1

Measurement of Vapor-Liquid Equilibria for the Binary Mixture of

Propylene (R-1270) + Propane (R-290)

Quang Nhu Hoa, Kye Sang Yooa, Byung Gwon Leea*, Jong Sung Limb

aDivision of Environment and Process Technology, Korea Institute of Science and Technology

(KIST), P.O. Box 131, Cheongryang, Seoul 130-650, South Korea

bDepartment of Chemical and Biomolecular Engineering, Sogang University, P.O. Box 1142,

Seoul 100-611, South Korea

Abstract

Isothermal vapor-liquid equilibria data for the binary mixture of propylene (R-1270) +

propane (R-290) at 273.17, 278.15, 283.15, 293.15, 303.15 and 313.15 K were measured by

using a circulation-type equilibrium apparatus. The experimental data were correlated with the

Peng-Robinson equation of state (PR-EOS) combined with the Wong-Sandler mixing rule. It

is confirmed that the data calculated by this equations of state are in good agreement with

experimental data. The azeotropic behaviour was not found in this mixture over range of

temperature studied here.

Keywords: Propane (R-290); Propylene (R-1270); Hydrocarbon mixture; Vapor-Liquid

Equilibria (VLE); Peng-Robinson equation of state (PR-EOS).

(*) Corresponding author: Tel.: 82-2-958-5857; e-mail address: bglee@kist.re.kr

2

1. Introduction

Chlorofluorocarbons (CFCs) have been widely used in a variety of industrial, commercial and

household applications such as refrigerants, blowing agents, propellants, or cleaning agents

due to their outstanding properties. However, CFCs also have a negative effect on the Earth’s

environment, particularly ozone layer. For this reason, the production and use of CFCs will be

completely prohibited within a decade. Initially, some hydrochlorofluorocarbons (HCFCs)

was considered as an alternative of CFCs, but they will be phased out around 2030 because

their ozone depletion potentials (ODPs) and global warming potentials (WGPs) are relatively

high. Hence, much effort has been made to find the suitable replacement for CFCs and

HCHCs. Hydrofluorocarbons (HFCs) - synthetic refrigerants with zero ODPs - were proposed

as promising replacements of these materials. Unfortunately, HFCs have been included in the

basket of green house gases to be regulated by Kyoto Protocol 1997 because their WGPs are

several thousand times higher than CO2. Furthermore high manufacturing cost of these HFCs

will lead to reduce the use and production of HFCs gradually.

In recent years, the utilization of light hydrocarbons, such as propane, butane, propylene, etc.,

as effective refrigerants is believed as an alternative solution because these hydrocarbons are

rather cheap, plentiful and environmentally benign chemicals (zero ODPs and near zero

GWPs) and have many outstanding properties. Even though, flammability of these materials

has caused some concerns, but it was found that hydrocarbon are quite safe in small

applications such as domestic refrigeration and car air-conditioning, due to very small

amounts involved [1].

In this work, isothermal vapor-liquid equilibria data for the binary mixture of propylene (R-

1270) + propane (R-290), which are very important basic information in evaluating the

performance refrigeration cycles and in determining optimal composition of this mixture,

3

were measured at 273.17, 278.15, 283.15, 293.15, 303.15 and 313.15 K by using a

circulation-type equilibrium apparatus. The experimental data were correlated with the Peng-

Robinson [2] equation of state (PR-EOS) combined with the Wong-Sandler [3] mixing rule.

The interaction parameters and average deviations in pressures and in vapor phase

compositions obtained from this equation of state were presented.

2. Experimental Section

2.1. Chemicals

High-grade chemicals of propane and propylene were used for this investigation. Propylene of

purity higher than 99.5% by mass was supplied by Conley Gas Ltd., U.S.A. Propane

produced by M.G. Industries, U.S.A. had purity higher than 99.6 % by mass. The purity of

each chemical was validated by using gas chromatograph.

2.2. Vapor-liquid equilibrium apparatus

The vapor-liquid equilibrium apparatus used in this work was a circulation-type one in which

both liquid and vapor phase were continuously recirculated. Description of the experimental

apparatus has been reported in our previous work [4, 5] and is only briefly discussed here.

The equilibrium cell was a 316 stainless steel with an inner volume of about 85 mL. A pair of

Pyrex glass windows was installed on two sides of the cell to observe the inside during

operation. Inside the cell, a stirring bar rotated at variable speeds was used to accelerate the

attainment of the equilibrium state and to reduce concentration gradients in both phases. The

temperature of the equilibrium cell in the bath was maintained by a bath circulator (RCB-20,

Jeio Tech, Korea). The temperature in the cell was measured with a platinum resistance sensor

connected to a digital temperature indicator (F250 precision thermometer, Automatic Systems

Laboratories Ltd., UK). They were calibrated by NAMAS accredited calibration laboratory.

4

The total error is estimated to be within ± 0.01 K, including sensor uncertainty, ± 0.01 K,

temperature resolution, ± 0.001 K, and measurement uncertainty, ± 0.001 K. The pressure was

measured with a pressure transducer (model XPM60) and digital pressure calibrator indicator

(C106 model, Beamax, Finland). Pressure calibrations are traceable to national standards

(Center for Metrology and Accreditation Certificate Nos. M-95P077 dated 14-11-1995, M-

M730 dated 16-11-1995 and M-95P078 dated 16-11-1995), and total errors were estimated to

be within ± 1 kPa, including calibrator uncertainty was ± 0.5 kPa, sensor uncertainty was ± 1

kPa, and measurement uncertainty was ± 1 kPa. The vapor and liquid phases in the

equilibrium cell were continuously recirculated by a dual-head circulation pump (Milton Roy

Co. USA). After equilibrium was reached, the vapor and liquid samples were withdrawn from

the recycling loop and injected on-line into a gas chromatograph (Gow-Mac model 550P)

equipped with a thermal conductivity detector (TCD) and an Unibead 2S column (Altech Co.).

The signals from G.C were processed and converted to data by D520B computing integrator

(Young In Co., Korea).

2.3. Experimental procedures

Experiments to measure VLE data for the binary mixture R-290 + R-1270 at certain

temperature were performed by the following procedures. At first, the system was evacuated

to remove all inert gases. A certain amount of R-290 (less volatile than R-1270) was

introduced into the cell, and then the temperature of the entire system was maintained by

controlling the temperature of water bath system. After desired temperature was achieved, the

vapor pressure of the R-290 was measured. Then, a targeted amount of R-1270 was supplied

into the cell. Both the dual-head pump and stirrer should be turned on continuously until the

equilibrium state of the mixture in the cell was established. As soon as the equilibrium state

was confirmed, the compositions of sample and the pressure in the cell were measured.

5

Finally, the vapor pressure of pure R-2170 was measured in the same procedure mentioned

above for R-290. The GC was calibrated with pure components of known purity and with

mixtures of known compositions that were prepared gravimetrically. The composition

uncertainty of composition measurement was estimated within ± 0.002 mole fraction for both

liquid and vapor phase.

3. Correlation

In this work, the experimental VLE data were correlated with the Peng-Robinson [2] equation

of state (PR-EOS) combined with the Wong-Sandler mixing rule. The Pen-Robinson equation

of state is expressed as follows

( ))()( MMMM bVbbVV

TabV

RTP−++

−−

= (1)

( ) ( )TPTRTa α⎟⎟

⎠

⎞⎜⎜⎝

⎛=

c

2c

2

457235.0 (2)

c

c0777960bP

RT.= (3)

( ) ( )[ ]2c/11 TTkT −+=α (4)

226992.054226.137464.0 ωωk −+= (5)

where the parameter ‘a’ is a function of temperature, ‘b’ is constant, k is a constant

characteristic of each substance, ω is the acentric factor, P and Pc (MPa) are the absolute and

critical pressures, T and Tc (K) are the absolute and critical temperatures, Tr is the reduced

temperature, and VM is the molar volume.

The Wong-Sandler mixing rule [3] was used in this work to obtain equation of state

parameters for a mixture from those of the pure components. Wong and Sandler equated the

6

excess Helmholtz free energy at infinite pressure from an equation of state to the excess

Helmholtz free energy from any activity coefficient model, in such a way that a mixing rule is

obtained which simultaneously satisfies the quadratic composition dependence of the second

virial coefficient but also behaves like an activity coefficient model at high density. This

mixing rule for a cubic equation of state can be written

( )

⎟⎠

⎞⎜⎝

⎛−−

−=

∑

∑∑

∞i

iiiE

i jjji

m

//1

/

RTbaxCRTA

RTabxxb

i

(6)

with ( ) ( ) ( )[ ]( )ijjiij 1//21/ kRTabRTabRTab −−+−=− (7)

and CA

bax

ba E

i i

ii

m

m ∞+=∑ (8)

where C is a constant equal to ln ( ) 212 /− for the PR-EOS used in this work, kij is binary

interaction parameter. Also, E∞A is an excess Helmholtz free energy model at infinite pressure

which can be equated to a low-pressure excess Gibbs free energy [6]. In this study we use the

NRTL model [7] given by:

∑∑

∑=∞

rrir

jjijij

ii

E

Gx

Gxx

RTA

τ (9)

with

( ) )/(andexp RTA τG jijijijiji =−= τα (10)

where Gji is the local composition factor for the NRTL model, τji is the NRTL model binary

interaction parameter, Aji= (gji-gii), where gji is interaction energy between an i-j pair of

molecules, αji is a nonrandomness parameter, and R is the universal gas constant (8.314 J.K-

1mol-1). The critical properties (Tc, Pc) and acentric factors (ω) of R-290 and R-1270 used to

7

calculate the parameters for the PR-EOS are summarized in Table 1. We have set the non-

randomness parameter, αij, equal to 0.3 for the binary mixture investigated here. The

parameters of these equations were obtained by minimizing the following objective function:

2N

1i exp,i

cal,iexp,i100

N1functionObjective ∑

=⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −=

P

PP (11)

where N is the number of experimental points; Pexp and Pcal are experimental and calculated

pressures.

4. Results and discussion

4.1. Saturated vapor pressures of pure compounds

Comparison of measured saturated vapor pressures (Pv) of pure R-290 and R-1270 at various

temperatures with the data calculated from the database REFPROP 6.01 [8] are illustrated in

Table 2. The result indicates that the absolute deviations of vapor pressure (∆Pv) between

experimental and cited data were within ± 0.001 MPa for both R-290 and R-1270 and the

average absolute deviations (AAD%-Pv) were 0.04 % for R-1270 and 0.06 % for R-290. All

values are rather low and acceptable.

4.2. Vapor- liquid equilibria of the binary mixture

The measured and calculated VLE data for the binary mixture R-1270 (1) + R-290 (2) at

273.17, 278.15, 283.15, 293.15, 303.15 and 313.15 K as well as their deviations in pressure

and in vapor phase composition are presented in Table 3. The results of correlation including

all the values of determined k12, NRTL parameters (τ12, τ12) and the average absolute

percentage deviations in pressure and in vapor phase composition (AAD%-P and AAD%-y)

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between calculated and experimental data for this binary mixture are reported in Table 4. The

P-x-y diagrams for this system are shown in Figure 1 where the experimental data are

presented as symbols and the dashed lines represent the calculated values by PR-EOS. Both

experimental and calculated diagrams clearly indicated that the azeotropic behavior was not

found in this mixture over range of temperature studied here. From Figure 1, we can realize

that there was a small difference between experimental and calculated diagrams. It can be

demonstrated clearly by the deviations in vapor phase composition and in pressure of the

calculated data compared with experimental values at each point, which are shown in Figure 2

and Figure 3. From the results summarized in Table 4, it was found that in the temperature

range between 273.15 and 313.15 K, the values of AAD%-P varied within 0.06 ∼ 0.15 %

meanwhile the values of AAD-y varied within 0.51 ∼ 1.3%. Generally, all values are relatively

small and acceptable. In other way, the data calculated by using PR-EOS combined with the

Wong-Sandler mixing rule are in good agreement with the experimental data.

Based on the P-x-y diagram in Figure 1, we can realize that it is really difficult to produce

high purity propane (or propylene) from the mixture of propane + propylene by distillation

due to the very close distance between dew–point curve and bubble-point curve.

5. Conclusions

Measurements of the vapor-liquid equilibria for the binary mixture R-290 + R-1270 at 273.17,

278.15, 283.15, 293.15, 303.15 and 313.15 K were carried out by using a circulation-type

equilibrium apparatus and ninety VLE data for this mixture were reported in detail in this

paper. It was confirmed that this mixture did not exhibite azeotropic behavior in the studied

temperature range.

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The experimental VLE data were correlated with the PR-EOS combined with the Wong-

Sandler mixing rule. The calculated data obtained from the equation of state are in good

agreement with experimental data. The result means that the model equation used in this study

can be used to estimate the thermodynamic properties of the binary mixture R-1270 + R-290

in the range of temperature from 273.15 to 313.15 K. However, additional experiments are

necessary to apply to further ranges.

10

List of symbol

AE∞ an excess Helmholtz free energy

a (T) function of temperature

b constant

C a numerical constant equal to ln ( ) 212 /− for the PR-EOS

k12 interaction parameter between species 1 and 2

gij an interaction energy parameter of the i-j component

Gij the local composition factor for the NRTL model

k a constant characteristic of each substance

n number of components in a mixture

N number of experiments

P, Pc, Pv pressure, critical pressure, vapor pressure (MPa)

R gas constant, R = 8.3144 (J mol-1 K-1)

T, Tc absolute temperature, critical temperature, (K)

Tr reduced temperature

VM molar volume

x, y mole fraction in liquid phase, vapor phase

Greek letters

α(T) temperature dependent

α12 nonrandomless parameter

γ activity coefficient

∆, δ change in a quantity

ω acentric factor

11

Subscripts

a. azeotropic property

c critical property

cal. calculated

exp. experimental

i, j ith, jth component of the mixture

m mixture

v vapor phase

Ave. average

12

References

[1] E. Aisbeet and T. Pham, Natural replacements for ozone-depleting refrigerants in Eastern

and Southern Asia, seminar on environment and development in Vietnam, National

Center for Development Studies, Australian National Univ., Dec. 6-7th, 1996.

[2] D. Y. Peng, D. B. Robinson, A New Two-Constant Equation of State, Ind. Eng. Chem.

Fundam. 15 (1976) 59-64.

[3] D. S. H. Wong and S. I. Sandler, A Theoretically Correct Mixing Rule for Cubic Equations

of State, AIChE J. 38 (1992) 671-680.

[4] J. S. Lim, Q. N Ho, J. Y. Park and B. G. Lee, Measurement of Vapor-Liquid Equilibria

for the Binary Mixture of Propane (R-290) + Isobutane (R-600a), Chem. Eng. Data J. 49

(2004) 192-198.

[5] Q. N. Ho, B. G. Lee, J. Y. Park, J. D. Kim and J. S. Lim, Measurement of Vapor-Liquid

Equilibria for the Binary Mixture of Propylene (R-2170) + 1,1,1,2 Tetrafluoroethane

(HFC-134a), Fluid Phase Equilibria 225 (2004) 125-132.

[6] D. S. H. Wong, H. Orbey and S.I. Sandler, Equation of State Mixing Rule for Nonideal

Mixtures Using Available Activity Coefficient Model Parameter and That allows

Extrapolation over Large Ranges of Temperature and Pressure, Ind. Eng. Chem. Res. 31

(1992) 2033- 2039.

[7] H. Renon and J. M. Prausnitz, Local Compositions in Thermodynamic Excess Functions

for Liquid Mixtures, AIChE J. 14 (1968) 135-144.

[8] M. O. McLinden, S. A. Klein, E.W. Lemmon, A.P. Peskin, Thermodynamic Properties of

Refrigerants and Refrigerant Mixtures Database, REFPROP V.6.01, NIST, 1998.

13

List of tables

Table 1. Characteristic properties of R-290 and R-1270

Table 2. Comparisons of the vapor pressure (Pv) of pure components between experimental

data and data obtained from the database REFPROP 6.01

Table 3. Comparison of deviations in pressure and in vapor phase composition between

experimental and calculated VLE data for the mixture of R-1270 (1) + R-290 (2) at various

temperatures

Table 4. Interaction parameters k12, NRTL parameters (τ12, τ21), average absolute deviations in

pressures (AAD%-P), and in vapor phase composition (AAD%-y)

14

Table 1. Characteristic properties of R-290 and R-2170 a

Characteristic property R-290 R-1270

Chemical formula CH3CH2CH3 CH2CHCH3

Molar mass 44.10 42.08

Boiling point, Tb (K) 231.06 225.46

Critical temperature, Tc (K) 369.85 365.57

Critical pressure, Pc (MPa) 4.248 4.665

Critical density, ρc (kg/m3) 220.5 223.4

Acentric factor, ω 0.1524 0.1408

a Source: database REFPROP 6.01 (1998) [8]

15

Table 2. Comparisons of the vapor pressure (Pv) of pure components between

experimental data and data obtained from the database REFPROP 6.01

Component T(K) Pv,exp (MPa) Pv,REF (MPa) |∆Pv| (MPa) a |∆Pv|/Pv,exp (%)

R-290 273.15 0.4740 0.4743 0.0003 0.06

278.15 0.5508 0.5510 0.0002 0.04

283.15 0.6360 0.6364 0.0004 0.06

293.15 0.8362 0.8362 0.0000 0.00

303.15 1.0776 1.0787 0.0011 0.10

313.15 1.3680 1.3690 0.0010 0.07

Ave. 0.06

R-1270 273.15 0.5860 0.5859 0.0001 0.02

278.15 0.6785 0.6782 0.0003 0.04

283.15 0.7808 0.7809 0.0001 0.01

293.15 1.0190 1.0199 0.0009 0.09

303.15 1.3076 1.3084 0.0008 0.06

313.15 1.6522 1.6520 0.0002 0.01

Ave. 0.04

a ∆Pv = Pv,exp - Pv,REF

16

Table 3. Comparison of deviations in pressure and in vapor phase composition between

experimental and calculated VLE data for the mixture of R-1270 (1) + R-290 (2) at

various temperatures

x1,exp y1,exp Pexp (MPa) y1,cal Pcal (MPa) ∆P/Pexp (%)a ∆y1/ y1, exp (%)b

T1 = 273.15 K

0.000 0.000 0.4740 0.000 0.4735 0.10 - 0.092 0.112 0.4890 0.115 0.4877 0.28 -2.50 0.162 0.191 0.4985 0.196 0.4978 0.14 -2.83 0.261 0.299 0.5116 0.307 0.5117 -0.02 -2.85 0.355 0.394 0.5232 0.405 0.5239 -0.14 -2.69 0.442 0.483 0.5338 0.492 0.5345 -0.13 -1.78 0.531 0.568 0.5437 0.577 0.5446 -0.16 -1.48 0.657 0.687 0.5574 0.692 0.5575 -0.02 -0.73 0.758 0.780 0.5675 0.784 0.5668 0.13 -0.49 0.825 0.840 0.5736 0.843 0.5723 0.22 -0.30 0.917 0.923 0.5805 0.925 0.5792 0.22 -0.18 0.994 0.995 0.5856 0.995 0.5844 0.21 -0.01 1.000 1.000 0.5860 1.000 0.5847 0.22 0.00

T2 = 278.15 K

0.000 0.000 0.5508 0.000 0.5501 0.12 - 0.049 0.060 0.5601 0.061 0.5587 0.25 -1.66 0.077 0.093 0.5647 0.095 0.5634 0.22 -1.93 0.153 0.181 0.5765 0.184 0.5760 0.09 -1.88 0.233 0.270 0.5886 0.274 0.5886 0.01 -1.59 0.326 0.366 0.6017 0.372 0.6022 -0.08 -1.61 0.430 0.470 0.6155 0.476 0.6164 -0.15 -1.32 0.528 0.566 0.6283 0.571 0.6290 -0.11 -1.01 0.622 0.656 0.6399 0.659 0.6402 -0.04 -0.53 0.705 0.732 0.6493 0.735 0.6494 -0.01 -0.44 0.799 0.817 0.6595 0.820 0.6590 0.08 -0.38 0.871 0.882 0.6669 0.884 0.6658 0.16 -0.20 0.921 0.928 0.6717 0.929 0.6704 0.20 -0.15 0.960 0.964 0.6745 0.964 0.6737 0.12 0.01 1.000 1.000 0.6785 1.000 0.6770 0.22 0.00

a ∆P = Pexp– Pcal ; b ∆y1 = y1,exp – y1,cal

17

Table 3. (Continue)

x1,exp y1,exp Pexp (MPa) y1,cal Pcal (MPa) ∆P/Pexp (%) ∆y1/ y1, exp (%)

T3 = 283.15 K

0.000 0.000 0.6360 0.000 0.6357 0.05 - 0.075 0.090 0.6518 0.092 0.6505 0.20 -2.78 0.116 0.138 0.6592 0.142 0.6586 0.10 -2.83 0.170 0.199 0.6691 0.204 0.6686 0.07 -2.47 0.233 0.268 0.6801 0.274 0.6801 0.00 -2.24 0.328 0.366 0.6956 0.374 0.6965 -0.12 -2.07 0.424 0.463 0.7111 0.470 0.7119 -0.11 -1.60 0.530 0.567 0.7268 0.573 0.7277 -0.12 -1.09 0.612 0.646 0.7386 0.649 0.7388 -0.03 -0.51 0.703 0.732 0.7505 0.732 0.7502 0.04 -0.05 0.774 0.793 0.7590 0.796 0.7583 0.09 -0.30 0.856 0.869 0.7680 0.870 0.7669 0.15 -0.01 0.914 0.923 0.7735 0.922 0.7724 0.15 0.10 0.973 0.975 0.7787 0.975 0.7775 0.16 0.04 1.000 1.000 0.7808 1.000 0.7797 0.14 0.00

T4 = 293.15 K

0.000 0.000 0.8362 0.000 0.8360 0.02 - 0.037 0.046 0.8474 0.045 0.8448 0.31 2.18 0.097 0.118 0.8612 0.116 0.8590 0.26 1.11 0.167 0.198 0.8761 0.197 0.8752 0.11 0.46 0.259 0.298 0.8949 0.297 0.8956 -0.07 0.10 0.350 0.388 0.9132 0.392 0.9148 -0.18 -1.11 0.436 0.474 0.9309 0.479 0.9322 -0.14 -1.16 0.518 0.554 0.9466 0.559 0.9478 -0.12 -0.85 0.590 0.627 0.9604 0.627 0.9606 -0.02 0.10 0.658 0.688 0.9725 0.690 0.9721 0.04 -0.17 0.709 0.738 0.9815 0.737 0.9803 0.12 0.20 0.772 0.792 0.9910 0.793 0.9898 0.12 -0.20 0.838 0.854 1.0005 0.854 0.9992 0.13 0.02 0.902 0.911 1.0082 0.911 1.0076 0.06 0.01 0.951 0.956 1.0139 0.955 1.0136 0.03 0.05 1.000 1.000 1.0190 1.000 1.0192 -0.02 0.00

18

Table 3. (Continue)

x1,exp y1,exp Pexp (MPa) y1,cal Pcal (MPa) ∆P/Pexp (%) ∆y1/ y1, exp (%)

T3 = 303.15 K

0.000 0.000 1.0776 0.000 1.0798 -0.20 - 0.037 0.045 1.0891 0.044 1.0896 -0.05 2.00 0.104 0.124 1.1074 0.121 1.1072 0.01 2.11 0.169 0.198 1.1253 0.195 1.1247 0.06 1.62 0.232 0.266 1.1415 0.264 1.1414 0.01 0.53 0.283 0.318 1.1544 0.318 1.1546 -0.02 -0.13 0.358 0.396 1.1738 0.397 1.1740 -0.02 -0.15 0.432 0.472 1.1924 0.472 1.1927 -0.02 -0.04 0.511 0.550 1.2118 0.550 1.2119 0.00 0.00 0.587 0.622 1.2290 0.622 1.2294 -0.03 -0.10 0.681 0.708 1.2503 0.710 1.2500 0.03 -0.20 0.765 0.785 1.2678 0.787 1.2673 0.04 -0.27 0.838 0.853 1.2818 0.854 1.2815 0.03 -0.12 0.905 0.912 1.293 0.914 1.2935 -0.04 -0.25 1.000 1.000 1.3076 1.000 1.3092 -0.12 0.00

T4 = 313.15 K

0.000 0.000 1.3680 0.000 1.3725 -0.33 - 0.050 0.059 1.3857 0.058 1.3876 -0.14 2.36 0.120 0.138 1.4098 0.138 1.4096 0.02 0.65 0.204 0.231 1.4377 0.232 1.4371 0.04 -0.39 0.293 0.320 1.4672 0.328 1.4663 0.06 -2.72 0.366 0.397 1.4890 0.404 1.4897 -0.05 -1.76 0.429 0.463 1.5094 0.469 1.5099 -0.03 -1.30 0.517 0.550 1.5366 0.555 1.5365 0.01 -0.84 0.615 0.645 1.5640 0.647 1.5641 0.00 -0.42 0.678 0.703 1.5811 0.706 1.5809 0.02 -0.33 0.754 0.772 1.6000 0.776 1.6001 -0.01 -0.49 0.817 0.830 1.6150 0.834 1.6154 -0.02 -0.47 0.875 0.884 1.6289 0.886 1.6285 0.03 -0.24 0.930 0.935 1.6407 0.936 1.6407 0.00 -0.10 0.956 0.960 1.6465 0.960 1.6465 0.00 -0.04 1.000 1.000 1.6522 1.000 1.6558 -0.22 0.00

19

Table 4. Interaction parameters k12, NRTL parameters (τ12, τ21), average absolute

deviations in pressures (AAD%-P), and in vapor phase composition (AAD%-y)

T/K k12 τ12 τ21 AAD%-P a AAD%-y b

273.15 0.06497 0.29532 -0.31633 0.15 1.30

278.15 -0.00651 -0.04485 0.20684 0.13 0.91

283.15 0.06546 0.30697 -0.33060 0.10 1.15

293.15 0.06561 0.34273 -0.38285 0.11 0.51

303.15 0.07347 0.37903 -0.46805 0.05 0.54

313.15 0.17985 -0.27589 -0.22214 0.06 0.81

a ∑=

=−N

1i i exp,

ical,iexp, - 100N1%AAD

PPPP ; b ∑

=

=−N

1i i exp,

ical,iexp, - 100N1AAD%

yyyy

20

List of figures

Figure 1. P-x-y diagram for the mixture of R-1270 (1) + R-290 (2) at various temperatures

Figure 2. Deviations in pressure between experimental and calculated for the mixture of R-

1270 (1) + R-290 (2) at various temperatures

Figure 3. Deviations in vapor phase composition between experimental and calculated data

for the mixture of R-1270 (1) + R-290 (2) at various temperatures

21

Figure 2. P-x-y diagram for the mixture propylenen/HFC-134a at different temperatures

Mole fraction of R-1270 (x1,y1)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Pres

sure

(MPa

)

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80PR-EOS273.15 K278.15 K283.15 K293.15 K303.15 K313.15 K

Figure 1. P-x-y diagrams for the mixture of R-1270 (1) + R-290 (2) at various temperatures

22

Mole fraction of R-1270, x1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

100(

P exp.

- P ca

l.)/ P

exp.

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

273.15 K278.15 K283.15 K293.15 K303.15 K313.15 K

Figure 2. Deviations in pressure between experimental and calculated for

the mixture of R-1270 (1) + R-290 (2) at various temperatures

23

Mole fraction of R-1270, x1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

100

(y 1,

exp -

y1,

cal )

/ y1,

exp

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.00 1

273.15 K278.15 K283.15 K293.15 K303.15 K313.15 K

Figure 3. Deviations in vapor phase composition between experimental and

calculated data for the binary mixture of R-1270 (1) + R-290 (2) at

various temperatures