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Fluid Phase Equilibria 202 (2002) 29–47

Vapor–liquid equilibrium data for thepropane+ 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at

temperatures from 293.16 to 353.18 K and pressures up to 3.4 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 21 December 2001; received in revised form 1 March 2002; accepted 8 March 2002

Abstract

Isothermal vapor–liquid equilibrium (VLE) data for the propane+ 1,1,1,2,3,3,3-heptafluoropropane (R227ea)binary system were measured at 293.16, 303.14, 313.14, 333.15, 343.16 and 353.18 K and pressures up to 3.5 MPa.The experimental method, used in this work, is of the static-analytic type. It takes advantage of two pneu-matic capillary samplers (RolsiTM, Armines’ patent) developed in the Cenerg/TEP laboratory. The peculiarityof R227ea–propane binary system is to present azeotropic behavior at each studied temperature.

The six sets of isothermalP, x, y data are represented with the Soave–Redlich–Kwong (SRK) equation of state(EoS) and several mixing rules involving the NRTL model.© 2002 Published by Elsevier Science B.V.

Keywords: Vapor–liquid equilibrium; 1,1,1,2,3,3,3-Heptafluoropropane; R227ea–propane binary system

1. Introduction

In 1987, the modification of the Montreal protocol has prohibited the use and the production of chlo-rofluorocarbons (CFCs) in industrialized nations. Accurate knowledge of the thermophysical propertiesof mixtures containing HFC and hydrocarbons, which are proposed as alternative refrigerants is of greatimportance to evaluate the performance of refrigeration cycles and to determine the optimum compositionof new working fluids.

During the Second Workshop on Refrigerants held at Ecole des Mines in Paris, France, under theauspices of IUPAC, Dr. J. Morley (DuPont Fluoroproducts, Hemel Hempstead, UK) addressed the ques-tion “are we near an industry standard for refrigerant properties?” He discussed the various important

∗ Corresponding author. Tel.:+33-164694965; fax:+33-164694968.E-mail address: [email protected] (D. Richon).

0378-3812/02/$ – see front matter © 2002 Published by Elsevier Science B.V.PII: S0378-3812(02)00056-0

30 A. Valtz et al. / Fluid Phase Equilibria 202 (2002) 29–47

world-wide activities which were taking place to determine accurate thermophysical properties of candi-date alternative refrigerant working fluids.

Knowledge of vapor–liquid equilibrium (VLE) data for new mixtures allows to choose those offeringthe best suitable thermodynamic properties. The development of models for representation and predictionof physical properties and phase equilibria, as well as the improvement of current equations of state cannotbe handled seriously without VLE data.

Using an apparatus based on a static-analytic method, the isothermal VLE measurements on thepropane+ 1,1,1,2,3,3,3-heptafluoropropane (R227ea) binary mixture were performed at temperaturesbetween 293.16 and 353.18 K. The obtained data are fitted using the Soave–Redlich–Kwong (SRK)equation of state (EoS).

2. Experimental section

2.1. Materials

Propane is from Messer Griesheim with a certified purity higher than 99.95 vol.%. The R227ea usedwas purchased from Solvay Fluor und Derivate (Hannover, Germany) and had a certified purity higherthan 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 vaporphase sampling. This apparatus is similar to that described by Laugier and Richon[1].

The equilibrium cell is immersed in a thermo-regulated liquid bath, the temperature control is performedwithin 0.01 K. In order to perform accurate measurement of temperature in the equilibrium cell and tocheck for thermal gradients, two platinum resistance thermometer probes (Pt100) are inserted insidewells drilled directly into the body of the equilibrium cell at different levels (seeFig. 1) and connectedto an HP data acquisition unit (HP34970A). These two Pt100 are carefully and periodically calibratedagainst a 25� reference platinum resistance thermometer (TINLEY Precision Instruments). The resultinguncertainty is not higher than 0.02 K. The 25� reference platinum resistance thermometer was calibratedby 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; the pressure transduceris maintained at constant temperature (temperature higher than the highest temperature of the study) bymeans of a home-made air-thermostat, which is controlled by a PID regulator (WEST instrument, model6100). The uncertainty in the pressure measurements is estimated to be within±0.3 kPa, as a resultof a pressure calibration against a dead weight balance (Desgranges and Huot 5202S, CP 0.3–40 MPa,Aubervilliers, France).

The HP online 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 alongthe different isothermal runs.

The analytical work was carried out using a gas chromatograph (VARIAN model CP-3800) equippedwith a thermal conductivity detector (TCD) connected to a data acquisition system (BORWIN ver 1.5,from JMBS, Le fontanil, France). The analytical column is HaySep T 100/120 Mesh (silcosteel tube,

A. Valtz et al. / Fluid Phase Equilibria 202 (2002) 29–47 31

Fig. 1. Flow diagram of the equipment: C, carrier gas; EC, equilibrium cell; FV, feeding valve; LB, liquid bath; LS, liquidsampler; PP, platinum resistance thermometer probe; PrC, propane 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.

length 1.6 m, diameter 1/8 in. from Restek). The TCD was repeatedly calibrated by introducing knownamounts of each pure compound through a syringe in the injector of the gas chromatograph. Taking intoaccount the uncertainties due to calibration and the dispersion of analyses, accuracy on vapor and liquidmole fractions is estimated to be within±1.0% over the whole range of concentration.

The experimental procedure is the following: at room temperature, the equilibrium cell and its loadinglines are evacuated down to 0.1 Pa. One thermal compressor is loaded with propane (TC1) and the secondwith R227ea (TC2). At the required equilibrium temperature (equilibrium temperature is assumed to bereached when the two Pt100 give the same temperature value within their temperature uncertainty for at theleast 10 min), a volume of about 5 cm3 of R227ea is introduced into the equilibrium cell. The vapor pressureof the heaviest component (R227ea) is then recorded at this temperature. To describe the two-phaseenvelope with at least 10 twin points (liquid and vapor), given amounts of the light component (propane)are introduced step by step, leading to successive equilibrium mixtures. Equilibrium is assumed whenthe 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 withdrawnusing the pneumatic samplers RolsiTM [2] and analysed in order to check for measurement repeatability.


3. Correlations

Isothermal VLE measurements on the system R227ea–C3H8 were performed in the temperature rangefrom 293.16 to 353.18 K and at pressures up to 3.5 MPa. The critical temperature (TC), critical pres-sure (PC), and acentric factor (ω), for each of the two pure components are provided inTable 1 [3].Our experimental VLE data are correlated by means of a home-made software. We have used the SRKequation[4] of state given below, which gives good results for VLE of either non-polar or slightly polarmixtures.

R227ea is a polar compound, and the use of the Soaveα-function results in a systematic devia-tion between experimental and calculated vapor pressures. Therefore, we prefer to use the Mathias–Copemanα-function [5] with three adjustable parameters, which was especially developed for polarcompounds.

α(T ) =1 + c1

(1 −

√T

TC

)+ c2

(1 −

√T

TC

)2

+ c3

(1 −

√T

TC

)32

(1)

wherec1, c2 andc3 are the three adjustable parameters. Mathias–Copeman coefficients were evaluatedfor our whole temperature domain using a modified simplex algorithm. The objective function is:

F = 100

N

∑(Pexp − Pcal

Pexp

)2

(2)

whereN is the number of data points,Pexp is the measured pressure, andPcal is the calculated pressure.In our EoS approach, we need a mixing rule and an activity coefficient model. The first mixing rule

used to correlate the VLE is the van der Waals mixing rule:

a =∑

i

∑j

xixjaij (3)

b =∑

i

xibi (4)

where

aij = √aiaj (1 − kij) (5)

wherekij is the binary interaction parameter. This parameter is found by a careful curve fitting involvingour mixture data.

Two other mixing rules have been used to improve the representation of the equilibrium data. First,we have selected the modified Huron–Vidal (MHV1) mixing rule proposed by Michelsen[6] where the

Table 1Critical parameters and acentric factors[3]

Compound PC (MPa) TC (K) ω

Propane 4.25 369.83 0.1523R227ea 2.98 375.95 0.3632


attractive parameter is calculated from:

a = b

[∑i

xi

ai

bi

− RT

q1

∑i

xi ln

(bi

b

)+ GE

γ (T , P, xi)

q1

](6)

The reference pressure isP = 0 andb is calculated fromEq. (4). Michelsen recommendsq1 = −0.593.The second approach is that of Wong and Sandler[7], which is based on the Huron–Vidal approach andthe van der Waals mixing rules.

b =∑

i

∑j xixj (b − (a/RT))ij

1 − ((∑

ixi(ai/bi)/RT) + (AEγ (T , P = ∞, xi)/CRT))

(7)

b − a

RT=∑

i

∑j

xixj

(b − a

RT

)ij

(8)

(b − a

RT

)ij

= 1

2

[(b − a

RT

)i+(b − a

RT

)j

](1 − kij) (9)

wherekij is a binary interaction parameter. Wong and Sandler have shown that the excess Helmholtzenergy of mixing at infinite pressure,AE

γ (T , P = ∞, xi), is approximately equal to the excess Gibbsenergy at low pressure. Consequently, they assumed:

AEγ (T , P = ∞, xi)

RT= GE

γ (T , P = 0, xi)

RT(10)

The excess Helmholtz energy is calculated using the NRTL[8] local composition model.

GET ,P

RT=∑

i

xi

∑j

xj exp(−αj,i(τj,i/RT ))∑kxkexp(−αk,i(τk,i/RT ))

τj,i (11)

τi,i = 0 andαi,i = 0. Here,αj ,i , τ j ,i andτ i ,j are adjustable parameters. For our system, which belongsto a given polar mixture type, it is recommended[8] to useαj,i = 0.3. Theτ j ,i andτ i ,j are adjusteddirectly to VLE data through a modified simplex algorithm using the objective function:

F = 100

N

[∑(Pexp − Pcal

Pexp

)2

+∑(

yexp − ycal

yexp

)2]

(12)

4. Results and discussion

4.1. Vapor pressures

The values of the SRK EoS Mathias–Copeman coefficients fitted to vapor pressures of R227ea arereported inTable 2. Table 3compares the calculated pressures and experimental data. In this work, wehave compared our measured propane vapor pressures with the values calculated using McLinden[9]


Table 2Adjusted Mathias–Copeman coefficients

Coefficients R227ea Propane

C1 1.134 0.823C2 −1.965 −1.552C3 8.690 6.097

Table 3Experimental and calculated vapor pressures of R227ea

T (K) Pexp (MPa) Pcal (MPa)

293.17 0.3892 0.3891313.33 0.7076 0.7079318.21 0.8070 0.8074323.21 0.9198 0.9196328.19 1.0429 1.0425333.20 1.1792 1.1783338.19 1.3269 1.3266348.20 1.6667 1.6670353.03 1.8531 1.8541

correlation (seeEqs. (13) and (14)). As the relative deviation is less than 0.15%, we trust the McLindencorrelation to determine the Mathias–Copeman coefficients.

P(bar) = A2 exp

[A3T0

1 − T0+ A4T0 + A5T

1,890 + A6T

30

](13)

T0 = 1 − T

A1(14)

with theAi coefficients reported inTable 4.Mathias–Copeman coefficients for propane are reported inTable 2. Table 5summarizes the calculated

pressures using the McLinden correlation and the SRK–Mathias–Copeman. The vapor pressures of bothpure compounds are accurately represented (within 1.0 kPa).

4.2. Vapor–liquid equilibrium

The VLE data obtained are listed inTables 6–11. At each temperature, the van der Waals mixing rule bi-nary parameter is adjusted and can be represented by a linear temperature dependencyEq. (15)(seeFig. 2).

k12 = −0.017+ 0.00046T (15)

Table 4McLinden correlation coefficients for propane

A1 A2 A3 A4 (bar) A5 A6

369.82 42.5 −6.477 −0.1583 2.756 −4.363


Table 5Propane calculated pressuresPML (from McLinden equation) along with calculated pressuresPcal from RKS EoS and adjustedMathias–Copeman coefficients

T (K) PML (MPa) Pcal (MPa)

293.17 0.8374 0.8373313.33 1.3751 1.3753318.21 1.5359 1.5360323.21 1.7146 1.7145328.19 1.9073 1.9071333.20 2.1170 2.1168338.19 2.3427 2.3425348.20 2.8505 2.8507353.03 3.1245 3.1248

The results of the correlation are reported inTables 6–11and plotted inFig. 3.The SRK EoS+ MHV1 mixing rules combined with the NRTL model gives a better fit than the SRK

EoS+van der Waals mixing rules. The two NRTL parameters are slightly temperature dependent. Linearrelationships are convenient for these purposes:

τ12 = 3737.70− 2.456T (16)

τ21 = 1573.63− 3.420T (17)

The results of the correlation are reported inTables 6–11and plotted inFig. 4.The SRK EoS+Wong–Sandler mixing rules and NRTL model gives a better representation of the data

than the SRK EoS+ van der Waals mixing rules. Temperature dependence of NRTL parameters is givenby Eqs. (18) and (19).

Fig. 2. The van der Waals mixing rules: binary parameterkij as a function of temperature. (�) Fitted to isotherms; (—)Eq. (15).

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Fig. 3. Pressure as a function of propane mole fraction in the propane–R227ea mixture at different temperatures. (×) 293.16 K;(�) 303.15 K; (+) 313.14 K; (�) 333.15 K; (*) 343.16 K; (�) 353.18 K. Solid lines: calculated with RKS EoS and van der Waalsmixing rules withkij from Eq. (5).

τ12 = 4033.40− 5.556T (18)

τ21 = 188.29+ 3.036T (19)

In this case thek12 binary parameter is temperature independent; its value is 0.25. The results of thiscorrelation are reported inTables 6–11and plotted inFig. 5.

The binary parameters of the various mixing rules used at each condition are reported inTable 12.

Table 12Binary parameters of various mixing rules used at each temperature

T (K) van der Waals mixing rules MHV1 mixing rules Wong–Sandler mixing rules

293.16 0.118 3017.70 571.03 2404.60 1078.32303.15 0.122 2993.16 536.86 2349.10 1108.65313.15 0.127 2968.60 502.66 2293.54 1139.01333.15 0.136 2919.48 434.26 2182.42 1199.73343.15 0.141 2894.92 400.06 2126.86 1230.09353.18 0.145 2870.29 365.76 2071.13 1260.54

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Fig. 4. Pressure as a function of propane mole fraction in the propane–R227ea mixture at different temperatures. (×) 293.16 K;(�) 303.15 K; (+) 313.14 K; (�) 333.15 K; (*) 343.16 K; (�) 353.18 K. Solid lines: calculated with RKS EoS and the MHV1mixing rules with adjusted parameters fromEq. (11).

The mean relative absolute percentage deviations on pressure (MRDP) and the mean relative percentagedeviations on vapor phase mole fraction (MRDY) are defined by:

MRDU =(

100

N

)∑[∣∣∣∣Ucal − Uexp

Uexp

∣∣∣∣]

(20)

whereU = P or y1, are listed inTable 13; N is the number of data points.

Table 14Composition and pressure of the azeotrope at each temperature (MHV1 mixing rules)

T (K) xaz P (MPa)

293.16 0.8090 0.8886303.15 0.8012 1.1482313.14 0.7940 1.4578333.15 0.7813 2.2548343.16 0.7754 2.7582353.18 0.7700 3.3525


Fig. 5. Pressure as a function of propane mole fraction in the propane–R227ea mixture at different temperatures. (×) 293.16 K; (�)303.15 K; (+) 313.14 K; (�) 333.15 K; (*) 343.16 K; (�) 353.18 K. Solid lines: calculated with RKS EoS and the Wong–Sandlermixing rules with adjusted parameters fromEqs. (9) and (11).

Fig. 6. Azeotropic composition as a function of temperature.


Fig. 7. Azeotropic pressure as a function of temperature.

We also calculated the BIAS listed inTable 13for all the cases:

BIAS =(

100

N

)∑(Uexp − Ucal

Uexp

)(21)

Table 13shows that the Wong–Sandler mixing rules give a better representation of the experimentaldata than the other mixing rules.

4.3. Azeotrope

Table 14andFigs. 6 and 7show the coordinates of the azeotrope (pressure, temperature and composi-tion). When the temperature increases, the azeotropic composition of propane decreases.

5. Conclusion

In this paper we present the VLE data for the propane–R227ea system at six different temperatures. Weused a static-analytic method to obtain the experimental data. The SRK EoS, with the Mathias–Copemanα-function is chosen to fit these data with different mixing rules. In each case, the data are found consistentwith the models and the best results are obtained with the Wong–Sandler mixing rules. The deviations ofpressures and propane vapor compositions are less than 1.0%.

List of symbolsa parameter of the EoS (energy parameter)A Helmhotz energy


b parameter of the EoS (co-volume parameter)C numerical constant= ln(1/2)F objective functionG Gibbs energykij binary interaction parameterP pressure (MPa)R gas constant (J/(mol K))T temperature (K)x liquid mole fractiony vapor mole fractionZ compressibility factor

Greek lettersαij NRTL model parameter (Eq. (11))� deviationτ ij NRTL model binary interaction parameter (Eq. (11); J/mol)ω acentric factor

SuperscriptE excess property

Subscriptsaz azeotropecal calculated propertyC critical propertyexp experimental propertyi, j molecular species∞ infinite pressure reference stateML from McLinden equation1 propane2 R227ea

References

[1] S. Laugier, D. Richon, Rev. Sci. Instrum. 57 (1986) 469–472.[2] P. Guilbot, A. Valtz, H. Legendre, D. Richon, Analysis 28 (2000) 426–431.[3] M. Huber, J. Gallagher, M.O. McLinden, G. Morrison, Thermodynamic Properties of Refrigerants and Refrigerant Mixtures

Database, REFPROP V.6.01, National Institute of Standards and Technology, Boulder, CO, 1996.[4] G. Soave, Chem. Eng. Sci. 4 (1972) 1197–1203.[5] P.M. Mathias, T.W. Copeman, Fluid Phase Equilib. 13 (1983) 91–108.[6] M. Michelsen, Fluid Phase Equilib. 60 (1990) 213–219.[7] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680.[8] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144.[9] M.O. McLinden, Int. Rev. Refrig. 13 (1990) 149–162.