Molecular Simulation Studies on the VaporâLiquid Phase Equilibria of

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Molecular Simulation Studies on the Vapor−Liquid Phase Equilibria of Binary Mixtures of R‑1234yf and R‑1234ze(E) with R‑32 and CO2 Gabriele Raabe* Institut für Thermodynamik, Technische Universität Braunschweig, Hans-Sommer-Strasse 5, 38106 Braunschweig, Germany ABSTRACT: Different fluoropropenes are currently considered as refrigerants, either as pure compounds or as components in low GWP (global warming potential) refrigerant mixtures. However, experimental data for the thermophysical properties of fluoropropenes and their mixtures are in general rare, which hampers the exploration of their performance in technical applications. In our earlier work [Raabe, G.; Maginn, E. J. J. Phys. Chem. B 2010, 114, 10133−10142; Raabe, G. J. Phys. Chem. B 2012, 116, 5744−5751], we introduced a transferable force field for fluoropropenes that enables reliable predictions of the properties of different fluoropropenes. In this work, we apply the force field model for fluoropropenes to molecular simulation studies on the vapor−liquid phase equilibria in binary mixtures of the tetrafluoropropenes R1234yf or R-1234ze(E) with the difluoromethane R-32 and CO2 at temperatures from T = (273.15 to 313.15) K. Additionally, we present correlations of the VLE by the PC-SAFT equation of state.

1. INTRODUCTION Owing to their low global warming potential (GWP), hydrofluorolefins (HFOs) such as 2,3,3,3-tetrafluoro-1-propene (R-1234yf) and trans-1,3,3,3-tetrafluoro-1-propene (R-1234ze(E)) have been proposed as alternative refrigerants1,2 However, their use as a pure component refrigerant causes concern due to their flammability, and in addition, they usually show smaller volumetric cooling capacities than conventional hydrofluorocarbon (HFC) refrigerants.3 Thus, blends of HFOs and nonflammable HFC compounds are regarded as suitable choices to yield refrigerants that have on one hand reduced flammabilities and higher volumetric refrigerant capacities compared to the pure HFOs and on the other hand lower GWPs than the pure HFC refrigerants. Refrigerant blends that have recently attracted attention are for instance the binary mixtures R-1234ze(E) + R-324 and R-1234yf + R-325 as candidates to replace the refrigerant blend R-410Aa mixture of difluoromethane R-32 and pentafluoroethane R-125in domestic heat pump or air conditioning systems. Another refrigerant blend of interest is AC-6, that is, R-445A, which is discussed as an alternative refrigerant for mobile air conditioning (MAC) systems.6 This refrigerant is a ternary mixture of CO2, the tetrafluoroethane R-134a, and the trans1,3,3,3-tetrafluoro-1-propene (R-1234ze(E)). The exploration of the performance of these refrigerant mixtures in potential technical applications requires a detailed knowledge of their thermodynamic and transport properties. However, only a limited number of experimental studies of mixtures containing fluoropropenes is available in literature. Experimental data for vapor−liquid equilibria in literature only comprise studies on mixtures of R-1234yf with the HFC R-32, R-134a, and R-1257 and mixtures of R-1234ze(E) and isobutene8 and R-32.9 Additional experimental information is © XXXX American Chemical Society

available for some thermophysical properties in the liquid or vapor phase, that is, the isochoric heat capacities of R1234ze(E) + CO2 mixtures,9 the thermal conductivity of R1234ze(E) + R-32,11 and PVTx measurement in systems of the CO2 + R-1234yf.12 In principle, molecular modeling can be used to predict the relevant properties of refrigerant blends to complement experimental data, provided that adequate intermolecular potential functions (“force fields”) for the compounds exist. In our earlier work,13−15 we have introduced a transferable force field for fluoropropenes comprising the compounds 3,3,3trifluoro-1-propene (HFO-1243zf), 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf), hexafluoro-1-propene (HFO-1216), trans- and cis-1,3,3,3- tetrafluoro-1-propene (HFO-1234ze(E), HFO-1234ze), and the cis-1,2,3,3,3-pentafluoro-1-propene (HFO-1225ye(Z)). The performance and predictive ability of the molecular model have been tested by simulation studies on the vapor−liquid phase equilibria and liquid phase properties of the pure compounds. The simulation studies have shown that the new force field for fluoropropenes yields reliable reproductions and predictions for a wide range of thermophysical properties of the pure compounds, as the simulated data in general agree well with experimental data and correlations where available.14,15 In this paper, we employ the force field model for fluoropropenes to study mixtures of R-1234yf and R1234ze(E) with R-32 and CO2. We have therefore developed a new molecular model for R-32 compatible with our model for fluoropropenes, whereas we have employed a common model Received: March 18, 2013 Accepted: April 20, 2013

A

dx.doi.org/10.1021/je4002619 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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from literature16 for CO2. We here present Gibbs Ensemble Monte Carlo simulations on the vapor−liquid equilibria of the mixtures in the temperature range from T = (273.15 to 313.15) K. The simulation results are correlated with the PC-SAFT equation of state17 and compared to experimental data where available.

energy change. The parameters for the torsion potentials were calculated from torsion scanning calculations. All ab initio simulations to derive the parameters of the intramolecular terms were performed on the B3LYP/DGDZVP level of theory, using the Gaussian 03 package.19 The partial charges were calculated for all compounds individually from ab initio simulations by the ESP approach with the CHELPG fitting scheme.20 The electrostatic potentials have been determined for the isolated molecules at the HF/6-31G* level of theory. The Lennard-Jones parameters for the different atoms types (see Figure 1) were established to fine-tune agreement the experimental data for selected compounds. It should be noted that the force field enables reliable predictions for the cis and trans isomere of R-1234ze (see ref 15) although no LJ parameters have be adjusted to improve agreement with experimental data for these compounds. This validates both the predictive ability of the force field, and the transferability of the parameters. More details on the parametrization of the molecular model are given in an earlier work,14,15 whereas the Supporting Information of ref 15 provides a complete list of parameters of the fluoropropene force field, and an overview which compounds were involved in the determination of the different transferable force field parameters. For carbon dioxide, we have employed the TraPPE model by Potoff and Siepmann, 16 for which the calculation of intermolecular interaction is also based on LJ site and fixed partial charges on the three atomic sites. Though, contrary to our fully flexible model for fluoropropenes, the TraPPE force field models CO2 as rigid molecule. However, there is no model for R-32 available in literature that can be combined with our force field for fluoropropenes. The model from Potter et al.21 uses a “manual mixing rules”, that is, explicitly set LJ parameters for the interaction between the hydrogen and the fluorine atom, where as in our force field, all LJ parameters for unlike atoms are obtained from the Lorentz−Berthelot combining rule. The molecular model by Stoll et al.22 describes R-32 as a single Lennard-Jones bead with a superimposed point dipole, which is not compatible with our handling of electrostatic interactions by fixed point charges on the atomic sites. Thus, following the same procedure as for the fluoropropenes,14 we have developed a new flexible all atoms force field model for R-32. The force constants for the C−F bond and the F−C−F angle were taken from the fluoropropene force field. As in our fluoropropenes model, we used hydrogen parameters from the AMBER force field,18 that is, the H2 parameter for a hydrogen attached to a carbon with two electron-withdrawing substituents (fluorine atoms). The LJ parameters for the carbon and fluorine atom were adjusted to fine-tune agreement with reference data for the VLE.23 The parameters of the new model are given in Table 1. Figure 2 shows simulation results for the vapor pressures in comparison with calculations based on REFPROP.23 The comparison illustrates that our new force field model yields a good reproduction of the VLE of the pure compound. Please note that all LJ parameters for interactions between unlike atoms, both in studies on pure compounds as well as for the simulation of mixtures are obtained from the Lorentz− Berthelot combining rule; that is,

2. COMPUTATIONAL METHODS Force Field Model. The structure of the compounds studied in this work, and the nomenclature used for the different Lennard-Jones (LJ) -atom types (CT, CM, FCT, etc.) are shown in Figure 1. In our force field model for

Figure 1. Structures of the refrigerants studied in this work: 2,3,3,3tetrafluoro-1-propene (R-1234yf) and trans-1,3,3,3-tetrafluoro-1-propene (R-1234ze(E)), difluoromethane (R-32), and carbon dioxide (CO2) and nomenclature for the different Lennard-Jones atom types.

fluoropropenes, the potential energy is expressed by the following standard functional form18 UConf =

∑

kr(r − r0)2 + ∑ kθ(θ − θ0)2

bonds

angles

+

∑

kχ [1 + cos(nχ − δ)]

dihedral

⎧ ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj ⎫ σij ⎥ ⎪ ⎪ ⎢ σij 1 ⎬ + ∑ ∑ ⎨4εij⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥ + rij ⎠ rij ⎠ 4πε0 rij ⎪ ⎝ ⎝ i j>i ⎪ ⎣ ⎦ ⎭ ⎩ (1)

Therein, the calculation of intermolecular interactions is based on Lennard-Jones (LJ) site−site terms and electrostatic interactions between fixed partial charges on the atomic sites. The intramolecular potential energy is modeled by harmonic terms for bond stretching and angle bending, and a cosine term accounts for energies arising from internal rotations of the dihedral angles. Nonbonded Lennard-Jones (LJ) and electrostatic interactions between atoms separated by exactly three bonds (1−4 interactions) are scaled by a factor of 1/2 and 1/1.2, respectively, whereas full LJ and electrostatic interactions are considered between atoms separated by more than three bonds. Our molecular model for fluoropropenes is a transferable force field with regard to both the intramolecular terms and the Lennard-Jones parameters; that is, we used for instance the same parameters for the FCT−CT−FCT angle bending or the CM Lennard-Jones atom type for all compounds. The averaged nominal bond lengths r0 and bond angles θ0 were obtained from ab initio simulations from which we also derived the force constants for the bond stretching and angle bending by perturbing the bond lengths or angles around their equilibrium value and fitting of the harmonic potential to the resulting

εij = B

εiiεjj ,

σij =

σii + σjj 2

(2)



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Figure 2. Gibbs ensemble (GEMC) simulation results for the vapor pressure of R-32 (circled plus signs) obtained in this work and the calculated vapor pressure curve (solid line) using REFPROP23.

(GEMC) simulations in the isothermal−isobaric (NPT) ensemble using the simulation code Towhee.25 Each system consisted of 400 molecules in the sum, with varying number of the molecules of both components, depending on the mixture studied. The Ewald sum technique26,27 was employed to deal with the electrostatic interactions with a cutoff radius adjusted to half the box length. The cutoff radius for the Lennard-Jones interactions was set to 12 Å, and standard long-range corrections to the energy and pressure were applied.27 Estimates for overall (feed) compositions lying in the two phase region of the binary mixtures at the chosen temperatures and pressures were derived from experimental data or REFPROP23 calculations. In general, simulations were then started from equal initial compositions in both boxes matching the feed composition. The simulations were equilibrated for 200 000 cycles, followed by production runs of 300 000 to 400 000 cycles. Each cycle consisted of 400 attempted moves, such as a translational or volume move, rotational-bias and configurational-bias interbox molecule transfer, intrabox configurational-bias molecule transfer, molecule regrowth, translation, and rotation around the center-of-mass.28 The moves were selected at random with a fixed probability, and the ratios for attempted moves were in the order of (0.3−0.5) % volume moves, 35 % interbox molecular transfer moves and 65 % intrabox moves. However, the probabilities of the different moves for the two components in the mixture were manually adjusted to ensure that the equilibrium conditions were satisfied, that is, that the simulated chemical potentials of both components in both phases agreed within the error bars. Standard deviations of all ensemble averages were determined by the standard block average technique.27 We used similar settings for the simulation studies on the VLE of the pure compound R-32, but with N = 340 molecules in the system, and the GEMC simulations were performed in the canonical (NVT) ensemble.

Thus, no interaction parameters were used in the simulation studies on the mixtures, and therefore all our simulations present pure predictions. Simulation Details. Vapor−liquid equilibria of the binary mixtures were calculated via Monte Carlo Gibbs ensemble24

3. RESULTS AND DISCUSSION The GEMC simulation results for the compositions of the liquid and vapor phase and for the saturation densities of the vapor−liquid equilibria of the mixtures R-32 + R-1234yf, R-32 + R-1234ze(E), CO2 + R-1234yf and CO2 + R-1234ze(E) in

Table 1. Force Field Parameters for the New R-32 Model atom

ε/k /K

σ/A

C F H2

54.6 44.0 7.9

3.15 2.94 2.2293

bond

kr/kJ mol−1 Å−2

r0 /Å

C−F

1544.61

1.369

C−H angle

1472.89 1.094 kθ/kJ mol−1 rad−2 θ0/deg

force constant

q/e

source

0.43960 −0.26138 0.04158 equilibrium geometry

H−C−H F−C−F

146.54 367.61

113.6 108.7

H−C−F

249.92

108.6

this work this work Amber LJ parameter18

this work, kr from ref 14 (CT-FCT) this work this work this work, kθ from ref 14 (FCTCT-FCT) this work

Table 2. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Gas-Phase Mole Fraction y, Saturated Liquid Density ρL and Saturated Vapor Density ρv of the VLE for the System R-32 (1) + R-1234yf (2) T/K

p/MPa

u(p)/MPa

x1

273.15

0.325 0.45 0.55 0.60 0.65 0.831 0.596 0.8 1.0 1.1 1.528 1.022 1.65 1.8 1.9 2.461

0.067

0.000 0.171 0.297 0.391 0.500 1.000 0.000 0.147 0.345 0.459 1.000 0.000 0.322 0.402 0.471 1.000

293.15

313.15

0.033 0.070

0.067 0.086

0.036

u(x1) 0.010 0.017 0.017 0.015

0.017 0.008 0.011

0.012 0.013 0.016

y1

u(y1)

0.000 0.405 0.548 0.632 0.708 1.000 0.000 0.328 0.569 0.660 1.000 0.000 0.508 0.578 0.642 1.000

0.025 0.023 0.013 0.016

0.016 0.006 0.006

0.014 0.015 0.016

C

ρL/kg m−3

u(ρL)/kg m−3

ρV/kg m−3

u(ρV)/kg m−3

1178.8 1163.2 1149.1 1139.4 1128.5 1064.9 1110.9 1092.8 1067.0 1049.4 981.1 1031.1 978.5 966.5 956.3 851.7

5.7 4.7 27.4 7.3 5.1 4.3 11.8 5.7 8.1 8.4 8.2 10.7 10.5 6.3 9.1 8.0

18.4 19.7 22.1 22.7 23.3 23.0 33.0 36.8 39.4 40.5 43.8 56.9 70.4 74.2 75.2 72.6

4.5 0.8 2.2 0.4 0.6 1.1 4.7 3.7 0.3 0.8 2.7 6.1 1.2 1.9 1.8 1.1



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Table 3. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Gas-Phase Mole Fraction y, Saturated Liquid Density ρL and Saturated Vapor Density ρv of the VLE for the System R-32 (1) + R-1234ze(E) (2) T/K

p/MPa

u(p)/MPa

x1

273.15

0.212 0.4 0.5 0.6 0.831 0.448 0.6 0.8 1.0 1.1 1.528 0.790 1.2 1.6 2.0 2.461

0.028

0.000 0.266 0.420 0.591 1.000 0.000 0.129 0.281 0.483 0.604 1.000 0.000 0.206 0.424 0.664 1.000

293.15

313.15

0.033 0.064

0.067 0.051

0.036

u(x1) 0.010 0.014 0.017

0.008 0.010 0.022 0.020

0.012 0.017 0.014

y1

u(y1)

0.000 0.588 0.717 0.818 1.000 0.000 0.339 0.557 0.727 0.805 1.000 0.000 0.421 0.649 0.813 1.000

0.021 0.013 0.017

0.013 0.021 0.017 0.015

0.016 0.018 0.010

ρL/kg m−3

u(ρL)/kg m−3

ρV/kg m−3

u(ρV)/kg m−3

1265.0 1231.3 1208.5 1177.9 1064.9 1199.5 1182.6 1160.1 1126.8 1097.9 981.1 1123.8 1094.8 1058.7 1000.0 851.7

5.6 5.5 5.3 5.4 4,.3 7.6 7.0 7.4 8.3 8.7 8.2 7.7 9.6 7.6 7.9 8.0

11.4 14.8 17.1 19.1 23.0 23.7 25.9 29.3 34.1 35.2 43.8 41.1 49.8 58.5 67.3 72.6

1.6 2.4 0.2 0.5 1.1 3.7 1.0 1.7 2.0 2.4 2.7 2.9 1.0 1.3 1.3 1.1

Table 4. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Gas-Phase Mole Fraction y, Saturated Liquid Density ρL and Saturated Vapor Density ρv of the VLE for the System CO2 (1) + R-1234yf (2) T/K

p/MPa

u(p)/MPa

x1

273.15

0.325 1.0 1.5 2.0 3.467 0.997 2.5 3.5 4.5

0.067

0.000 0.246 0.419 0.576 1.000 0.000 0.281 0.445 0.591

310.92

0.063 0.062

u(x1) 0.013 0.014 0.013

0.013 0.013 0.016

y1

u(y1)

0.000 0.716 0.850 0.904 1.000 0.000 0.615 0.748 0.821

0.019 0.012 0.012

0.021 0.016 0.016

ρL/kg m−3

u(ρL)/kg m−3

ρV/kg m−3

u(ρV)/kg m−3

1178.8 1147.1 1109.1 1072.6 935.4 1041.7 981.3 932.5 879.0

5.7 7.5 6.3 9.4 1.4 8.8 12.3 13.8 18.6

18.4 31.6 41.5 53.6 93.0 55.8 89.2 114.5 144.8

4.5 0.9 0.8 1.3 2.3 4.6 3.4 5.4 6.3

Table 5. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Gas-Phase Mole Fraction y, Saturated Liquid Density ρL and Saturated Vapor Density ρv of the VLE for the System CO2 (1) + R-1234ze(E) (2) T/K

p/MPa

u(p)/MPa

x1

273.15

0.212 0.5 1.0 1.5 2.0 3.467 0.448 1.0 1.5 2.0 2.5 3.5 5.684

0.028

0.000 0.128 0.317 0.491 0.636 1.000 0.000 0.169 0.289 0.402 0.511 0.696 1.000

293.15

0.063 0.064

0.223

u(x1) 0.007 0.016 0.016 0.014

0.008 0.013 0.014 0.018 0.011

y1

u(y1)

0.000 0.600 0.816 0.904 0.941 1.000 0.000 0.601 0.739 0.819 0.867 0.927 1.000

0.011 0.020 0.010 0.006

0.021 0.020 0.013 0.012 0.004

ρL/kg m−3

u(ρL)/kg m−3

ρV/kg m−3

u(ρV)/kg m−3

1265.0 1243.6 1206.1 1162.2 1118.1 935.4 1199.4 1165.4 1143.7 1113.7 1080.1 1014.4 797.8

5.6 5.5 8.5 8.4 9.6 1.4 7.6 6.2 8.4 9.1 12.3 8.3 16.6

11.4 17.0 27.7 37.9 50.2 93.0 23.7 33.3 44.3 55.2 67.1 93.4 173.6

1.6 3.9 0.8 1.1 0.7 2.3 3.7 0.9 3.6 1.4 1.6 2.1 15.6

Ares Ahc Apert = + NkBT NkBT NkBT

the temperature range from (273.15 to 313.15) K are given in the Tables 2 to 5. To correlate the vapor−liquid equilibra (VLE), we employed the PC-SAFT equation of state,17 in which the molecules are modeled as hard chains (hc) formed by m equal spherical segments, which interact according to a modified square-well potential. The dispersive, attractive interactions between molecules are treated as a perturbation to the reference hard chain fluid. Thus, the residual free energy Ares of the system is given by

(3)

as a function of the molecular parameters m, σ*, and ε*. The segment diameter σ* and the interaction-energy parameter ε* are here marked with an asterisk to distinguish the PC-SAFT parameters from the LJ-parameters of the force field model used in molecular simulations. For CO2, we used the PC-SAFT parameters proposed in ref 17, whereas the parameters of the R-32 were taken from Vinš and Hrubý.29 To our best knowledge, there are no PC-SAFT parameters available in D



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Table 6. PC-SAFT Parameters for the Refrigerants Studied in This Work refrigerant

M/g mol−1

m

σ*/A

ε*/k /K

source

R-32 CO2 R-1234yf R-1234ze(E)

52.02 44.01 114.01 114.01

2.57587 2.07274 2.89776 3.17339

2.76916 2.7852 3.36482 3.21344

180.9438 169.21 174.9142 175.3067

Vinš and Hrubý29 Gross and Sadowski17 this work, fitted to expt data in ref 30 to 32 this work, fitted to expt data in ref 33

literature for the tetrafluoropropene compounds R-1234yf and R-1234ze(E). Thus, the parameters were derived in this work by fitting calculated vapor pressure and liquid densities to experimental data.30−33 The PC-SAFT parameters used in this work are listed in Table 6. To model the refrigerant mixtures, we used the common combining rules for the PC-SAFT parameters εij* =

εii*εjj* (1 − kij),

σij* =

σii* + σjj* 2

(4)

that employ an interaction parameter kij for the interaction energy ε*ij between unlike segments. For the mixture R-32 + R1234yf, for which experimental data for the VLE at different temperatures are available in literature,7 the kij was derived by fitting correlation results to the experimental data. For the other mixture, that is, R-32 + R-1234ze(E), CO2 + R-1234yf, and CO2 + R-1234ze(E), the interaction parameters kij for the PCSAFT correlations were fitted to our predicted VLE data from molecular simulation. The interaction parameters kij and the resulting deviations between the PC-SAFT correlations and experimental data or GEMC simulation results for the pressure and the molar composition of the vapor phase are summarized in Table 7.

Figure 3. Comparison between GEMC simulation results (boxed plus sign) obtained in this work, experimental data (circled dot7) and PCSAFT correlations (as lines, with kij fitted to the experimental data) for the VLE in the binary system R-32 + R-1234yf at 273.15 K, 293.15 K, and 313.15 K.

Table 7. PC-SAFT Interaction Parameters kij, and Correlation Results for the Vapor−Liquid Equilibria of the Binary Refrigerant Mixtures Studied in This Work refrigerant mixture R-32 + R-1234yf R-32 + R-1234ze(E) CO2 + R-1234yf CO2 + R-1234ze(E)

kij

Δp, RAD/%

Δy, AAD/mol mol−1

data used for fitting

0.03376

0.79

0.005

0.02700

2.74

0.004

0.03746

1.59

0.008

0.01029

1.83

0.002

expt data from ref 7 simulation results, this work simulation results, this work simulation results, this work

Figure 4. Comparison between GEMC simulation results (boxed plus sign) obtained in this work and PC-SAFT correlations (as lines, with kij fitted to the GEMC simulation results) for the VLE in the binary system R-32 + R-1234ze(E) at 273.15 K, 293.15 K, and 313.15 K. Also shown are experimental data (solid circle9) at temperatures from T = (292.55 to 292.77) K.

parameter for the PC-SAFT calculations were fitted to our GEMC simulations results, as they also cover a broader temperature range (40 K) than the experimental data. Again, we found generally good agreement between experimental data, molecular simulation results, and PC-SAFT correlations. However, deviations between PC-SAFT-correlations and GEMC simulation results are again observed at 313.15 K, which also result in the comparatively higher averaged deviation in pressure (Δp = 2.74 %) for this system. The GEMC simulation results for the VLE of the zeotropic mixtures CO2 + R-1234yf and CO2 + R-1234ze(E) and correlations by PC-SAFT are shown in Figures 5 and 6. To our best knowledge, no experimental data are available in the literature for these systems. Thus, the PC-SAFT interaction parameters were again fitted to our molecular simulation results. For these refrigerant mixtures, we observe a much higher pressure drop between bubble and dew point curve as

The depiction of the GEMC simulation results, experimental data, and calculated isotherms for the mixtures R-32 + R-1234yf in Figure 3 illustrates the capability of the PC-SAFT EOS to reproduce the vapor−liquid equilibria in this system. However, most importantly the good agreement between the molecular simulation results and experimental data attests the predictive ability of our force field models used in the GEMC simulations studies. Solely at 313.15 K, some discrepancies between the GEMC simulations and experimental data and accordingly PCSAFT-calculations can be observed. Still, over all temperatures, deviations between GEMC simulation results, and PC-SAFT calculations average to only Δp = 1.8 % and Δy = 0.006 mol mol−1. For the binary mixture R-32 + R-1234ze(E) experimental data9 are only available at (282 and 292) K, which in addition reveal some scattering as shown by the depiction of the data for the 293 K isotherm in Figure 4. Thus, for this mixture, the kij E



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saturated densities for the mixtures CO2 + R-1234yf and CO2 + R-1234ze(E). We have also correlated the VLE with the PC-SAFT model that yields a good description of the refrigerant mixtures. With this, we also provide PC-SAFT parameters for the pure compounds R-1234yf and R-1234ze(E) and for the binary mixtures studied in this work.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 531 391 2628. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

Figure 5. GEMC simulation results (boxed plus sign) obtained in this work for the VLE in the binary system CO2 + R-1234yf at 273.15 and 310.92 K. Also shown as lines are correlation results from the PCSAFT EOS with kij fitted to the molecular simulation results.

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ACKNOWLEDGMENTS We thank Dr. Ryo Akasaka, Kyushu Sangyo University, for sharing his experimental information for the system R-32 + R1234ze(E) with us.

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REFERENCES

(1) Spatz, M.; Minor, B. HFO-1234yf, a low GWP refrigerant for MAC. VDA Alternative Refrigerant Winter Meeting, Saalfelden, Austria, 2008. (2) Yana Motta, S. F.; Vera Bercerra, E. D.; Spatz, M. W. Analysis of LGWP alternatives for small refrigeration (plugin) applications. Int. Refrig. Air Condition. Conf. Purdue 2010, Paper No. 1149. (3) Ref rigerant Report 17; Bitzer Kühlmaschinenbau GmbH: Germany, 2012. (4) Koyama, S.; Takada, N.; Matsuo, Y.; Yoshitake, D.; Fukuda, S. Possibility to introduce HFO-1234ze(E) and its mixtures with HFC32 as low-GWP alternative for heat pump/refrigeration systems. 2010 International Symposium on Next-Generation Air Conditioning and Refrigeration Technology, Tokyo, Japan, 2010. (5) Fujitaka, A.; Tsutomu, S.; Shigehiro, S.; Kawabe, Y. Application of low global warming potential refrigerants for room air conditioner. 2010 International Symposium on Next-Generation Air Conditioning and Refrigeration Technology, Tokyo, Japan, 2010. (6) Peral-Antŭnez, E. MAC refrigerant blend cooperative research programUpdate. TMSS Symposium SAE International, Scottsdale Arizona, USA, 2012. (7) Kamiaka, T.; Dang, C.; Hihara, E. Vapor−liquid equilibria measurement for the binary mixtures of R1234yf with R32, R125, and R134a. Int. J. Refrig., article in press (8) Dong, X.; Gong, M.; Shen, J.; Wu, J. Vapor−liquid equilibria of the trans-1,3,3, tetrafluoropropene (R1234ze(E)) + isobutane (R600a)) system at various temperatures from (258.15 to 288.15)K. J. Chem. Eng. Data 2012, 57, 541−544. (9) Asasaka, R. Vapor−liquid equilibrium modeling for mixtures of HFC-32 + Isobutane and HFC-32 + HFO-1234ze(E). Int. J. Air-Cond. Refrig. 2011, 19 (2), 93−97. (10) Yamaya, K.; Matsuguchi, A.; Kagawa, N.; Koyama, S. Isochoric specific heat capacity of trans-1,3,3,3 tetrafluoropropene (HFO1234ze(E)) and the HFO-1234ze(E) + CO2 mixtures in the liquid phase. J. Chem. Eng. Data 2011, 56, 1535−1539. (11) Di Nicola, G.; Di Nicola, C.; Arteconi, A.; Styjek, R. PVTx measurement of the carbon dioxide + 2,3,3,3-tetrafluoroprop-1-ene binary system. J. Chem. Eng. Data 2012, 57, 450−455. (12) Miyara, A.; Tsubaki, K.; Sato, N. Thermal conductivity of HFO1234ze(E) + HFC-32 mixtures. International Symposium on NextGeneration Air Conditioning and Refrigeration Technology, Tokyo, Japan, 2010. (13) Raabe, G.; Maginn, E. J. Molecular modeling of the vapor− liquid equilibrium properties of the alternative refrigerant 2,3,3,3tetrafluoro-1-propene HFO-1234yf. J. Phys. Chem. Lett. 2010, 1, 93− 96.

Figure 6. GEMC simulation results (circled plus sign) obtained in this work for the VLE in the binary system CO2 + R-1234ze(E) at 273.15 and 293.15 K. Also shown as lines are correlations from the PC-SAFT EOS with kij fitted to the molecular simulation results.

for the R-32 mixtures. The highest difference between bubble and dew point pressure for the mixture CO2 + R-1234zeE is round about 1.69 MPa at a total mole fraction zCO2 = 0.8, whereas for CO2 + R-1234yf it is approximately 1.38 MPa at zCO2 = 0.75. Our predicted p−x diagrams for these mixtures are similar to the experimental isotherms34 for the mixture CO2 + R134a, from which we conclude that our GEMC simulation studies also yield reliable predictions for vapor−liquid equilibria of the mixtures CO2 + R-1234yf and CO2 + R-1234ze(E).

4. CONCLUSION We have presented GEMC molecular simulation studies for the vapor−liquid phase equilibria in the binary mixtures R-32 + R1234yf, R-32 + R-1234ze(E), CO2 + R-1234yf and CO2 + R1234ze(E) at temperatures from (273.15 to 313.15) K. The simulation studies were based on our force field model for fluoropropenes,13−15 a new molecular model for R-32 proposed in this work, and the TraPPE model16 for CO2. Standard combining rules with no adjusted interaction parameters were used to determine the Lennard-Jones parameter between unlike atom types: Thus, all molecular simulation results for the mixtures are purely predictive. The good agreement between our GEMC simulation results and experimental data for R-32 + R-1234yf and R-32 + R-1234ze(E) attests the predictive capability of our molecular simulation studies. Our GEMC simulations also provide first information on the VLE including F



Article

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