Vapor Liquid Phase Equilibrium for Azeotropic Isobutane + trans-1,3,3

Feb 6, 2018 - ICCT conference (July 28−August 2, 2002, Rostock, Germany).3. Generally ...... Natural Science Foundation (Grant 3171002), and the You...
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Vapor Liquid Phase Equilibrium for Azeotropic Isobutane + trans-1,3,3,3-Tetrafluoropropene + Trifluoroiodomethane System at Temperatures from 243.150 to 283.150 K Yanxing Zhao,† Quan Zhong,†,‡ Jingzhou Wang,†,‡ Xueqiang Dong,*,† Huiya Li,† Bo Gao,† Jun Shen,†,‡ and Maoqiong Gong*,†,‡ †

Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190, China ‡ University of Chinese Academy of Sciences, Beijing 100039, China ABSTRACT: In this paper, the investigation on the vapor liquid phase equilibrium (VLE) of the ternary system isobutane + trans-1,3,3,3-tetrafluoropropene + trifluoroiodomethane was carried out. The measurements were performed using an apparatus based on the recirculation method at temperatures ranging from 243.150 to 283.150 K. Three models, namely PR-vdW, PR-BM, and PR-MHV2-NRTL, were employed to describe the VLE properties of the system concerned. PR-MHV2-NRTL was the best model, which gave the maximum average absolute pressure relative deviation of 0.85% and the average absolute vapor phase fraction deviation of 0.011. With the regressed binary parameters from ternary VLE data, the binary VLE were well-predicted. A maximum-point ternary azeotropic behavior was exhibited.

1. INTRODUCTION Mixed fluids play a crucial role in the thermodynamic cycle such as refrigerating, heat pump, and organic Rankine cycles, as the pure working medium cannot meet the needs of all. For example, mixing hydrofluorocarbons (HFC) with hydrocarbons (HC) can reach a compromise between the global warming potential (GWP) value and the flammability and may realize a higher refrigerating capacity than its component,1,2 if they form an azeotrope. Therefore, the azeotropic mixtures draw chemical engineers’ special attention, especially in the field of refrigeration. Accurate vapor liquid equilibrium (VLE) data is the key to the reliable calculation of the thermodynamic cycle. The importance of reliable VLE data was stressed during the second IUPAC Workshop (April 9−11, 2001) on refrigerants (Ecole des Mines, Paris, France) and the third IUPAC Workshop held during the ICCT conference (July 28−August 2, 2002, Rostock, Germany).3 Generally, the azeotropic refrigerants consisting of two or three components are practical. Binary azeotropic behavior has been studied experimentally and theoretically, and many successful azeotropic prediction methods have been developed.4−7 Ternary VLE data is usually obtained by the thermodynamic model with the known binary interaction parameters regressed from binary data. The semiempirical model such as Peng− Robinson8 equation with certain mixing rules has been successfully applied in the calculation of ternary VLE. Hou9 developed the group contribution method to describe the VLE of the refrigerant mixtures and reproduced the VLE of a ternary system. Barley10 predicted a saddle point azeotrope with Wilson activity coefficient model, which was confirmed by Aslam11 with © XXXX American Chemical Society

a method establishing the pressure dependency of azeotropic composition. Ternary VLE data also play an important role in estimating the capability of the mixing rules. One of the most stringent tests for a proposed model is its ability to predict ternary behavior when only the binary behavior is known.12,13 According to the previous prediction,14 only a few ternary systems can form azeotropes, and only two of them form maximum azeotropes. The investigated mixture consisting of three environment-friendly refrigerants R600a, R1234ze(E), and R13I1 is one of the two. Therefore, the VLE behavior of R600a + R1234ze(E) + R13I1 system draws our attention. Three isothermal measurements (T = 243.150, 263.150, and 283.150 K) were carried out, and the VLE data were regressed by three phase equilibrium models based on Peng−Robinson (PR) equation with van der Waals (vdW), BM (Boston-Mathia), and modified Huron−Vidal second-order (MHV2) mixing rules.

2. EXPERIMENTAL SECTION 2.1. Materials. R600a, R1234ze(E), and R13I1 were supplied by Nanjing Yuji Tuohao Co. LTD with declared purities (mole fraction) of 0.999, 0.999, and 0.995, respectively. Each sample underwent several cycles of freezing with liquid nitrogen, evacuation, thawing, and analyzing to eliminate the noncondensable gases. The samples were then used with no further purification. The critical temperatures, critical pressures, and Received: November 5, 2017 Accepted: January 19, 2018

A

DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Mole Fraction Purities, Critical Parameters (Tc, pc), and Acentric Factors (ω) for R600a, R1234ze(E), and R13I1 componentsa

CAS no.

Tc/K

pc/MPa

ω

mole fraction puritye

purification method

b

75-28-5 29118-24-9 2314-97-8

407.810 382.513 396.440

3.6290 3.6349 3.9530

0.184 0.313 0.176

0.999 0.999 0.995

freezing with liquid nitrogen, evacuation, and thawing

R600a R1234ze(E)c R13I1d

a Supplied by Nanjing Yuji Tuohao Co., Ltd. bCritical parameters of R600a are taken from ref 15. cCritical parameters of R1234ze(E) are taken from ref 16. dCritical parameters of R13I1 are taken from ref 17. eAnalyzed by GC.

Table 2. Experimental (pexp) and Reference Data (pref) and the Deviation (Δp) between pexp and pref of R600a, R1234ze(E), and R13I1a R600a

R1234ze(E)

R13I1

T/K

pexp

prefc

Δpb/MPa

pexp

prefd

Δpb/MPa

pexp

prefe

Δpb/MPa

243.150 253.150 263.150 273.150 283.150

0.0467 0.0726 0.1087 0.1574 0.2210

0.0466 0.0725 0.1085 0.1570 0.2206

−0.0001 −0.0001 −0.0002 −0.0004 −0.0004

0.0610 0.0970 0.1477 0.2164 0.3083

0.0611 0.0969 0.1474 0.2166 0.3084

0.0001 −0.0001 −0.0003 0.0002 0.0001

0.0717 0.1090 0.1604 0.2282 0.3163

0.0719 0.1092 0.1602 0.2279 0.3156

0.0002 0.0002 −0.0002 0.0003 0.0007

a

Standard uncertainties u are u(T) = 0.005 K and u(p) = 0.0005 MPa. Declared mole fraction purities: R600a (0.999), R1234ze(E) (0.999), and R13I1 (0.995). bΔp = pref − pexp. cRef 15. dRef 16. eRef 17.

Table 3. Experimental VLE data of the R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 Ka T/K

p/MPa

x1

x2

x3

y1

y2

y3

243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 243.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 263.150 283.150 283.150 283.150 283.150 283.150 283.150 283.150 283.150

0.0704 0.0720 0.0732 0.0735 0.0746 0.0731 0.0788 0.0790 0.0793 0.0795 0.0770 0.0745 0.0805 0.0796 0.1556 0.1569 0.1606 0.1631 0.1636 0.1658 0.1635 0.1760 0.1784 0.1794 0.1796 0.1765 0.1717 0.1804 0.1771 0.1702 0.3050 0.3062 0.3116 0.3206 0.3233 0.3257 0.3211 0.3457

0.669 0.571 0.504 0.383 0.246 0.307 0.312 0.277 0.258 0.209 0.135 0.099 0.268 0.465 0.765 0.664 0.569 0.459 0.373 0.254 0.302 0.302 0.270 0.249 0.204 0.128 0.093 0.262 0.465 0.657 0.774 0.664 0.569 0.492 0.373 0.280 0.309 0.309

0.129 0.112 0.096 0.087 0.069 0.055 0.262 0.350 0.400 0.518 0.685 0.792 0.553 0.389 0.166 0.136 0.122 0.104 0.088 0.062 0.050 0.269 0.350 0.403 0.513 0.694 0.778 0.552 0.389 0.252 0.169 0.136 0.122 0.106 0.086 0.067 0.048 0.271

0.202 0.317 0.401 0.530 0.685 0.638 0.426 0.373 0.342 0.273 0.180 0.108 0.180 0.146 0.069 0.200 0.309 0.437 0.539 0.684 0.648 0.429 0.380 0.348 0.283 0.178 0.129 0.186 0.146 0.091 0.057 0.200 0.309 0.402 0.541 0.653 0.643 0.420

0.498 0.442 0.379 0.301 0.248 0.248 0.258 0.244 0.236 0.219 0.186 0.159 0.273 0.399 0.592 0.511 0.442 0.401 0.300 0.238 0.246 0.249 0.233 0.224 0.219 0.164 0.136 0.264 0.393 0.496 0.621 0.523 0.457 0.397 0.308 0.235 0.251 0.254

0.276 0.231 0.192 0.148 0.123 0.092 0.328 0.390 0.423 0.492 0.606 0.683 0.520 0.461 0.329 0.276 0.222 0.198 0.145 0.110 0.083 0.338 0.402 0.437 0.489 0.629 0.701 0.545 0.462 0.399 0.319 0.254 0.213 0.180 0.140 0.104 0.080 0.340

0.227 0.327 0.429 0.551 0.629 0.660 0.413 0.366 0.341 0.289 0.208 0.159 0.207 0.140 0.079 0.213 0.336 0.401 0.555 0.652 0.671 0.413 0.365 0.339 0.292 0.207 0.163 0.191 0.145 0.105 0.060 0.223 0.330 0.423 0.552 0.661 0.669 0.406

B

DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. continued T/K

p/MPa

x1

x2

x3

y1

y2

y3

283.150 283.150 283.150 283.150 283.150 283.150 283.150 283.150 283.150 283.150

0.3535 0.3552 0.3579 0.3539 0.3469 0.3603 0.3503 0.3317 0.3105 0.3208

0.270 0.250 0.206 0.130 0.091 0.260 0.480 0.651 0.626 0.392

0.349 0.401 0.519 0.688 0.781 0.548 0.375 0.248 0.121 0.089

0.381 0.349 0.275 0.182 0.128 0.192 0.145 0.101 0.253 0.519

0.234 0.223 0.198 0.153 0.122 0.253 0.401 0.508 0.491 0.297

0.402 0.441 0.523 0.649 0.726 0.554 0.456 0.389 0.229 0.156

0.364 0.336 0.279 0.198 0.152 0.193 0.143 0.103 0.280 0.547

a

Standard uncertainties u are u(T) = 5 mK and u(p) = 0.0005 MPa and u(x) = u(y) = 0.005. Declared mole fraction purities: R600a (0.999), R1234ze(E) (0.999), and R13I1 (0.995).

Figure 1. Pressure deviation between the calculated values and the experimental values for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at T = 243.150, 263.150, and 283.150 K. The calculated values were calculated by (■): PR-vdW model; (○): PR-BM model; (△): PR-MHV2-NRTL.

Figure 3. Deviation between the calculated values by PR-BM model and the experimental values for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at T = 243.150, 263.150, and 283.150 K. (■): y1cal − y1exp; (○): y2 cal − y2exp; (△): y3 cal − y3exp.

Figure 4. Deviation between the calculated values by PR-MHV2NRTL model and the experimental values for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at T = 243.150, 263.150, and 283.150 K. (■): y1cal − y1exp; (○): y2cal − y2exp; (△): y3cal − y3exp.

Figure 2. Deviation between the calculated values by PR-vdW model and the experimental values for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at T = 243.150, 263.150, and 283.150 K. (■): y1cal − y1exp; (○): y2cal − y2exp; (△): y3cal − y3exp.

than 3 mK. The combined standard uncertainty of the temperature measurement was estimated to be less than 5 mK. The pressures in the cell were measured by a Mensor Series 6000 digital pressure transducer with an uncertainty of 0.00025 MPa. The pressure fluctuation at the equilibrium state was less than 0.0001 MPa. The combined standard uncertainty of the pressure measurement was estimated to be ±0.0005 MPa. The samples were analyzed by a gas chromatograph (Shimadzu GC2014) equipped with a thermal conductivity detector. The uncertainty of the GC was 0.001 in the mole fraction. The column

acentric factors of R600a, R1234ze(E), and R13I1 were taken from refs 15−17 and are provided in Table 1. 2.2. Apparatus. The apparatus for the VLE measurements was based on the recirculation method. The core device of the measurement system is a stainless steel cell with a volume of 150 mL. A detailed description is presented in ref 18. The temperatures were measured by a PT25 platinum resistance thermometer with an uncertainty of 3 mK. The temperature fluctuation in the equilibrium cell at the set point was less C

DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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least three analyses to ensure the deviations within 0.002. The combined standard uncertainty for the sampling was estimated to be within 0.005, considering the calibration and the dispersion of analyses. 2.3. Experimental Procedure. Experiments for the R600a + R1234ze(E) + R13I1 ternary system were performed by the following procedure: filling the mixtures in the cell, setting up the equilibrium temperatures, and measuring at equilibrium state. After the equilibrium cell had been evacuated to under 10 Pa, it was cooled. The three pure components, usually with decreasing boiling point, were introduced into the equilibrium cell. Then, the fluid in the cell reached the desired temperature by the PID procedure adjusting the refrigerator and the electrical heater. After the temperature and pressure fluctuation in the cell was less than ±3 mK and ±100 Pa, respectively, for at least 30 min, the equilibrium state was considered to be established. Then, the vapor and liquid phases were analyzed by gas chromatography three times at least to ensure deviations within 0.002, and the average value was recorded. The procedure was repeated for each temperature and several concentrations. At last, after evacuating the equilibrium cell, the saturation vapor pressures for each component were measured.

Figure 5. Percentage errors of PR-vdW K-values of R600a, R1234ze(E), and R13I1 at T = 243.150, 263.150, and 283.150 K.

3. THERMODYNAMICS MODELS PR-vdW, PR-BM, and PR-MHV2-NRTL models were applied to correlate the experimental data. The Peng−Robinson8 equation of state (PR EoS) is one of the most widely used equations to describe the vapor and liquid phase properties in the engineering field. It has the advantage of both simple form and acceptable precision. All the three models used in this work are based on the Peng−Robinson equation of state, which is expressed in the following form:

Figure 6. Percentage errors of PR-BM K-values of R600a, R1234ze(E), and R13I1 at T = 243.150, 263.150, and 283.150 K.

p=

RT a − v−b v(v + b) + b(v − b)

(1)

, ⎡ R2Tc2 a = 0.457235⎢1 + (0.37464 + 1.54226ω − pc ⎢⎣ ⎛ 0.26992ω )⎜⎜1 − ⎝ 2

T Tc

⎞⎤ ⎟⎟⎥ ⎠⎥⎦

2

(2)

, Figure 7. Percentage errors of PR-MHV2-NRTL K-values of R600a, R1234ze(E) and R13I1 at T = 243.150, 263.150, and 283.150 K.

b = 0.077796

RTc pc

(3)

where p is the pressure in Pa, v the molar volume in m3·mol−1, T the temperature in K, R the gas constant in J·mol−1·K−1, pc and Tc the critical pressure and temperature, and ω the acentric factor of the pure component, respectively. To describe the VLE of the mixture, an appropriate mixing rule must be selected. The mixing rule is actually used to

packing was Porapack Q with a length of three meters, and the column temperature was 313.15 K. The gas chromatograph was calibrated by the gravimetrical method. At least 3 samples with known weight were analyzed to ensure deviations in mole fractions within ±0.0005. Then, a standard curve was drawn with the multipoint calibration method. Each sample underwent at

Table 4. Regressed Binary Interaction Coefficients kij = kji in PR-vdW Model for R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 K 243.150 K

263.150 K

283.150 K

kij

1

2

3

1

2

3

1

2

3

1 2 3

0

0.1056 0

0.0295 0.0491 0

0

0.1068 0

0.0300 0.0487 0

0

0.1073 0

0.0260 0.0473 0

D

DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Regressed Binary Interaction Coefficients kij = kji and lij = lji in PR-BM model for R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 K 243.150 K

263.150 K

283.150 K

ki\lji

1

2

3

1

2

3

1

2

3

1 2 3

0 −0.0047 0.0304

0.1019 0 0.0607

0.0356 0.0540 0

0 0.0181 0.0387

0.1090 0 −0.0192

0.0388 0.0512 0

0 0.0000 −0.0326

0.1070 0 −0.0254

0.0254 0.0476 0

Table 6. Regressed Binary Interaction Coefficients τij in PR-MHV2-NRTL Model for R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 K 243.150 K

263.150 K

283.150 K

τij

1

2

3

1

2

3

1

2

3

1 2 3

0 0.6002 −0.0529

1.3472 0 0.1809

0.5944 0.6411 0

0 0.6193 −0.3729

0.9951 0 0.5604

0.9718 0.1616 0

0 0.4234 1.1929

0.9822 0 0.3071

−0.5864 0.2879 0

Figure 8. Calculated data and the experimental data for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at 243.150 K. Experimental data: liquid phase (■); vapor phase (□). Calculated vapor phase data by PR-vdW( ○ ); PR-BM(△ ) model; PR-MHV2NRTL (▽).

Figure 9. Calculated data and the experimental data for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at 263.150 K. Experimental data: liquid phase (■); vapor phase (□). Calculated vapor phase data by PR-vdW (○); PR-BM (△) model; PR-MHV2NRTL (▽).

establish the relationship between the mixed energy parameters am and ai of its components as well as the covolume parameters bm and bi. vdW.19 vdW one-fluid mixing rule, with only one interaction parameter, may be the simplest mixing rule. The geometric mean rule and the arithmetic mean rule are used for the cross energy parameter and the cross covolume parameter, respectively. Only one adjusting parameter is needed; it is quite effective for mixtures consisting of hydrocarbons and hydrofluorocarbons.20

⎛ ⎞3 1/3 1/3⎟ ⎜ a = ∑ ∑ xixj aiiajj (1 − kij) + ∑ xi⎜∑ xj aiaj l ji ⎟ ⎝ j ⎠ i j i

a=

∑ ∑ xixjaij , aij = i

b=

i

j

Obviously, BM mixing rule equals to vdW mixing rule, if lji equals zero. MHV2.22 On the basis of the thought that the excess Gibbs energies from an EoS and from an activity coefficient model at zero reference pressure are equal, Michelsen22 developed a modified Huron−Vidal second-order (MHV2) mixing rule.

aiiajj (1 − kij) (4)

j

∑ ∑ xixjbij , bij =

(6)

⎛ q1⎜⎜αm − ⎝

bii + bjj 2

(5)

21

BM. To extend the vdW-type mixing rules to more complex systems, Mathias21 proposed a mixing rule by increasing a nonquadratic term to the energy parameter a:

= E

n

⎞

⎛

n

⎠

⎝

i=1

⎞

∑ xiαii⎟⎟ + q2⎜⎜αm2 − ∑ xiαii2⎟⎟ i=1

E Gm,0

RT

+

∑ xi ln( b ) i

bii

⎠

(7) DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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The thermodynamic condition for the VLE is the equality of the fugacities of each component in each phase, which is expressed as

fiV = fiL

(12)

where f Vi andf Li represent the fugacity of the vapor phase and liquid phase, respectively. The binary interaction coefficients in equations 5, 7, and 11 were regressed by the VLE data based on the minimum of the following objective function OF: N

OF =

∑ |pexp − pcal |

(13)

i

where N is the number of the experiment points and pexp and pcal are the experimental and calculated pressures, respectively.

4. RESULTS AND DISCUSSION 4.1. Statured Vapor Pressures. The saturated vapor pressures of the R600a, R1234ze(E), and R13I1 were measured, as shown in Table 2. The maximum deviation between the experimental and reference data is 0.0007 MPa. 4.2. VLE Data Measurements. The experimental data of the R600a + R1234ze(E) + R13I1 system are shown in Table 3. PR-vdW, PR-BM, and PR-MHV2-NRTL models were employed to regress the experimental data, respectively. Figure 1 shows the pressure deviation between the calculated values and the experimental values for the R600a + R1234ze(E) + R13I1 ternary system at T = 243.150, 263.150, and 283.150 K. The deviation distribution calculated by PR-MHV2-NRTL is in a narrower region, from −1.5 to 1.1% in terms of relative pressure. Figures 2−4 show the vapor phase deviation between the experimental values and the calculated values by PR-vdW, PRBM, and PR-MHV2-NRTL models, respectively. Meanwhile, the experimental data and calculated vapor phase compositions by the three models at each temperature are presented in the ternary phase diagram Figures 5−7, respectively. The PR-MHV2NRTL model showed better performance than the PR-vdW and PR-BM models. It is unsurprising because the PR-MHV2-NRTL model has two adjusting parameters, and the MHV222 mixing rule is superior to the simple EoS-type mixing rules for polar systems. According to Mathias,24 analysis of data using relative volatilities enables improved data evaluation. Figures 5−7 give the relative volatilities of R600a, R1234ze(E), and R13I1 in the mixtures with different models. PR-MHV2-NRTL shows the best performance with all deviation between experimental and calculated K-values within ±15%. The binary interaction coefficients in PR-vdW, PR-BM, and PR-MHV2-NRTL at each experimental temperature are shown

Figure 10. Calculated data and the experimental data for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at 283.150 K. Experimental data: liquid phase (■); vapor phase (□). Calculated vapor phase data by PR-vdW (○); PR-BM (△) model; PR-MHV2NRTL (▽). n

b=

∑ xibi

(8)

i=1

αm =

am bmRT

(9)

where n is the number of the components, q1 = −0.478, and q2 = −0.0047. NRTL.23 The excess Gibbs energy was calculated by NRTL activity coefficient model, which is rewritten as xixjτjiGji

GE = RT

∑∑

ln γi =

1 ∂ (nGE) RT ∂ni

i

j

∑k xkGki

, Gji = exp( −αjiτji) (10)

,

=

∑ j

xjτjiGji ∑k xkGki

+

∑ j

⎛ ∑ xτ G ⎞ ⎜⎜τij − n n nj nj ⎟⎟ ∑k xkGkj ⎠ ∑k xkGkj ⎝ xjGij

(11)

where τij (i ≠ j, τij ≠ τji, while i = j, τii = 0) and αij (αij = αji and i = j, τii = 0) are binary interaction parameters. For the simplicity, αij was used as the recommended value of 0.3.

Table 7. AARDpa and AADyb Calculated Using PR-vdW, PR-BM, and PR-MHV2-NRTL Models for the R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 K PR-vdW

a

PR-BM

PR-MHV2-NRTL

T/K

AARDp (%)

AADy1

AADy2

AADy3

AARDp (%)

AADy1

AADy2

AADy3

AARDp (%)

AADy1

AADy2

AADy3

243.150 263.150 283.150

1.03 0.73 0.60

0.014 0.013 0.009

0.007 0.008 0.005

0.017 0.012 0.005

1.03 0.59 0.59

0.010 0.011 0.008

0.007 0.008 0.006

0.014 0.010 0.004

0.85 0.53 0.45

0.005 0.010 0.007

0.005 0.008 0.006

0.011 0.009 0.004

AARDp =

1 N ∑ N i

abs(pexp − pcal )/pexp × 100 bAADy =

1 N ∑ N i

abs(yexp − ycal ) F

DOI: 10.1021/acs.jced.7b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 8. Azeotropic Compositions Calculated by PR-vdW, PR-BM, and PR-MHV2-NRTL Models for the R600a (1) + R1234ze(E) (2) + R13I1 (3) Ternary System at T = 243.150, 263.150, and 283.150 K PR-vdW

PR-BM

PR-MHV2-NRTL

T/K

p/MPa

x1 = y1

x2 = y2

x3 = y3

p/MPa

x1 = y1

x2 = y2

x3 = y3

p/MPa

x1 = y1

x2 = y2

x3 = y3

243.150 263.150 283.150

0.0810 0.1814 0.3597

0.112 0.113 0.119

0.373 0.423 0.476

0.516 0.464 0.405

0.0811 0.1815 0.3598

0.120 0.121 0.127

0.375 0.425 0.479

0.505 0.454 0.395

0.0804 0.1803 0.3598

0.197 0.157 0.135

0.433 0.456 0.496

0.370 0.387 0.369

pressure (AARDp) and the average absolute deviation of vapor phase mole fraction (AADy) for the ternary system are reported in Table 7. As the experimental vapor phase data are not used in the regression, a comparison of the experimental vapor phase values with those predicted by the model represents a measure of thermodynamics consistency.25 The results show that the VLE measurements for the R600a + R1234ze(E) + R13I1 system meet the thermodynamic consistency test, which demonstrated that the PR−vdW, PR-BM, and PR-MHV2-NRTL models are all suitable to describe this ternary system, although the latter is better than the former two. 4.3. Azeotrope. The azeotropic behavior was found and then confirmed by the thermodynamics models. The necessary but not sufficient condition was given by deriving the Gibbs− Duhem equation at the azeotropic point,26 which can be defined as ⎛ ∂p ⎞ ⎜ ⎟ =0 ⎝ ∂xi ⎠T , x

(14)

j

Figure 11. Azeotropic point for the R600a (1) + R1234ze(E) (2) + R13I1 (3) ternary system at 263.150 K. Experimental data (■); calculated data by PR-vdW (○); PR-BM (△); PR-MHV2-NRTL (▽).

. For a ternary system, the second order partial derivative composes the Hessen matrix, which gives as ∂ 2p D2p(x1 , x 2) =

∂x12

∂ 2p ∂x1x 2

∂ 2p ∂ 2p ∂x 2x1 ∂x 22

(15)

The pressure will have extreme values if the matrix norm det(D2p(x1,x2)) > 0, and if ∂2p/∂x2i < 0, (i = 1, 2), the pressure has a maximum point; otherwise, the pressure has a minimum point. If det(D2p(x1,x2)) < 0, the pressure has a saddle point, and if det(D2p(x1,x2)) = 0, the stagnated pressure cannot be verified only by second order partial derivative. The azeotropic points calculated by PR-vdW, PR-BM, and PR-MHV2-NRTL models are shown in Table 8, and a maximum-point azeotropic behavior was exhibited. Figure 11 shows the azeotropic point for the R600a + R1234ze(E) + R13I1 ternary system at 263.150 K. Different models give similar calculated data, while there are major deviations between the predicted azeotropic points and the experimental data. The dew point pressures and bubble point pressures were plotted in the ternary phase diagram, as shown in Figure 12, which shows an obvious maximum-point azeotropic behavior. Figure 13 shows ternary phase diagram near the azeotropic point. It is worth noting that there is a broad nearly flat region near the azeotropic point, namely nearazeotropic region, as shown in Figure 12. That leads to a major difference when different models or different interaction parameters were applied to obtain the azeotropic points. 4.4. Estimation of Binary System. The VLE for the binary systems, including R600a + R1234ze(E), R600a + R13I1, and R1234ze(E) + R13I1 systems, were predicted using the interaction

Figure 12. Ternary vapor liquid phase equilibrium diagram of the R600a (1) + R1234ze(E) (2) + R13I1 (3) system at T = 283.150 K. The VLE data were calculated using the PR-vdW model.

in Tables 4−6, respectively, and Figures 8−10. The kij values in PR-vdW and PR-BM are similar, which on the one hand suggests PR-BM may have no big improvement compared to PR-vdW for this ternary system, although it needs one more adjusting parameter, lji. The average absolute relative deviation of G

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Figure 15. VLE data of R600a + R13I1 binary system at T = 263.150 and 283.150 K. Experimental data are from literature.28 The solid lines () were predicted using the PR-vdW model; the dashed lines (---) were predicted using the PR-BM model, and the dotted lines (···) were predicted using the PR-MHV2-NRTL model. All of the binary parameters were taken from Tables 4−6.

Figure 13. Ternary vapor liquid phase equilibrium diagram of the R600a (1) + R1234ze(E) (2) + R13I1 (3) system at T = 283.150 K near the azeotropic point. The VLE data were calculated using the PR-vdW model.

coefficients obtained from ternary VLE data correlation. Good agreements were found between the predicted values and the experimental data from literature, as shown in Figures 14−16

Figure 16. VLE data of R1234ze(E) + R13I1 binary system at T = 258.150, 268.150, and 278.150 K. Experimental data are from literature.29 The solid lines () were predicted using the PR-vdW model; the dashed lines (---) were predicted using the PR-BM model, and the dotted lines (···) were predicted using the PR-MHV2-NRTL model. All of the binary parameters were taken from Tables 4−6.

to describe the VLE properties of this system. PR-MHV2-NRTL was the best model, which gave the maximum AARDp of 0.85% and ARDy of 0.011. With the regressed binary parameters from ternary VLE data, the binary VLE were well-predicted. A maximum-point ternary azeotropic behavior was exhibited, and the broad near-azeotropic region leads to a major difference of the calculated azeotropic points between PR-MHV2-NRTL and PR-vdW/PR-BM.

Figure 14. VLE data of R600a + R1234ze(E) binary system at T = 258.150, 268.150, 278.150, and 288.150 K. Experimental data are from literature.27 The solid lines () were predicted using the PR-vdW model; the dashed lines (---) were predicted using the PR-BM model, and the dotted lines (···) were predicted using the PR-MHV2-NRTL model. All of the binary parameters were taken from Tables 4−6.

■

AUTHOR INFORMATION

Corresponding Authors

*Tel./Fax: +86 10 82543736; E-mail: [email protected]. *Tel./Fax: +86 10 82543728; E-mail: [email protected].

which, to some extent, demonstrates the reliability of the ternary VLE data. And once again, the PR-MHV2-NRTL model showed superiority compared to PR-vdW and PR-BM.

ORCID

Yanxing Zhao: 0000-0001-7491-900X Xueqiang Dong: 0000-0003-1957-4007

5. CONCLUSIONS In this paper, an investigation on the vapor liquid equilibrium for the ternary mixture R600a + R1234ze(E) + R13I1 at temperatures from 243.150 to 283.150 K was conducted. Three models, namely PR-vdW, PR-BM, and PR-MHV2-NRTL, were employed

Funding

This work is financially supported by the National Key R&D Program of China (Grant 2016YFE0204200), the National Natural Sciences Foundation of China (Grant 51376188), Beijing H

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Natural Science Foundation (Grant 3171002), and the Youth Innovation Promotion Association CAS (Grant 2015021). Notes

The authors declare no competing financial interest.

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NOMENCLATURE

Abbreviations

AAD, average absolute deviation AARD, average absolute relative deviation MHV2, modified Huron−Vidal second-order NRTL, nonrandom two liquids PR, Peng−Robinson R600a, isobutane R1234ze(E), trans-1,3,3,3-tetrafluoropropene R13I1, trifluoroiodomethane vdW, van der Waals VLE, vapor liquid equilibrium Symbols

a, attractive parameter in the EoS aij, cross parameter of an EoS b, covolume in the EoS f , fugacity G, excess molar Gibbs energy kij, binary interaction parameter between components i and j p, pressure R, universal gas constant T, temperature x, liquid phase composition y, vapor phase composition Greek Letters

μ, chemical potential ω, the acentric factor of the pure component τ, α, binary interaction coefficients in NRTL activity model Subscripts

c, the critical parameter i, j, component index m, mixture r, reduced parameter Superscripts

V, vapor phase L, liquid phase

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