Molecular Simulation Studies on the Thermophysical Properties of the

Article pubs.acs.org/jced

Molecular Simulation Studies on the Thermophysical Properties of the Refrigerant Blend R‑445A Gabriele Raabe* Institut für Thermodynamik, Technische Universität Braunschweig, Hans-Sommer-Str. 5, 38106 Braunschweig, Germany ABSTRACT: The ternary mixture of CO2, the tetrafluoroethane R-134a, and the trans-1,3,3,3-tetrafluoro-1-propene (R-1234ze(E)) has recently been proposed as refrigerant blend R-445A for mobile air conditioning (MAC) systems. However, the lack of experimental data for the thermophysical properties of this refrigerant blend hampers studies on its performance in MAC systems or other potential 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 have introduced a force field model for different fluoropropenes. In this work, we employ the molecular model for Gibbs ensemble simulation studies on the vapor−liquid equilibrium (VLE) properties of the ternary refrigerant blend R-445A in the temperature range from T = (260 to 330) K. In addition, we present predictions from molecular dynamics simulations for the densities and viscosities of the mixture in the liquid phase at temperatures from T = (270 to 315) K and pressures up to 1.6 MPa. All simulation results are compared to calculations by REFPROP 9.1 Agreement between simulation and correlation is in general good, which attests the predictive capability of the molecular simulation studies.

1. INTRODUCTION Due to their low global warming potential (GWP), hydrofluoroolefines (HFOs) such as the trans-1,3,3,3-tetrafluoro-1propene (R-1234ze(E)) have been proposed as new refrigerants.1,2 However, tetrafluoropropenes are flammable,3 and they also have smaller volumetric cooling capacities than conventional hydrofluorocarbon (HFC) refrigerants.4 Thus, blends of HFOs and nonflammable compounds are regarded as suitable choice to yield refrigerants that have reduced flammabilities and higher volumetric refrigerant capacities than pure HFOs and low enough GWPs. With this, also blends are discussed as alternative refrigerants for mobile air conditioning (MAC) systems. One blend that has recently attracted attention is AC6,5 that is, R-445A, which is a ternary zeotropic blend of CO2, the tetrafluoroethane R-134a, and the trans-1,3,3,3-tetrafluoro1-propene (R-1234ze(E)). Investigations on the performance of this refrigerant mixture in MAC systems or other potential technical applications though demand a detailed knowledge of its thermodynamic and transport properties. Potential issues arising from the use of zeotropic refrigerant blends in a MAC system are composition changes during the refrigerant cycle and selective leakages. CO2 is more volatile than R-134a and R-1234ze(E); thus, its high composition in the vapor phase results in its highest potential leak rate. Thus, also information on the compositions of the vapor and liquid phase at relevant working conditions of vaporization and condensation are needed. However, to our best knowledge, there exist no such experimental data for the ternary mixture. For the classical modeling of mixtures by equations of state, experimental data for the binary subsystems are required to derive mixing parameters. Though only a © 2013 American Chemical Society

limited number of experimental studies of the binary subsystems are available in literature. These studies only comprise vapor−liquid equilibrium (VLE)6−8 and PVTx9 measurements for the binary mixture CO2 + R-134a and experimental information on isochoric heat capacities of the CO2 + R-1234ze(E) mixture.10 Molecular simulation studies are a useful tool to provide predictions on relevant properties of mixtures to complement experimental data, provided that adequate molecular models, that is, force fields for the compounds exist. In our earlier work,11−13 we have introduced a transferable force field for different fluoropropene compounds such as R-1234yf or R1234ze(E). Simulation studies on the vapor−liquid phase equilibria and liquid phase properties of the pure compounds have shown that the force field model enables reliable reproductions and predictions for a wide range of their thermophysical properties. In our recent work,14 we have employed the force field for predictive simulation studies on the vapor−liquid phase equilibria in binary mixtures of the tetrafluoropropenes R-1234yf or R-1234ze(E) with the difluoromethane R-32 and CO2. We have there found good agreement between our simulation results and experimental data (where available), which attests to the predictive capability of our molecular simulation studies also for mixtures. In this work, we employ the force field model for fluoropropenes together with common models from literature for CO215 and R-134a16 for simulation studies in the system Received: August 15, 2013 Accepted: October 15, 2013 Published: November 1, 2013 3470

dx.doi.org/10.1021/je400738r | J. Chem. Eng. Data 2013, 58, 3470−3476

Journal of Chemical & Engineering Data

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CO2 + R-134a + R-1234ze(E). Thus, we first present Gibbs ensemble Monte Carlo (GEMC) simulations on the VLE in the binary subsystems CO2 + R-134a, CO2 + R-1234ze(E), and R134a + R-1234ze(E). We then provide predictions on the VLE of the refrigerant blend R-445A, which is a mixtures of 6 % CO2 + 9 % R-134a + 85 % R-1234ze(E) (by mass). The GEMC simulations on the phase equilibria properties were performed in the temperature range from T = (260 to 330) K and pressure range from p = (0.3 to 1.68) MPa to cover typical working conditions in the evaporator and condenser of a mobile air conditioning cycle. Additionally, we present MD simulation results on the liquid densities and viscosities of the ternary mixture at temperatures from T = (270 to 315) K and pressures up to 1.6 MPa. All simulation studies are compared with predictions by REFPROP 9.1.17

without any adjusted interaction parameters. Thus, all simulation results on mixtures are purely predictive! Simulation Details. VLE of the binary subsystems and the ternary R-445A mixture were studied by Monte Carlo Gibbs ensemble19 (GEMC) simulations in the isothermal−isobaric (NPT) ensemble using the simulation code TOWHEE.20 The Ewald sum technique21,22 was used to calculate the long-range electrostatic interactions, for which the cutoff radius was adjusted to half the box length. For the LJ interactions the cutoff radius was set to 12 Å, and standard long-range corrections22 were applied to the energy and pressure. For simulations in the binary mixtures, all systems consisted of N = 400 molecules in the sum. However, the number of the molecules of both components varied, depending on the mixture and the state point. Estimates for feed compositions lying in the two-phase region at given temperatures and pressures were derived from REFPROP calculations. In the simulation studies on the ternary refrigerant blend R445A, the system contained N = 396 molecules, that is, 56 CO2 + 36 R-134a + 304 R-1234ze(E) to give the required molar composition of xCO2 = 0.141, xR‑134a = 0.091, and xR‑1234ze(E) = 0.768. For studies on the R-445A with given feed composition, REFPROP calculations were used to estimate the temperature range of the VLE for the chosen pressure. All simulations were 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 300 000−400 000 cycles. Each cycle consisted of N attempted moves, such as a volume exchange move between both boxes,23 rotational-bias,24 and configurational-bias25 interbox molecule transfer, intrabox configurational-bias molecule transfer, molecule regrowth, or molecular translation and rotation around the center-of-mass. The moves were selected at random with fixed probabilities, which were in the order of (0.3 to 0.5) % volume moves, (35 to 55) % interbox molecular transfer moves, and (45 to 65) % intrabox moves. The probabilities of the moves for the different components in the mixture were manually adjusted to ensure that the equilibrium conditions were satisfied, that is, that the simulated chemical potentials of all components in both phases agreed within the error bars. We have additionally performed molecular dynamics (MD) simulation studies on liquid R-445A using the DL_POLY simulation package.26 The cubic boxes consisted again of N = 396 molecules (56 CO2 + 36 R-134a + 304 R-1234ze(E)), and periodic boundary conditions were applied. The cutoff radii were set to 15 Å, and the Ewald sum was used to deal with the electrostatic interactions. To obtain averaged liquid densities at given temperatures and pressures, we first performed simulations in the Nosé−Hoover27,28 NpT ensemble. The trajectories were integrated by the velocity Verlet algorithm22 with a time step of Δt = 0.0005 ps. The thermostat and barostat relaxation times were set to of τT = 0.1 ps and τp = 1.0 ps, respectively. The systems were equilibrated for 2.5 ns, followed by a productions run of again 2.5 ns. The shear viscosities of liquid R-445A were derived from additional simulations in the Nosé−Hoover−NVT ensemble27 with a thermostat coupling constant of τT = 0.5 ps. The systems were again equilibrated for 1 ns at the average densities obtained from the NpT-simulations, before we performed production runs of 10 ns in the NVT ensemble, in which we

2. COMPUTATIONAL METHODS Force Field Models. In our fully flexible all-atoms force field for fluoropropenes, the potential energy is expressed by the following standard functional form18 Uconf =

∑

kr(r − r0)2 +

bonds

∑

+

∑

kθ(θ − θ0)2

angles

kχ [1 + cos(nχ − δ)]

dihedral

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

Therein, the intermolecular interaction energy is presented by Lennard−Jones (LJ) site−site terms and electrostatic interactions between fixed partial charges on the atomic sites. The calculation of the intramolecular potential energy is based on harmonic terms for bond stretching and angle bending and a cosine term to account for energy changes due to internal torsions. Full LJ and electrostatic interactions are considered between atoms in the same molecules separated by more than three bonds, whereas interactions between atoms separated by exactly three bonds (1−4 interactions) are scaled by a factor of 1/2 (LJ) and 1/1.2 (electrostatic). More details on the parametrization of the molecular model are given in earlier works.11,12 The Supporting Information of ref 13 provides a complete list of our force field parameters for the fluoropropene modeling. The all-atom force field for R-134a by Peguin at al.16 follows a similar approach as we used in our fluoropropene force field. However, their description of the intramolecular energy only includes angle bending and torsion terms, whereas the bonds are considered rigid. Furthermore, they use a different functional form for the torsion potential, that is, a cosine series. In the TraPPE model by Potoff and Siepmann15 for carbon dioxide, the calculation of intermolecular interaction is also based on LJ site and fixed partial charges on the three atomic sites. However, the TraPPE force field models CO2 as a rigid molecule. In our simulation studies, all LJ parameters for interactions between unlike atoms are obtained from the Lorentz−Berthelot combining rule, that is, εij =

εiiεjj

σij =

σii + σjj 2

(2) 3471



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Table 1. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Vapor-Phase Mole Fraction y, Saturated Liquid Density ρL, and Saturated Vapor Density ρV of the VLE for the System CO2 (1) + R-134a (2)a T

p

K

MPa

MPa

x1

273.15

0.310 0.4 0.7 1.0 1.4 1.8 2.0 3.467 0.608 0.8 1.4 2.0 3.0 5.684 1.100 1.2 2.0 3.0 4.0 5.0

0.033

0.0 0.037 0.138 0.254 0.392 0.511 0.598 1.0 0.0 0.053 0.196 0.335 0.545 1.0 0.0 0.030 0.164 0.329 0.482 0.626

293.15

313.15

a

ρL

u(p)

0.063 0.058

0.223 0.056

u(x1)

y1 0.0 0.242 0.556 0.725 0.823 0.881 0.913 1.0 0.0 0.254 0.585 0.732 0.853 1.0 0.0 0.129 0.456 0.659 0.768 0.842

0.003 0.009 0.014 0.021 0.018 0.012

0.004 0.010 0.018 0.020

0.002 0.010 0.012 0.017 0.017

u(y1) 0.016 0.019 0.022 0.017 0.010 0.004

0.012 0.020 0.015 0.013

0.006 0.022 0.015 0.014 0.010

u(ρL) −3

kg·m

1283.6 1275.0 1259.2 1231.7 1195.9 1162.3 1121.5 935.4 1213.0 1200.8 1170.8 1132.6 1062.0 797.8 1136.5 1119.0 1093.6 1044.7 984.0 908.6

kg·m

−3

4.6 7.0 7.1 8.5 11.1 10.5 7.3 1.4 7.3 7.1 8.2 12.0 15.1 16.6 8.6 8.9 9.4 12.3 17.3 19.8

ρV kg·m

u(ρV) −3

15.1 16.8 23.6 29.4 38.2 47.5 51.4 92.9 29.2 32.7 45.6 58.8 83.0 173.6 53.6 53.2 73.7 96.2 122.6 152.5

kg·m−3 1.8 0.2 0.5 0.8 0.9 0.7 0.5 2.3 2.3 0.4 1.1 1.6 1.9 15.6 3.4 0.5 1.9 2.4 3.4 3.5

U denotes standard deviations of the simulation results derived by the standard block average technique.

the mixture at 273 K and 293 K, presented in our earlier work.14 For the binary mixture R-134a + R-1234ze(E) though, no experimental or simulation data are available until now. Thus, for this mixture, an estimation scheme to approximate the interaction parameters is used in REFPROP. GEMC Simulation Studies on the Binary Systems. Prior to simulation studies in the ternary mixture, we performed GEMC simulations on the VLE of the binary system CO2 + R134a, for which experimental data exist, to check, if the combination of the two force field models from literature yield a reliable description of the mixture. The molecular simulation results for the compositions and saturated densities of the liquid and vapor phase of the VLE at 273.15 K, 293.15 K, and 313.15 K are given in Table 1. Figure 1 shows a comparison of calculated isotherms by REFPROP, experimental data by

saved the pressure tensors every 0.0025 ps for further analysis by in-house programs. The shear viscosities were then computed by the Green− Kubo22 method of integrating the averaged autocorrelation function of the three independent off-diagonal elements of the viscous pressure tensor pαβ. η=

V 3k bT

∫0

∞

[⟨pxy (0) ·pxy (t )⟩ + ⟨pxz (0) ·pxz (t )⟩

+ ⟨pyz (0) ·pyz (t )⟩]dt

(3)

Standard deviations of all simulation results from GEMC and MD were determined by the standard block average technique,22 dividing the simulation runs into 10 blocks.

3. RESULTS AND DISCUSSION In this section we present GEMC simulation results for the compositions of the liquid and vapor phase and for the saturation densities of the VLE of the binary mixtures CO2 + R134a, CO2 + R-1234ze(E), and R-134a + R-1234yf and the ternary blend R-445A, as well as liquid densities and viscosities of R-445A from molecular dynamics studies. All simulation results are compared to predictions using REFPROP 9.1,17 which employs accurate Helmholtz energy equations of state to model the thermodynamic properties of the pure compounds CO2,29 R-134a,30 and R-1234ze(E).31 The viscosity calculation for the pure compounds is based on fluid specific correlations for CO232 and R-134a33 and an extended corresponding state model for R-1234ze(E).17 Correlations for mixture properties in REFPROP though require the fitting of binary mixing parameters. For the binary system CO2 + R-134a, for which experimental data are available, REFPROP uses experimentally based values for the mixture parameters. The REFPROP parameters for the binary system CO2 + R-1234ze(E) were obtained from our molecular simulation results for the VLE in

Figure 1. Comparison between GEMC simulation results (green crossed □, xCO2; green crossed ○, yCO2) obtained in this work, experimental data8 (gray ■, gray ●) and REFPROP 9.117 calculations (as lines, binary interaction parameters fitted to the exp. data) for the VLE in the binary system CO2 + R-134a at 273.15 K, 293.15 K, and 313.15 K. 3472



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Table 2. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Vapor-Phase Mole Fraction y, Saturated Liquid Density ρL, Saturated Vapor Density ρV, and Standard Deviations u of the Properties for the VLE in the Systems CO2 (1) + R-1234ze(E) (2) and R-134a (1) + R-1234ze(E) (2) T

p

ρL

u(p)

K

MPa

MPa

x1

313.15

0.790 2.0 3.0 4.0 5.0 6.0

0.051

0 0.235 0.412 0.553 0.681 0.787

273.15 293.15 313.15

0.25 0.5 0.9

0.237 0.288 0.313

u(x1)

y1

u(y1)

CO2 (1) + R-1234ze(E) (2) 0 0.011 0.606 0.019 0.012 0.765 0.015 0.023 0.837 0.015 0.018 0.887 0.010 0.018 0.917 0.009 R-134a (1) + R-1234ze(E) (2) 0.002 0.319 0.022 0.008 0.361 0.011 0.012 0.376 0.014

u(ρL) −3

kg·m

kg·m

−3

ρV kg·m

u(ρV) −3

kg·m−3

1159.6 1076.6 1022.7 968.4 902.5 813.4

7.7 10.7 13.7 19.1 24.5 53.8

30.2 67.6 89.4 116.7 146.5 188.8

3.3 2.1 3.1 3.9 5.2 13.3

1268.6 1202.7 1128.1

5.9 4.7 5.2

12.4 25.3 45.6

0.7 0.5 0.9

Duran-Valencia et al.,8 and GEMC simulation results from this work. The good agreement between the simulation results and both experimental data and REFPROP calculations illustrates that the combination of the two force field models from literature is well-suited to describe this mixture. GEMC simulation results for the VLE in the mixture CO2 + R-1234ze(E) at 273.15 K and 293.15 K were already presented in our earlier work14 and were used to derive the REFPROP mixture parameter for this binary subsystem. Thus, in Table 2 we only provide additional simulation results for the 313.15 K isotherm. Our predicted p−x diagrams for this mixture in Figure 2 are similar to the isotherms for the system CO2 + Figure 3. Comparison between GEMC simulation results (purple crossed □, xR‑134a; purple crossed ○, yR‑134a) obtained in this work, and REFPROP calculations (as lines, binary interaction parameters estimated) for the VLE in the binary system R-134a + R-1234ze(E) at 273.15 K, 293.15 K, and 313.15 K.

mixture are very narrow and therefore challenging to study by GEMC simulations. Thus, we have only performed exemplary simulations for this mixture, which are also given in Table 2. The depiction of the GEMC simulation results in Figure 3 shows fair agreement with the predictions by REFPROP. However, the molecular simulations in general yield higher R134a compositions in both the liquid and the vapor phases. GEMC Simulation Studies on the VLE of R-445A. GEMC simulation results for the molar compositions of the liquid and vapor phases of the VLE in R-455A are given in Table 3, together with simulation results for the saturation densities. The general trend found in the simulations is that, at constant pressure, the CO2 composition in both the liquid and the vapor phases decreases with increasing temperature. The R134a compositions in the liquid phase only change a little in the temperature and pressure range studied here, whereas yR‑134a increases with increasing temperature. It is worth mentioning that, in the composition range of R-445A, the R-134a compositions in the liquid and vapor phases are always very similar, and they become nearly identical for the VLE at higher temperatures, that is, T = (300 to 330) K. The use of R-445A in MAC systems raises the question of the selective leakage of CO2. This necessitates knowledge of the CO2 composition in the vapor phase during vaporization and condensation. Figure 4 shows predictions by REFPROP for the CO2 composition in the coexisting phases as a function of

Figure 2. Comparison between GEMC simulation results (red crossed □, xCO ; red crossed ○, yCO ) obtained in this work, and REFPROP17 2 2 calculations (as lines, binary interaction parameters fitted to molecular simulation results) for the VLE in the binary system CO2 + R1234ze(E) at 273.15 K, 293.15 K, and 313.15 K.

R134a shown in Figure 1. This would be expected as the alternative refrigerant R-1234ze(E) shall offer comparable thermophysical properties to R-134a. From this correctly predicted similarity of the phase diagrams for the both mixtures, we conclude that the molecular modeling and the GEMC simulation studies also yield reliable predictions for the VLE in the mixture CO2 + R-1234ze(E), for which no experimental data are available. To our best knowledge, there are no experimental data in literature for the VLE in the mixture R-134a + R-1234ze(E). Thus, the calculated isotherms in Figure 3 are based on estimated mixture parameters in REFPROP. The predictions by REFPROP indicate that the phase envelopes in this azeotropic 3473



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Table 3. GEMC Simulation Results for the Temperature T, Pressure p, Liquid-Phase Mole Fraction x, Vapor-Phase Mole Fraction y, Saturated Liquid Density ρL, and Saturated Vapor Density ρV of the VLE for the Ternary Refrigerant Blend R-445A of 0.141 CO2 (1) + 0.091 R-134a(2) + 0.768 R-1234ze(E) (3) (Molar Feed Composition)a T

a

ρL

p

u(ρL) −3

K

MPa

x1

u(x1)

x2

u(x2)

y1

u(y1)

y2

u(y2)

kg·m

260.0 265.0 270.0 260.0 265.0 270.0 278.2 273.2 278.2 305.0 310.0 315.0 320.0 320.0 320.0 330.0 320.0

0.30 0.30 0.30 0.35 0.35 0.35 0.35 0.40 0.40 1.15 1.15 1.15 1.40 1.50 1.60 1.60 1.68

0.095 0.074 0.049 0.123 0.096 0.063 0.032 0.076 0.053 0.112 0.084 0.053 0.069 0.088 0.109 0.055 0.119

0.008 0.008 0.014 0.008 0.012 0.004 0.003 0.007 0.006 0.008 0.006 0.006 0.012 0.007 0.021 0.004 0.007

0.093 0.093 0.091 0.092 0.093 0.092 0.082 0.093 0.090 0.092 0.091 0.088 0.089 0.092 0.092 0.087 0.092

0.009 0.001 0.003 0.001 0.001 0.002 0.005 0.001 0.003 0.001 0.003 0.003 0.002 0.009 0.004 0.002 0.002

0.563 0.480 0.358 0.637 0.539 0.406 0.232 0.449 0.344 0.426 0.333 0.224 0.257 0.308 0.362 0.191 0.385

0.037 0.042 0.022 0.032 0.055 0.022 0.009 0.037 0.026 0.028 0.021 0.021 0.044 0.024 0.032 0.014 0.022

0.069 0.080 0.256 0.060 0.069 0.086 0.097 0.081 0.091 0.079 0.088 0.093 0.092 0.088 0.084 0.093 0.082

0.008 0.008 0.006 0.007 0.007 0.006 0.004 0.006 0.005 0.004 0.003 0.003 0.003 0.003 0.003 0.001 0.004

1292.9 1279.1 1266.3 1288.2 1275.8 1268.1 1244.2 1253.6 1241.1 1137.7 1124.1 1110.7 1089.4 1084.9 1076.2 1040.6 1074.3

kg·m

−3

6.3 8.1 7.0 6.6 7.5 7.3 8.6 6.9 8.2 9.0 7.0 10.8 9.5 7.6 10.0 10.5 9.3

ρV kg·m

u(ρV) −3

10.8 11.4 12.5 11.3 12.7 14.1 15.8 15.4 16.6 43.8 47.5 51.9 62.1 63.9 65.3 74.8 66.8

kg·m−3 0.4 0.5 0.3 0.7 0.7 0.3 0.1 0.6 0.4 2.1 1.3 1.2 2.9 2.4 3.4 1.6 2.8

Also given are the standard deviations u of the simulation results determined from block average technique.

conditions of evaporation at low temperatures and pressures. To receive an impression how the composition of the coexisting phases would change due to a CO2 loss, the ternary phase diagram of mixtures of CO2 + R-134a + R1234ze(E) at 278 K and 0.35 MPa is depicted in Figure 5, with calculated

Figure 4. GEMC simulation results obtained in this work for the CO2 compositions in the liquid (blue crossed □, xCO2) and vapor phase (blue crossed ○, yCO2) in the VLE of R-445A as a function of temperature at different pressures. Also shown are REFPROP calculations for different pressures: 0.3 MPa (black line), 0.35 MPa (black dashed line), 0.4 MPa (black dotted line), 1.15 MPa (gray line), and 1.6 MPa (gray dashed−dotted line).

Figure 5. VLE ternary phase diagram of mixtures of CO2 + R-134a + R-1234zeE at 278 K and 0.35 MPa with calculated dew and bubble point lines by REFPROP. GEMC simulation results obtained in this work for the composition in the liquid (blue crosssed □) and vapor phase (blue crossed ○). The cyan filled square marks the feed composition of R-445A, the cyan crossed square the feed composition with reduced CO2-content (40 molecules), and the cyan arrow describes the change in feed composition due to CO2 loss.

temperature at different isobaric conditions of vaporization (p = (0.3 to 0.4) MPa) and condensation (p = (1.15 and 1.6) MPa). Also shown are GEMC simulation results from this work. Both GEMC simulations and REFPROP calculations agree well in describing the decreasing CO2 composition in the liquid and vapor phase for increasing temperatures at p = const. At lower temperatures [(260 to 278) K], the simulation results for the CO2 composition in the liquid phase are in good agreement with the predictions by REFPROP, whereas the simulations tend to yield higher CO2 compositions in the vapor phase compared to the REFPROP calculations. At higher temperatures, the GEMC simulations estimate lower CO2 compositions in both the liquid and the vapor phase than REFPROP. The depiction of the CO2 compositions in Figure 4 shows that the highest CO2 compositions in the vapor phase occur at

dew and bubble point lines by REFPROP. The two-phase region is quite narrow and ranges from the VLE in the subsystem CO2 + R-1234ze(E) to the azeotropic point in the R-134a + R-1234ze(E) mixture. Also shown are GEMC simulation results for the vapor and liquid phase composition of R-445A and the binary subsystem CO2 + R-1234ze(E). Again good agreement is found between the molecular simulation results and predictions by REFPROP for the 3474



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compositions of the coexisting phases. The cyan filled square represents the feed composition of R-445A, and the cyan crossed square the feed composition with a CO2 content reduced from 56 to 40 molecules. The simulation results for the compositions of the vapor and liquid phase for this feed composition are also shown, and they are very close to the equilibrium compositions in the VLE of the original R-445A composition. Though, the feed composition of the refrigerant mixture with reduced CO2 content is shifted closer to the boiling curve. The cyan arrow marks the change in composition of the refrigerant blend when more CO2 is removed from mixtures, and it ends in the liquid phase region of the R-134a + R-1234ze(E) binary mixture. MD Simulations on Liquid-Phase Properties of R445A. We have additionally performed MD simulation studies to derive predictions for the densities and viscosities of R-445A in the liquid phase. The simulation results for the temperature range from T = (270 to 315) K and pressures from p = (1 to 1.6) MPa are summarized in Table 4 and depicted in Figure 6.

dependence of the shear viscosities and densities of liquid R445A is negligible in the pressure range studied here. This is also reproduced by the MD simulations, as results at one temperature and different pressures agree with each other within their uncertainties. In general, the MD simulation studies yield densities that are by up to 1.5 % higher than the predictions by REFPROP 9.1. The simulated viscosities though deviate from REFPROP calculations by −2.7 to +4 %. However, both the simulation results and the REFPROP data describe the same temperature dependence for the densities and shear viscosities of R-445A.

4. CONCLUSION We have presented GEMC molecular simulation studies for the vapor−liquid phase equilibria of the ternary refrigerant blend R445A (0.141 CO2 + 0.091 R-134a + 0.768 R-1234ze(E), molar composition) at temperatures from T = (273.15 to 330) K, and for its binary subsystems CO2 + R-134a, R-134a + R1234ze(E), and CO2 + R-1234ze(E) at temperatures from T = (273.15 to 330) K. Additionally we have performed MD simulation studies on the densities and viscosities in the liquid phase region of R-445A at various temperatures and pressures. The simulation studies were based on our force field model for fluoropropenes,11−13 the TraPPE model15 for CO2, and the R134a force field model by Peguin et al.16 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. Our simulation results for both the VLE and the liquid-phase properties are compared with calculations by REFPROP 9.1. The modeling of the mixtures in REFPROP is based on binary interaction parameters that were fitted to experimental data for CO2 + R-134a, to our GEMC simulation results for CO2 + R1234ze(E) from earlier work, and estimated for the mixture R134a + R1234ze(E). In general we found good agreement between predictions from molecular simulation and REFPROP calculations. This attests the capability of our molecular simulation studies to provide reliable predictions for the VLE, densities, and viscosities of the refrigerant blend R-445A, for which no experimental data are available yet.

Table 4. MD Simulation Results for the Liquid Density ρL and Liquid Viscosity ηL at Different Temperatures T and Pressures p for the Ternary Refrigerant Blend R-445A of 0.141 CO2 (1) + 0.091 R-134a (2) + 0.768 R-1234ze(E) (3) (Molar Overall Composition)a

a

T

p

ρL

u(ρL)

ηL

u(ηL)

K

MPa

kg·m−3

kg·m−3

mPa·s

mPa·s

275.0 295.0 270.0 280.0 290.0 300.0 295.0 300.0 315.0

1.00 1.00 1.15 1.15 1.15 1.15 1.60 1.60 1.60

1243.5 1172.1 1258.7 1227.3 1194.4 1155.8 1174.4 1158.6 1099.6

11.8 14.0 11.9 11.5 12.4 13.3 12.9 13.4 16.7

0.2366 0.1872 0.2661 0.2381 0.1968 0.1852 0.1942 0.1784 0.1474

0.0226 0.0169 0.0198 0.0211 0.0028 0.0155 0.0133 0.0100 0.0116

u(ρL) and u(ηL) are the standard deviations of the simulation results.

■

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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REFERENCES

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Figure 6. Comparison between MD simulation results (blue crossed □) obtained in this work, and REFPROP 9.1 calculations (as lines) for the liquid densities and viscosities of the refrigerant blend R-445A as a function of temperature. Both simulations and calculations cover pressures from p = (1.0 to 1.6) MPa.

Different data points at a single temperature in Figure 6 represent simulation results at different pressures. Also shown are calculations by REFPROP for 1 MPa and 1.6 MPa. The calculated lines are very close, which indicates that the pressure 3475



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Molecular Simulation Studies on the Thermophysical Properties of the

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