Vapor–liquid equilibrium data for the CO2 + 1,1,1,2,3,3,3,-heptafluoropropane (R227ea) system at temperatures from 276.01 to 367.30 K and pressures up to 7.4 MPa

Fluid Phase Equilibria 207 (2003) 53–67

Vapor–liquid equilibrium data for the CO2 + 1,1,1,2,3,3,3,-heptafluoropropane (R227ea) system at temperatures from 276.01 to 367.30 K and pressures up to 7.4 MPa A. Valtz, C. Coquelet, A. Baba-Ahmed, D. Richon∗ Centre d’Energétique, Ecole Nationale Supérieure des Mines de Paris CENERG/TEP, 35 Rue Saint Honoré, 77305 Fontainebleau, France Received 4 October 2002; accepted 12 December 2002

Abstract Isothermal vapor–liquid equilibrium data for the binary system CO2 + R227ea (1,1,1,2,3,3,3-heptafluoropropane) were measured at 276.01, 293.15, 303.15, 305.17, 313.15, 333.15, 353.15 and 367.30 K and pressures up to 7.4 MPa. The experimental method used in this work is of the static-analytic type. It takes advantage of two pneumatic capillary samplers (RolsiTM , Armines’ patent) developed in the Cenerg/TEP laboratory. The eight sets of isothermal P, x, y data are represented with the Peng–Robinson equation of state using the Wong–Sandler mixing rules involving the NRTL model. © 2003 Elsevier Science B.V. All rights reserved. Keywords: VLE data; High pressures; Refrigerants; Modeling; EoS; Supercritical gas solubility

1. Introduction It is very important to have some accurate data concerning working fluids to develop industrial equipment (compressor, cooling equipment, etc.). Actually, industry must be careful about environnement problems, for limiting energy consumption and costs. Since 1987, the modification of the Montreal Protocol has prohibited the use and the production of chlorofluorocarbons (CFCs) worldwide. Accurate knowledge of thermophysical properties of mixtures containing HFCs, which are proposed as alternative refrigerants, is of great importance to evaluate the performance of refrigeration cycles and to determine the optimum composition of new alternative refrigerants. The R227ea is an alternative refrigerant principally used as propellant for pharmaceutical aerosols, fire extinguishing agent and refrigerant for air conditioning. Carbon dioxide (CO2 ), an “old” refrigerant used in industrial and marine refrigeration, was proposed as an alternative refrigerant, mainly because of its ∗

Corresponding author. Tel.: +33-164694965; fax: +33-164694968. E-mail address: [email protected] (D. Richon). 0378-3812/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0378-3812(02)00326-6

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nonflammability. It can also be used as fire extinguishing agent and aerosols. CO2 is a very cheap natural fluid, present in great quantities. Contrary to CFCs and HCFCs, ammonia, hydrocarbons, HFCs and CO2 all have a zero ozone depletion potential (ODP) and much lower global warming potentials (GWP). Knowledge of vapor–liquid equilibrium (VLE) data for new mixtures is essential to choose those working fluids offering the best suitable thermodynamic properties. The development of models for representation and prediction of physical properties and phase equilibria as well as the improvement of current equations of state can not be achieved without reliable VLE data. The different isotherms presented herein were obtained using an apparatus based on a static-analytic method. The experimental results are fitted using the Peng–Robinson equation of state (PR EoS) and the Wong–Sandler mixing rules.

2. Experimental section 2.1. Materials CO2 is obtained from Messer Griesheim with a certified purity higher than 99.995 vol.%. R227ea was purchased from DEHON (France) and had a certified purity higher than 99.99 vol.%. No further purification was performed before use. 2.2. Apparatus and experimental procedures The apparatus used in this work (Fig. 1) is based on a static-analytic method with liquid and vapor phase sampling. This apparatus is similar to that described by Laugier and Richon [1]. The equilibrium cell is immersed in a thermo-regulated liquid bath by which the temperature control is performed within 0.01 K. In order to perform accurate temperature measurements in the equilibrium cell and to check for thermal gradients, two platinum resistance thermometer probes (Pt100) are inserted inside wells directly drilled into the body of the equilibrium cell at different levels (see Fig. 1) and connected to an HP data acquisition unit (HP34970A). These two Pt100 probes are carefully and periodically calibrated against a 25
reference platinum resistance thermometer (TINSLEY Precision Instruments). The resulting uncertainty is not higher than 0.02 K. The 25
reference platinum resistance thermometer was calibrated by the Laboratoire National d’Essais (Paris) based on the 1990 International Temperature Scale (ITS 90). Pressures are measured by means of a pressure transducer (Druck, type PTX611, range: 0–0.6 MPa) connected to the same HP data acquisition unit (HP34970A) as the two Pt100 probes; the pressure transducer is maintained at constant temperature (at temperatures higher than the highest temperature of the study) by means of a home-made air-thermostat, which is controlled by a PID regulator (WEST instrument, model 6100). The uncertainty of the pressure measurements is estimated to be within ±0.3 kPa, as a result of a pressure calibration against a dead weight pressure balance (Desgranges & Huot 5202S, CP 0.3–40 MPa, Aubervilliers, France). The HP on-line data acquisition system is connected to a personal computer through a RS-232 interface. This complete system allows real time readings and recording of temperatures and pressures all along the different isothermal runs.

A. Valtz et al. / Fluid Phase Equilibria 207 (2003) 53–67 Fig. 1. Flow diagram of the equipment: C: carrier gas; EC: equilibrium cell; FV: feeding valve; LB: liquid bath; LS: liquid sampler; PP: platinum resistance thermometer probe; PrC: CO2 cylinder; PT: pressure transducer; RC: refrigerant cylinder; SM: sampler monitoring; ST: sapphire tube; TC1 and TC2 thermal compressors; Th: thermocouple; TR: temperature regulator; VS: vapor sampler; VSS: variable speed stirrer; VP: vacuum pump. 55

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The analytical work was carried out using a gas chromatograph (VARIAN model CP-3800) equipped with a thermal conductivity detector (TCD) connected to a data acquisition system (BORWIN ver 1.5, from JMBS, Le Fontanil, France). The analytical column is PORAPAK N 80/100 Mesh (silcosteel tube, length: 2 m, diameter: 3.2 mm from Restek). The TCD was repeatedly calibrated by introducing known amounts of each pure compound through a syringe in the injector of the gas chromatograph. Taking into account the uncertainties due to calibrations and dispersions of analyses, accuracy on vapor and liquid mole fractions is estimated to be within ±1.0% over the entire range of concentrations. The experimental procedure is the following: at room temperature, the equilibrium cell and its loading lines are evacuated down to 0.1 Pa. One thermal compressor is loaded with carbon dioxide (TC1 ) and the second with R227ea (TC2 ). At the required equilibrium temperature (equilibrium temperature is assumed to be reached when the two Pt100 probes give the same temperature value within their temperature uncertainty for at the least 10 min), a volume of about 5 cm3 of R227ea is introduced into the equilibrium cell. The vapor pressure of the heavier component (R227ea) is then recorded at this temperature. To describe the two-phase envelope with at least 10 x, y points (liquid and vapor), given amounts of the lighter component (carbon dioxide) are introduced step by step, leading to successive equilibrium mixtures. Equilibrium is assumed when the total pressure remains unchanged within ±1.0 kPa during a period of 10 min under efficient stirring. For each equilibrium condition, at least six samples of both vapor and liquid phases are withdrawn using the pneumatic samplers RolsiTM [2] and analyzed in order to check the measurement repeatability. 3. Correlations The critical temperature (TC ), critical pressure (PC ), and acentric factor (ω), for each of the two pure components are provided in Table 1. Our experimental VLE data are correlated by means of home-made software THERMOPACK, developed by Armines Ecole des Mines de Paris. We have used the PR EoS [3] to correlate the data. To have an accurate representation of vapor pressures of each component, we use the Mathias–Copeman alpha function [4] given below with three adjustable parameters, which was especially developed for polar compounds.     2  3 2    T T T  α(T ) = 1 + c1 1 − (1) + c3 1 − + c2 1 − TC TC TC If T > TC ,





α(T ) = 1 + c1 1 −



T TC

 2 (2)

Table 1 Critical parameters and acentric factors Compound

Pc (MPa)

Tc (K)

ω

CO2 R227ea

7.377 2.98

304.20 375.95

0.225 0.3632

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57

where c1 , c2 and c3 are three adjustable parameters that were evaluated for our entire temperature range from pure component vapor pressure data using a modified Simplex algorithm [5]. The objective function is N  100 Pexp − Pcal 2 F = N 1 Pexp

(3)

where N is the number of data points, Pexp the measured pressure, and Pcal the calculated pressure. To have the best representation of mixture VLE, we chose the Wong–Sandler mixing rules [6], which are based on the Huron–Vidal approach.

i j xi xj (b − (a/RT))ij   b= (4) E 1− i xi ((ai /bi )/RT) + Aγ (T , P = ∞, xi )/CRT b− 



a  a = xi xj b − RT RT ij i j

b−

   a  a  1  a  b− (1 − kij ) = + b− RT ij 2 RT i RT j

(5)

(6)

kij is a binary interaction parameter. Wong and Sandler have shown that the excess Helmholtz energy of mixing at infinite pressure, AEγ (T , P = ∞, xi ), is approximately equal to the excess Gibbs energy at low pressure. Consequently, they assumed AEγ (T , P = ∞, xi ) RT

=

GEγ (T , P = 0, xi ) RT

(7)

The excess Gibbs energy is calculated using the NRTL [7] local composition model. GE(T ,P ) RT

=

xj exp(−αj,i /(τj,i /RT))  xi

τk,i  τj,i k xk exp −αk,i RT i j

(8)

τi,i = 0 and αi,i = 0. α j ,i , τ j ,i and τ i ,j are adjustable parameters. For our system which belongs to a given polar mixture type it is recommended [8] to use αj,i = 0.3. τ j ,i and τ i ,j are adjusted directly to VLE data through a modified Simplex algorithm using the objective function  N  N  100 Pexp − Pcal 2 yexp − ycal 2 F = + N Pexp yexp 1 1

(9)

where N is the number of data points, Pexp the measured pressure, Pcal the calculated pressure, yexp the measured vapor phase mole fraction and ycal the calculated vapor phase mole fraction.

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4. Results 4.1. Vapor pressures The values of the PR EoS Mathias–Copeman coefficients fitted to vapor pressures of R227ea are reported in Table 2. Table 3 compares calculated pressures with experimental data. In this work, we have compared our measured CO2 vapor pressures with the values calculated using a correlation [9] (Eq. (9)). As the relative deviation is less than 0.15%, we trust in the correlation to determine the Mathias–Copeman coefficients. P sat = e(A+(B/T )+C ln(T )+D×T

E

)

(9)

Coefficients A, B, C, D and E are given in Table 4. The Mathias–Copeman coefficients for CO2 are tabulated in Table 2. Table 5 summarizes the calculated pressures using Eq. (9) and the PR–Mathias–Copeman EoS. The vapor pressures of both pure compounds are accurately represented (within 1.0 kPa).

Table 2 Adjusted Mathias–Copeman coefficients Coefficients

R227ea

CO2

C1 C2 C3

1.134 −1.965 8.690

0.871 −0.734 2.692

Table 3 Experimental and calculated vapor pressures of R227ea T (K)

Pexp (MPa)

Pcal (MPa)

276.01 293.15 303.15 353.16 333.15 367.30

0.2170 0.3886 0.5281 1.8577 1.1763 2.4999

0.2169 0.3890 0.5281 1.8590 1.1745 2.5049

Table 4 Correlation coefficients for CO2 (see Eq. (9)) A B C D E

140.54 −4735 −21.268 0.040909 1

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Table 5 CO2 Calculated pressures P (from correlation Eq. (9)) along with calculated pressures Pcal from PR EoS and adjusted Mathias–Copeman coefficients T (K)

P (MPa)

Pcal (Mpa)

250.15 255.15 260.15 265.15 270.15 275.15 280.15 285.15 290.15 295.15 300.15 304.20

1.7969 2.0972 2.4329 2.8066 3.2210 3.6793 4.1845 4.7401 5.3498 6.0176 6.7477 7.3896

1.7971 2.0970 2.4325 2.8063 3.2211 3.6799 4.1855 4.7412 5.3502 6.0160 6.7423 7.3772

4.2. Vapor–liquid equilibrium The experimental and calculated VLE data are summarized reported in Tables 6–13 and plotted in Fig. 2. The parameters adjusted and the values of the objective function corresponding to the PR EoS + Wong–Sandler mixing rules and the NRTL model are given in Table 14. All the data are well represented by this adjustment at each temperature independently. The deviations, MRDP, on pressures and MRDY, on vapor phase mole fractions are defined by    100  Ucal − Uexp  MRDU = (10)   N U exp

and they are listed in Table 15; N is the number of data points, and U = P or y1 Table 6 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 276.01 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

0.2170 0.4566 0.6378 0.9358 1.3352 1.7432 2.1842 2.5847 2.9437 3.1932 3.4423

0.0000 0.0934 0.1592 0.2615 0.3950 0.5188 0.6434 0.7471 0.8335 0.8887 0.9400

0.0000 0.5408 0.6822 0.7944 0.8680 0.9070 0.9366 0.9561 0.9696 0.9779 0.9875

0.2169 0.4605 0.6399 0.9318 1.3377 1.7429 2.1858 2.5893 2.9561 3.2078 3.4553

0.0000 0.5372 0.6744 0.7865 0.8630 0.9057 0.9362 0.9567 0.9720 0.9813 0.9899

P (MPa) 0.0001 −0.0039 −0.0021 0.0040 −0.0025 0.0003 −0.0016 −0.0046 −0.0124 −0.0146 −0.0130

y 0.0000 0.0036 0.0078 0.0080 0.0051 0.0013 0.0004 −0.0006 −0.0024 −0.0034 −0.0024

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Table 7 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 293.15 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

0.3886 0.5341 0.6599 0.7964 1.1036 1.4506 2.0758 2.8931 3.7823 4.4873 5.0116 5.2605 5.7433

0.0000 0.0423 0.0774 0.1125 0.1887 0.2752 0.4184 0.5886 0.7482 0.8539 0.9216 0.9518 1.0000

0.0000 0.2750 0.4153 0.5189 0.6622 0.7528 0.8385 0.8953 0.9360 0.9610 0.9769 0.9853 1.0000

0.3890 0.5395 0.6677 0.7988 1.0937 1.4462 2.0749 2.9113 3.8213 4.5264 5.0429 5.2964 5.7426

0.0000 0.2758 0.4153 0.5129 0.6488 0.7403 0.8290 0.8917 0.9339 0.9594 0.9765 0.9849 1.0000

P (MPa) −0.0004 −0.0054 −0.0078 −0.0024 0.0099 0.0044 0.0009 −0.0182 −0.0390 −0.0391 −0.0313 −0.0359 0.0007

y 0.0000 −0.0008 0.0000 0.0060 0.0134 0.0125 0.0095 0.0036 0.0021 0.0016 0.0004 0.0004 0.0000

We also calculated the BIAS listed in Table 15 for all the cases:  BIASU =

 100 Uexp − Ucal Uexp N

(11)

Binary interaction parameters: τ 12 , τ 12 and k12 are plotted as a function of temperature in Figs. 3–5. These figures exhibit different behavior below and above the critical temperature of CO2 . Table 8 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 303.15 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

0.5281 0.6556 0.8491 1.1931 1.5947 2.1875 2.8907 3.6928 4.5827 5.3774 6.0664 6.5547 6.8124 6.8799 7.1946

0.0000 0.0312 0.0767 0.1559 0.2432 0.3619 0.4899 0.6202 0.7460 0.8400 0.9103 0.9532 0.9728 0.9779 1.0000

0.0000 0.1894 0.3752 0.5598 0.6768 0.7744 0.8353 0.8806 0.9167 0.9424 0.9618 0.9772

0.5281 0.6578 0.8506 1.1979 1.6006 2.1896 2.8932 3.7059 4.6139 5.4006 6.0799 6.5588 6.7884 6.8746 7.2087

0.0000 0.1909 0.3713 0.5545 0.6704 0.7660 0.8319 0.8799 0.9171 0.9427 0.9629 0.9773 0.9728 0.9876 1.0000

0.9885 1.0000

P (MPa) 0.0000 −0.0022 −0.0015 −0.0048 −0.0059 −0.0021 −0.0025 −0.0131 −0.0312 −0.0232 −0.0135 −0.0041 0.0240 0.0053 −0.0141

y 0.0000 −0.0015 0.0039 0.0053 0.0064 0.0084 0.0034 0.0007 −0.0004 −0.0003 −0.0011 −0.0001 0.0009 0.0000

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Table 9 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 305.17 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

0.5606 1.0143 2.0000 2.9975 3.9966 4.9859 5.8863

0.0000 0.1083 0.3108 0.4899 0.6448 0.7736 0.8708

0.0000 0.4431 0.7310 0.8317 0.8848 0.9149 0.9453

0.5602 1.0170 1.9902 2.9990 4.0162 5.0085 5.8953

0.0000 0.4430 0.7225 0.8260 0.8818 0.9189 0.9461

P (MPa) 0.0004 −0.0027 0.0098 −0.0015 −0.0196 −0.0226 −0.0090

y 0.0000 0.0001 0.0085 0.0057 0.0030 −0.0040 −0.0008

Table 10 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 313.15 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (Mpa)

y1cal

0.9918 1.3022 1.7830 2.3864 2.9856 3.6832 4.3831 5.0909 5.6829 6.1118 6.4782 6.7879 6.9506 7.0737 7.1921

0.0596 0.1213 0.2097 0.3160 0.4152 0.5230 0.6206 0.7070 0.7691 0.8119 0.8442 0.8695 0.8832 0.8943 0.9048

0.2760 0.4468 0.5982 0.7046 0.7693 0.8198 0.8551 0.8797 0.8988 0.9098 0.9186 0.9254 0.9285 0.9298 0.9303

0.9915 1.3018 1.7674 2.3667 2.9742 3.7007 4.4329 5.1542 5.7244 6.1473 6.4851 6.7616 6.9155 7.0417 7.1612

0.2785 0.4454 0.5901 0.6957 0.7615 0.8137 0.8508 0.8786 0.8969 0.9089 0.9177 0.9245 0.9280 0.9308 0.9331

P (MPa) 0.0003 0.0004 0.0156 0.0197 0.0114 −0.0175 −0.0498 −0.0633 −0.0415 −0.0355 −0.0069 0.0263 0.0351 0.0320 0.0309

y −0.0025 0.0014 0.0081 0.0089 0.0078 0.0061 0.0043 0.0011 0.0020 0.0009 0.0009 0.0009 0.0005 −0.0010 −0.0028

5. Discussion From our point of view the phenomenon observed in Figs. 3–5 is certainly due to the absorption of a supercritical gas in a liquid very different to that of a subcritical gas. Maybe it generates new interactions that lead to a significant jump in the values of the binary interaction parameters. To emphasize this remark, we have analyzed data for another CO2 containing system: 1,1,1,2-tetrafluoroethane (R134a) + CO2 system studied by Silva-Oliver et al. [9] and Duran-Valencia et al. [10]. The corresponding data are represented with the PR EoS the Mathias–Copeman ␣-function and the Wong–Sandler mixing rules involving the NRTL model. We have plotted binary interaction parameters τ 12 and τ 21 as a function of temperature (Figs. 3–5). All binary interaction parameters behave similarly for both systems with CO2 . It is worth to note that the subcritical and supercritical regions of the R134a + CO2 system have been studied by two different laboratories.

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Table 11 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 333.15 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

1.1763 1.3690 1.8202 2.3899 2.9974 3.6513 4.2966 4.9977 5.5951 6.0181 6.2945 6.5034 6.6457

0.0000 0.0308 0.1010 0.1896 0.2740 0.3619 0.4417 0.5231 0.5899 0.6360 0.6670 0.6886 0.7118

0.0000 0.1200 0.3176 0.4701 0.5704 0.6428 0.6903 0.7322 0.7533 0.7610 0.7628 0.7614 0.7559

1.1745 1.3603 1.8007 2.3918 2.9938 3.6638 4.3125 5.0142 5.6167 6.0393 6.3195 6.5067 6.6906

0.0000 0.1206 0.3142 0.4683 0.5652 0.6367 0.6848 0.7222 0.7453 0.7571 0.7624 0.7642 0.7633

P (MPa) 0.0018 0.0087 0.0195 −0.0019 0.0036 −0.0125 −0.0159 −0.0165 −0.0216 −0.0212 −0.0250 −0.0033 −0.0449

y 0.0000 −0.0006 0.0034 0.0018 0.0052 0.0061 0.0055 0.0101 0.0080 0.0039 0.0005 −0.0028 −0.0074

Table 12 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 353.15 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

1.8577 2.0983 2.4903 2.8951 3.3031 3.7351 4.0976 4.5032 4.8324 5.0140 5.2042 5.2734

0.0000 0.0339 0.0871 0.1402 0.1914 0.2435 0.2864 0.3357 0.3756 0.3996 0.4298 0.4466

0.0000 0.0897 0.2023 0.2929 0.3588 0.4140 0.4497 0.4804 0.4972 0.5032 0.4985 0.4871

1.8586 2.0946 2.4842 2.8948 3.3086 3.7433 4.1067 4.5223 4.8469 5.0308 5.2395 5.3375

0.0000 0.0891 0.2023 0.2903 0.3570 0.4102 0.4445 0.4742 0.4905 0.4965 0.4991 0.4972

P (MPa) −0.0009 0.0037 0.0061 0.0003 −0.0055 −0.0082 −0.0091 −0.0191 −0.0145 −0.0168 −0.0353 −0.0641

y 0.0000 0.0006 0.0000 0.0026 0.0018 0.0038 0.0052 0.0062 0.0067 0.0067 −0.0006 −0.0101

Table 13 Vapor–liquid equilibrium pressures and phase compositions for CO2 (1) and R227ea(2) mixtures at 367.30 K, P is the deviation on pressure, y the deviation on vapor composition Pexp (MPa)

x1

y1exp

Pcal (MPa)

y1cal

2.4999 2.6866 2.8856 3.0862 3.3137 3.4966 3.6889 3.8395

0.0000 0.0246 0.0506 0.0763 0.1058 0.1299 0.1571 0.1843

0.0000 0.0453 0.0860 0.1222 0.1601 0.1833 0.2053 0.2146

2.5050 2.6895 2.8867 3.0826 3.3064 3.4858 3.6797 3.8551

0.0000 0.0451 0.0871 0.1231 0.1583 0.1820 0.2032 0.2170

P (MPa) −0.0051 −0.0029 −0.0011 0.0036 0.0073 0.0108 0.0092 −0.0156

y 0.0000 0.0002 −0.0011 −0.0009 0.0018 0.0013 0.0022 −0.0023

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Fig. 2. Pressure as a function of CO2 mole fraction in the CO2 + R227ea mixture at different temperatures. () 276.01 K; (+) 293.15 K; (䊊) 303.15 K; (×) 305.15 K; (䊐) 313.15 K; (䊉) 333.15 K; (䉫) 353.15 K; ( ) 367.30 K. Solid lines: calculated with PR EoS, Wong Sandler mixing rules and NRTL activity coefficient model with parameters from Table 14.

We have selected also a CO2 non-containing system: methane + butane studied by Elliot et al. [11], to verify the special behavior found around the critical point of the volatile component. Using either the PR EoS, the generalized alpha function, the WS mixing rules and the NRTL model or the UNIQUAC model [12] lead to the same behavior, but this time around the methane critical temperature (see Figs. 6–8). We think that we can trust on this comportment for all the binary systems. So, it would be dangerous to extrapolate temperature dependant binary parameters (adjusted only at temperatures above or below the volatile component’s critical temperature) to temperatures at the other side of the critical point.

Table 14 Values of the adjusted of the Wong–Sandler mixing rules parameters and objective function at each temperature T (K)

τ 12

τ 21

k12

F

276.01 293.15 303.15 305.17 313.15 333.15 353.15 367.30

3356 3606 1951 3797 1990 3639 9758 17599

−1472 −1606 −874 −1917 −890 −1839 −3105 −2223

0.2692 0.28328 0.2998 0.28823 0.30825 0.32242 0.33146 0.3422

0.0045 0.0125 0.0041 0.0042 0.0085 0.0085 0.0131 0.0086

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Table 15 MRDP, MRDY, and Bias using the Peng Robinson equation of state with the Wong–Sandler mixing rules T (K)

BIASP (%)

MRDP (%)

BIASY (%)

MRDY (%)

276.01 293.15 303.15 305.15 313.15 333.15 353.15 367.30

−0.22 −0.37 −0.19 −0.12 −0.02 −0.08 −0.26 0.02

0.31 0.60 0.27 0.28 0.52 0.38 0.34 0.21

0.24 0.62 0.24 0.24 0.40 0.41 0.49 0.02

0.41 0.62 0.28 0.39 0.45 0.69 0.86 0.80

Fig. 3. τ 12 binary parameter as a function of temperature. (䉫) R227ea + CO2 ; () R134a + CO2 . Vertical dot line represents CO2 critical temperature.

Fig. 4. τ 21 binary parameter as a function of temperature. (䉫) R227ea + CO2 ; () R134a + CO2 . Vertical dot line represents CO2 critical temperature.

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Fig. 5. k12 binary parameter as a function of temperature. (䉫) R227ea + CO2 ; () R134a + CO2 . Vertical dot line represents CO2 critical temperature.

Fig. 6. τ 12 UNIQUAC binary parameter as a function of temperature. (䊊) methane + butane. Vertical dot line represents methane critical temperature.

Fig. 7. τ 21 UNIQUAC binary parameter as a function of temperature. (䊊) methane + butane. Vertical dot line represents methane critical temperature.

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Fig. 8. k12 binary parameter as a function of temperature. (䊊) methane + butane. Vertical dot line represents methane critical temperature.

6. Conclusion In this paper we present VLE data for the system CO2 + R227ea at eight different temperatures. We used a static-analytic method to obtain the experimental data. The Peng Robinson (PR) equation of state, with the Mathias–Copeman alpha function is chosen to fit these data with the Wong–Sandler mixing rules. Generally, the data are found consistent with the models (deviations both in pressure and vapor composition are much <1%). As a final point, we stress the different behaviors of the system below and above the critical temperature of CO2 . List of symbols a parameter of the equation of state (energy parameter, J m3 /mol2 ) A Helmhotz energy (J/mol) b parameter of the equation of state (co volume parameter, m3 /mol) C numerical constant = ln(1/2) F objective function G Gibbs energy (J/mol) kij binary interaction parameter P pressure (MPa) R gas constant (J/(mol K)) T temperature (K) U deviation (Uexp − Ucal ) x liquid mole fraction y vapor mole fraction Z compressibility factor Greek letters α ij NRTL model parameter (Eq. (11)) τ ij NRTL model binary interaction parameter (Eq. (11)) (J/mol)

A. Valtz et al. / Fluid Phase Equilibria 207 (2003) 53–67

ω

acentric factor

Superscript E excess property Subscripts C critical property cal calculated property exp experimental property i,j molecular species ∞ infinite pressure reference state 1 CO2 2 R227ea

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