point Pressures for R1234ze(E) (1) + R290 (2)a T

ρs

ps

K

MPa

253.299 256.114 261.139 265.175 269.183 273.204 278.197 283.181

0.25575 0.28336 0.33673 0.38539 0.43747 0.49558 0.57250 0.66514

253.141 258.166 263.164 268.188 273.199 278.239 283.187 288.248 293.276

0.23634 0.28230 0.33350 0.39351 0.45834 0.53275 0.61345 0.70442 0.80723

kg·m

x1b −3

T

ps

ρs

K

MPa

kg·m−3

Method a

x1

Method b 680.21 676.35 670.01 662.22 655.74 648.23 640.01 630.77

0.1746 0.1746 0.1746 0.1746 0.1746 0.1746 0.1746 0.1746

253.446 258.142 263.154 268.170 273.175 278.201 283.201 288.221 293.283

0.21224 0.24999 0.29538 0.34661 0.40586 0.47151 0.54318 0.62367 0.71536

913.53 903.57 892.67 884.02 873.27 862.00 851.76 842.07 831.58

0.4965 0.4965 0.4965 0.4965 0.4965 0.4965 0.4965 0.4965 0.4965

253.441 258.204 263.174 268.196 273.177 278.190 283.186 288.214 293.284

0.15918 0.18998 0.22464 0.26624 0.31314 0.36801 0.42795 0.49752 0.57481

Method b

1067.62 1056.03 1043.42 1030.60 1017.60 1004.24 991.21 977.85 963.78

0.7006 0.7006 0.7006 0.7006 0.7006 0.7006 0.7006 0.7006 0.7006

1197.23 1186.23 1175.37 1162.41 1149.12 1135.29 1121.17 1106.57 1091.31

0.8803 0.8803 0.8803 0.8803 0.8803 0.8803 0.8803 0.8803 0.8803

Method b

a

Standard uncertainties u are u(T) = 5 mK, u(p) = 600 Pa, u(x1) = 0.003, ur(ρ) = 100·u(ρ)/ρ = 0.01%. Note: the uncertainty in density does not n 1 consider the uncertainty in mole fractions. bMole fraction x1 = n ∑i = 1 x1, i , where i is the sequence number of the measurements.

every measuring temperature with the same preprepared sample, that is, every temperature needs once filling of the fluid. The liquid phase compositions were measured at each given temperature, and the average values of the liquid phase compositions at these temperatures were taken as the final composition x1. The measurements with x1 = 0.1746 were performed under method a. In method b, the measuring cell was charged at the first temperature and evacuated at the last temperature, it only needs filling once for all the temperatures. With the same charge the temperatures were changed to measure the saturated properties. After changing the temperature, every 30 min the weighing sequence was started and several repetitions were made to get a uniform mixture. The liquid phase compositions were measured at least at three temperatures T = (253, 273, 293) K. The average of the liquid phase compositions at these temperatures were taken as the final composition x1. Then, the measuring cell was evacuated and charged with a solution with a new composition, and the saturated properties were measured at the various temperatures. The measurements with x1 = (0.4965, 0.7006, 0.8803) were performed under method b. The experimental procedure for mixture is briefly described as follows. Before the measurements were carried out, certain amount gas mixture was preprepared as a sample source. Then several repetitions of evacuating and filling up the measuring cell were done to remove the inert gases. When the setting temperature was reached, the measuring cell at vacuum state was filled up with the preprepared sample until the liquid level was above 80% of the liquid accumulator. If the fluctuations of temperature and pressure are within preset tolerances, the weighing sequence was started and several repetitions were made. Next, the liquid phase compositions of the binary mixture were analyzed by the GC equipped with a TCD. After that, the measuring cell was evacuated and the vacuum state point was measured. The average temperature, pressure, and density values were taken as (T, p, ρ) values of this state point.

MSA5203S-100-DE electronic balance with a resolution of 1 mg. The overall standard uncertainty of mole fraction was estimated to be less than 0.003, and mainly includes the standard uncertainty contributions from calibrated mixture 0.0003, GC 0.0010, and measurement process. During the measurement of “the same composition”, the max fluctuation of mole fraction at different temperatures was within ±0.0040, the calculation was treated as rectangular distribution. Thus, the overall standard uncertainty of mole fraction was obtained u(x1) =

⎛ 0.0040 ⎞2 (0.0003)2 + (0.0010)2 + ⎜ ⎟ ≈ 0.0025 ⎝ 3 ⎠ (3)

The pressure was measured by Mensor CPT6100 digital pressure transducer (DPT), one DPT1 has two ranges of (3.0 and 6.0) MPa, the other DPT2 has two ranges of (5.0 and 10.0) MPa. The DPTs have been calibrated in National Institute of Metrology, P. R. China. The overall standard uncertainty of pressure was estimated to be less than 600 Pa. It includes the contributions from DPT with a stated accuracy of 0.010% FS and fluctuation of pressure within ±800 Pa, the two contributions were treated as rectangular distribution u(p) =

⎛ 0.010% × 5.0 × 106 ⎞2 ⎛ 800 ⎞2 ⎟ ≈ 545 Pa ⎜ ⎟ +⎜ ⎝ 3⎠ 3 ⎝ ⎠ (4)

The overall standard density uncertainty, calculated based on the error transfer formula, was estimated to be less than 0.01%. Because the mole fractions were not contained in eq 139 that was used to determine the mixture densities, the uncertainty in density does not consider the uncertainty in mole fractions. 2.3. Experimental Procedure. In this work, two filling methods of the fluid were carried out denoted as “a” and “b”. In method a, the measuring cell was evacuated and charged at 3243



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Table 3. Pseudocritical Parameters of the Mixture Tcm1a

a

x1

K

0.1746 0.4965 0.7006 0.8803

372.11 376.18 378.75 381.01

ρcm1a kg·m

ρcm2b

Tcm2b

−3

K

273.45 363.29 415.47 458.62

kg·m

372.09 376.16 378.73 381.00

RDTcmc

RDρcmc

Tcmd

ρcmd

%

%

K

kg·m−3

0.005 0.005 0.005 0.003

−0.066 −0.247 −0.398 −0.551

372.10 376.17 378.74 381.01

273.54 363.74 416.30 459.89

−3

273.63 364.19 417.13 461.16

Calculated from eq 12. bCalculated from REFPROP 9.1. cRDX = 100·

X1 − X2 X2

(X = Tcm , ρcm ) dX =

X1 + X2 2

(X = Tcm , ρcm )

Table 4. Optimized Values for H1, H2, and H12 in Equations 5 and 6 eq 5 H1 H2 H12

eq 6

A

B

C

D

E

F

G

2.160566 2.047942 2.807207

5.541981 3.839509 −128.872092

−19.0196 −11.5618 563.574201

22.13374 12.87394 −711.308807

−0.008193 0.005764 −1.230885

−0.009105 0.000235 −0.202053

0.263360 0.279624 −0.322278

vc, ijTc, ij = (vc, iTc, ivc, jTc, j)1/2

3. EXPERIMENTAL RESULTS AND DISCUSSION The accuracy of the VLE measuring system was verified by measuring the vapor pressures and saturated liquid densities of HC290 at temperatures from (253.432 to 293.312) K in our previous work.31 Average absolute relative deviation (AARD) and maximum absolute relative deviations (MARD) between experimental saturated liquid densities and those data calculated from REFPROP 9.141 are 0.03% and 0.04%, respectively. It could be seen that the accuracy of the measuring system are reliable. In this work, saturated liquid densities and bubble point pressures for R1234ze(E) + R290 binary mixture were carried out at temperatures ranging from (253.141 to 293.284) K with mole fractions of R1234ze(E) from (0.1746 to 0.8803). The experimental results are listed in Table 2. 3.1. Correlation for Saturated Liquid Densities. To represent the saturated liquid density accurately, the VNDS equation (http://trc.nist.gov/TDE/Help/TDE103b/) [eq 5] and our modified Rackett equation31 [eq 6] were employed ρr = 1 + Aτ 0.35 + Bτ 2 + Cτ 3 + Dτ 4

ρr = (E + τ F )G−τ

ρr =

2/7

(H = A , B , C , D , E , F , G )

T Tcm

(8)

∑i ∑j xixjvc, ijTc, ij vcm 1 {∑ xivc, i + 3(∑ xivc, i 2/3)(∑ xivc, i1/3)} 4 i i i

(12)

(13)

where xi denotes the mole fraction of the corresponding component i. Saturated liquid densities from literature31,43,44 for R290 and literature25,31 for R1234ze(E) at temperatures from 250 to 295 K were employed to determine the values of H1 and H2, respectively. The present saturated liquid densities were used to obtain the values of H12. Objective function in eq 14 and Levenberg−Marquardt algorithm45 were used to obtain the optimized values of H1, H2, and H12 as presented in Table 4. The relative deviations of literature data for pure substances and the present saturated liquid density data are given in Table 5 and shown in Figures 3−5. From Table 4 and Figures 3 and 4, it can be found that a similar lever of accuracy is reached for pure substances regarding eq 5 or 6 with AARDρ and MARDρ within 0.02% and 0.05%, respectively. As for the mixture, eq 5 represents the experimental data with AARDρ and MARDρ of (0.20 and 0.58) %, whereas eq 6 reproduces the experimental data with AARDρ and MARDρ of (0.15 and 0.46) %. Good agreement was found between the two equations and the experimental data

(7)

where ρ and T are experimental density (kg·m ) and temperature (K), respectively; Tcm and ρcm are critical temperature and critical density of the mixture, respectively. Due to fact that the critical parameters of the mixture are not available in the open literature, in this work, they were evaluated by two methods. The first method is the mixing rules proposed in Hankinson−Thomson saturated density equation42

vcm =

vcm

Hm = x1H1 + x 2H2 + x1x 2H12

(6)

−3

Tcm =

1000 ∑i xiMi

where vc,i, Tc,i, and Mi are critical mole volume (cm3·mol−1), critical temperature (K), and mole mass (g·mol−1) of component i, respectively. REFPROP 9.141 is the second method. Critical parameters of the mixture were calculated under the recommended mixing rules in REFPROP 9.1. The critical parameters calculated from the two methods are shown in Table 3. A good consistency can be found between them, where the relative deviations of critical temperature and critical density are within 0.005% and 0.551%, respectively. In this work, the average values of critical parameters, calculated from the two methods, were used as pseudoexperimental critical parameters of the mixture. The coefficients for the mixture Am, Bm, Cm, Dm, Em, Fm, and Gm are calculated with the following mixing rule:20

(5)

ρ ρcm

τ=1−

ρcm =

(11)

(9)

(10) 3244



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Table 5. Deviations between Experimental Values and That Calculated from Equations 5 and 6 eq 5 pure/mixture (1 + 2) Grebenkov et al.25 Gong et al.31 Total Defibaugh and Moldover41 Glos et al.42 Gong et al.31 Total This work

AARDρ/%

eq 6

MARDρ/%

R1234ze(E) 0.01 0.02 0.01 0.02 0.01 0.02 R290 0.03 0.05 0.02 0.01 0.02 R1234ze(E) 0.20

0.04 0.02 0.05 + R290 0.58

AARDρ/%

MARDρ/%

0.02 0.01 0.01

0.03 0.02 0.03

0.03

0.05

0.02 0.01 0.02

0.04 0.02 0.05

0.15

0.46

Figure 5. Relative density deviations of the present data with values calculated from the two density equations: ■, x1 = 0.1746; ●, x1 = 0.4965; ▲, x1 = 0.7006; ▼, x1 = 0.8803. Symbol interior: solid, eq 5; half right, eq 6.

3.2. Correlation for Bubble Point Pressures. The PT46 EOS was employed to reproduce the bubble point pressures in the present work p=

RT a − v−b v(v + b) + c(v − b)

(15)

where p, v, and T stand for pressure (MPa), mole volume (cm3· mol−1), and temperature (K), respectively; R (8.314472 J· mol−1·K−1)47 is the universal gas constant. For pure components the three parameters a, b, and c are expressed as Figure 3. Relative density deviations of literature R1234ze(E) data with values calculated from the two density equations: ■, Grebenkov et al.;25 ●, Gong et al.31 Symbol interior: solid, eq 5; half right, eq 6.

⎛ R2T 2 ⎞ c ⎟ a = Ωa⎜⎜ ⎟α(Tr) p ⎝ c ⎠

(16)

⎛ RT ⎞ b = Ωb⎜⎜ c ⎟⎟ ⎝ pc ⎠

(17)

⎛ RT ⎞ c = Ωc⎜⎜ c ⎟⎟ ⎝ pc ⎠

(18)

Ωc = 1 − 3ζc

(19)

Ωa = 3ζc 2 + 3(1 − 2ζc)Ωb + Ωb 2 + 1 − 3ζc

(20)

where Ωb is the smallest positive root of the following cubic equation

Figure 4. Relative density deviations of literature R290 data with values calculated from the two density equations: ■, Defibaugh and Moldover;41 ●, Glos et al.;42 ▲, Gong et al.31 Symbol interior: solid, eq 5; half right, eq 6.

⎛ ρ − ρ ⎞2 cal exp ⎟ OF1 = ∑ ⎜⎜ ⎟ ρ ⎠i exp i=1 ⎝ N

Ωb 3 + (2 − 3ζc)Ωb 2 + 3ζc 2 Ωb − ζc 3 = 0

(21)

⎧ ζ = 0.329032 − 0.076799ω T ≤ 0.9 r ⎪ c0 2 ζc = ⎨ + 0.0211947ω , ⎪ ⎩ ζc − 10(ζc0 − Zc)(Tr − 0.9), 0.9 < Tr < 1.0

(22)

α(Tr) = [1 + m(1 − Tr1/2)]2

(23)

m = 0.452413 + 1.30982ω − 0.295937ω 2

(24)

where Tr = T/Tc is the reduced temperature; ω and Zc are acentric factor and critical compressibility factor of pure components, respectively.

(14) 3245



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Based on the vdW one-parameter mixing rules,48 am, bm, and cm of mixture are expressed as follows: am =

∑ ∑ xixjaij i

bm =

(25)

j

∑ xibi

(26)

i

cm =

∑ xici

(27)

i

aij = (aiiajj)1/2 (1 − kij)

(28)

where kij is the binary interaction parameter satisfied kii = kjj = 0 and kji = kij. The binary interaction parameters kij were optimized based on the following objective function using the present pressure data and available VLE data.37,38 AARD and MARD on the property h (p or ρ) are defined as OF2 =

1 N

N

∑

AARDh =

pcal − pexp pexp

i=1

100 N

Figure 6. Relative pressure deviations of the experimental data with values calculated from PT EOS: ■, Dong et al.;37 ●, Qi et al.;38 ▲, present work.

N

∑ i=1

(29)

i

hcal − hexp hexp

(30)

i

⎛ hcal − hexp MARDh = max⎜100 ⎜ hexp ⎝

⎞ ⎟ ⎟ i⎠

(31)

where N is the number of experimental data, and the subscripts cal and exp stand for calculated data and experimental data, respectively. The Levenberg−Marquardt algorithm was used to minimize the object function in eq 29. The binary interaction parameters kij and the relative deviations are summarized in Table 6. The Table 6. kij and Relative Deviations for PT EOS AARDp/% Dong et al.37 Qi et al.38 This work

0.31 0.72 0.43

MARDp/% k12 = 0.1073 1.46 3.26 0.88

AARDρ/%

Figure 7. Relative density deviations of the present data with values calculated from PT EOS: ■, x1 = 0.1746; ●, x1 = 0.4965; ▲, x1 = 0.7006; ▼, x1 = 0.8803.

MARDρ/%

(258.150, 263.150, 273.150, and 283.150) K were obtained as given in Table 7. 1.85

3.16

4. CONCLUSIONS In this work, saturated liquid densities and bubble point pressures of R1234ze(E) + R290 were measured by a compact single-sinker densimeter. The measurements covered temper-

relative deviations of bubble point pressure are plotted in Figure 6. The AARDp and MARDp of Dong et al.37 are 0.31% and 1.46%, respectively. That of of Qi et al.38 are 0.72% and 3.26%, respectively. Present pressures are consistent with that of Dong et al.37 with AARDp and MARDp of 0.43% and 0.88%, respectively. Figure 7 shows the deviations of saturated liquid density between the calculated and the experimental values with AARDρ and MARDρ of 1.85% and 3.16%, respectively. 3.3. Saturated Vapor and Liquid Densities at Azeotropy Point. The azeotropic pressure paz and mole fraction x1az of R1234ze(E) + R290 at temperatures T = (258.150, 263.150, 273.150, and 283.150) K were determined experimentally.37 A virial model was developed to accurately represent the gaseous pρTx properties of R1234ze(E) + R290 binary mixture.36 Extrapolating the virial model and applying the eqs 5 and 6 to the azeotropic states (T, paz, x1az), the saturated vapor and liquid densities at temperatures T =

Table 7. Saturated Vapor and Liquid Densities at Azeotropy Points T

paza

K

MPa

258.150 263.150 273.150 283.150

0.3020 0.3579 0.4924 0.6607

x1aza

ρsvb −3

0.153 0.157 0.164 0.170

ρslc −3

kg·m

kg·m

8.396 9.927 13.639 18.336

658.47 653.53 642.38 629.99

Tcmd

ρcmd

K

kg·m−3

371.83 371.88 371.97 372.05

267.15 268.33 270.41 272.19

a Taken from Dong et al.37 bExtrapolating the virial model36 to (T, paz, x1az) states. cAverage values calculated from eqs 5 and 6. dAverage values calculated from the two methods.

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Tr, reduced temperature u, standard uncertainty ur, relative standard uncertainty v, mole volume, cm3·mol−1 Vs, volume of the sinker, cm3 W, apparent mass of the sinker when immersed in the fluid, g x, liquid mole fraction Zc, critical compressibility factor

atures from (253.141 to 293.284) K, and mole fractions of R1234ze(E) from (0.1746 to 0.8803). The standard uncertainty in temperature, pressure, mole fraction, and density were estimated to be within 5 mK, 600 Pa, 0.003, and 0.01%, respectively. The VDNS and our modified Rackett density equations were used to represent the saturated liquid densities, whereas bubble point pressures were correlated with the PT EOS. In addition, saturated vapor and liquid densities of azeotropy point at temperatures T = (258.150, 263.150, 273.150, and 283.150) K were determined.

■

Greek Letters

α, alpha function in cubic EOS ζc, predicted critical compressibility factor in cubic EOS ρ, density, kg·m−3 τ, inverse reduced temperature ω, acentric factor Ωa, Ωb, Ωc, coefficients for parameters a, b, c

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Funding

Subscripts

This work is financially supported by the National Natural Science Foundation of China (Grant No. 51406219 and 51322605). Notes

The authors declare no competing financial interest.

■

NOMENCLATURE

Abbreviations

AARD, average absolute relative deviation ARB, automatic resistance bridge CFCs, chlorofluorocarbons CO2, carbon dioxide DPT, digital pressure transducer EOS, equation of state GC, gas chromatograph GWP, global warming potential HCs, hydrocarbons HCFCs, hydrochlorofluorocarbons HFCs, hydrofluorocarbons HFOs, hydrofluoroolefins MARD, maximum absolute relative deviation NH3, ammonia ODP, ozone depletion potential OF, objective function pρTx, pressure−density−temperature−mole fraction PT, Patel−Teja R1234ze(E), trans-1,3,3,3-tetrafluoropropene R290, propane SPRT, 25 Ω standard platinum resistance thermometer TCD, thermal conductivity detector VLE, vapor−liquid equilibrium

■

c, critical characteristic cal, calculated data exp, experimental data i, j, component index m, mixture r, relative value s, the sinker or saturation state sl, saturated liquid sv, saturated vapor

REFERENCES

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Symbols

a, b, c, parameters in the cubic equation of state A, B, C, D, parameters in the VNDS equation E, F, G, parameters in the modified Rackett equation h, pressure or density H, parameter kij, binary interaction parameter m, parameter in alpha function ms, true mass of the sinker in vacuum, g n, parameter in alpha function N, number of experimental data p, pressure, MPa R, universal gas constant, 8.314472 J·mol−1·K−1 T, temperature, K Tc, critical temperature, K 3247



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Experimental Study on the Saturated Liquid Density and Bubble Point

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