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Critical locus and vapor–liquid equilibria of HFC32–HFC125 system
Fluid Phase Equilibria 194–197 (2002) 995–1008
Critical locus and vapor–liquid equilibria of HFC32–HFC125 system Ryo Kato, Katsushi Shirakawa, Hideo Nishiumi∗ Chemical Engineering Laboratory, Hosei University, Koganei, Tokyo 184-8584, Japan Received 21 March 2001; accepted 17 October 2001
Abstract We measured vapor–liquid equilibria (VLE) and critical locus for the system of difluoromethane (HFC32)– pentafluoroethane (HFC125) ranging from 318.15 to 349.15 K. Composition differences between vapor and liquid phases on the P–(x–y) diagram were very small. The critical locus can be classified as type I behavior according to the system of van Konynenburg–Scott. The system of HFC32 and HFC125 is unusual in that the larger component in molecular weight has a lower critical temperature and vapor pressure than the smaller component. Using binary interaction parameter mij expressed as a linear function of composition and temperature, we obtained excellent correlation of the experimental data with an extended BWR equation of state. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Vapor–liquid equilibria; Critical locus; Fluorocarbon; HFC32; HFC125; Mixture; Pure; BWR equation of state; Binary interaction parameter
1. Introduction Although chlorodifluoromethane (HCFC22) is a popular and effective refrigerant in air conditioner systems, it depletes the ozone layer and therefore, its production is scheduled for termination. As alternative refrigerants, fluorocarbon mixtures are expected to be used. Three types of fluorocarbons without chlorine atoms, HFC32, HFC125 and 1,1,1,2-tetrafluoroethane (HFC134a) were selected on the basis for their potential as future refrigerants. Kobayashi and Nishiumi [1] measured saturated vapor pressures of components and vapor–liquid equilibria (VLE) at 273.15, 283.05, 293.15, 303.15 and 318.15 K for the system of HFC32–HFC125 and ternary VLE at 333.15 K and 2.43 MPa. In this work, we tried to measure the critical locus of the system and VLE at higher temperatures than Kobayashi and Nishiumi [1]. For system correlation, we develop a method based on the BWR equation of state [2,3] as modified by Nishiumi [5], and Nishiumi and Saito [4]. ∗
Corresponding author. Tel.: +81-42-387-6142; fax: +81-42-387-6142. E-mail address: [email protected] (H. Nishiumi). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 7 8 8 - 9
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R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
2. Experimental 2.1. Materials HFC32 and HFC125 supplied by Showa Denko. and Daikin Kogyo had a purity of more than 99.9 and 99.8%, respectively. 2.2. Experimental apparatus Fig. 1 shows an apparatus for both critical locus and vapor–liquid equilibrium measurement in this work. System pressure was measured with a 10 MPa bourdon gauge that had a full scale accuracy of 0.15%. Temperature measurement had an accuracy of 0.02 K. The critical point was taken to the maximum in scattering light as observed with transmitted light. The composition was analyzed by gas chromatography. Details can be found in Nishiumi and Ohno [6]. 2.3. VLE measurement for HFC32–HFC125 system Experimental VLE results ranging from 318.15 to 349.15 K are listed in Table 1. Fig. 2 shows the VLE and the critical points data for the system of HFC32 and HFC125 together with VLE data from Kobayashi and Nishiumi [1] ranging from 273.15 to 303.15 K. The calculated results are shown in the figure. The calculations from an equation of state will be discussed later. Composition difference between liquid and vapor phases were very small. Fig. 3 compares some experimental results of VLE for the system of HFC32–HFC125 at 333.15 K. Kubota [7] reported an azeotrope, but we were unable to distinguish it with our measurements.
Fig. 1. Schematic diagram of experimental apparatus: sample cylinder; sample charging; equilibrium cell; thermometer; six-port valve; stirrer; heater; magnetic pump; gas chromatograph (GC); helium gas cylinder; vacuum pump; pressure gauge; air bath for equilibrium cell; air bath for conduction to GC.
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008 Table 1 Experimental VLE for the system of HFC32–HFC125 Pressure (MPa)
Mole fraction of HFC32 Liquid
Vapor
318.15 K 2.350 2.407 2.522 2.709 2.736 2.751
0.134 0.214 0.380 0.704 0.768 0.811
0.151 0.238 0.409 0.718 0.778 0.819
333.15 K 3.370 3.620 3.740 3.810 3.840 3.870 3.890 3.890 3.900 3.900 3.910
0.185 0.434 0.581 0.674 0.731 0.785 0.833 0.856 0.891 0.912 0.953
0.200 0.454 0.599 0.685 0.731 0.792 0.828 0.855 0.893 0.912 0.953
340.15 K 4.051 4.150 4.199 4.238 4.336 4.405 4.463 4.522 4.552 4.75 4.79 4.82 4.82 4.82 4.86
0.7135 0.6226 0.5857 0.5417 0.4486 0.3636 0.2953 0.1947 0.1108 0.6296 0.691 0.8193 0.726 0.7151 0.9481
0.2865 0.3774 0.4143 0.4583 0.5514 0.6364 0.7047 0.8053 0.8892 0.6356 0.709 0.8218 0.7296 0.7165 0.9482
345.15 K 5.005 5.035 5.045 5.055 5.060
0.783 0.892 0.857 0.922 0.945
0.782 0.892 0.858 0.922 0.943
349.15 K 5.267 5.269
0.939 0.952
0.940 0.952
997
998
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
Fig. 2. VLE and critical points data for HFC32 (1)–HFC125 (2) system in this work. Closed: liquid phase, open: vapor phase VLE data: (1) 349.15 K; (2) 345.15 K; (3) 343.15 K; (4) 340.15 K; (5) 333.15 K; (6) 318.15 K (see Fig. 3); (7) 303.15 K [1]; (8) 293.05 K [1]; (9) 283.05 K [1]; (10) 273.15 K [1]; square with crosshair: critical point data; solid line: calculated from an extended BWR equation of state in this work.
2.4. Critical locus for HFC32–HFC125 system Table 2 lists the experimental critical locus data in this work. The P–x diagram relation was shown in Fig. 2. Fig. 4 shows the P–T diagram of the critical locus, which agrees well with the data by Nagel and Bier [8]. The critical locus was found to belong to the type I behavior according to the classification system of Table 2 Critical locus data for the system of HFC32–HFC125 in this work Tc (K)
Pc (MPa)
Mole fraction of HFC32
339.50 340.15 341.74 344.39 346.74 349.15 349.60
3.757 3.993 4.395 4.880 5.214 5.513 5.576
0.109 0.252 0.470 0.693 0.828 0.925 0.946
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Fig. 3. Comparison in VLE for the system of HFC32–HFC125 at 333.15 K. Closed: liquid phase; open: vapor phase VLE data. (䊉䊊) This work; (䊏䊐) Kobayashi and Nishiumi [1]; (䉱) Kubota [7]; (䉲) vapor pressure of components.
Fig. 4. Critical locus of HFC32 (1)–HFC125 (2) system: (䊉) this work; (䊊) Nagel and Bier [8]; (—) vapor pressure of HFC125 and HFC32.
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Fig. 5. Critical locus for the system of HFC32–HFC125: (䊐) critical points from data of Table 2.
van Konynenburg [9]. As shown in a left-hand side diagram of Fig. 5, the system of HFC32 and HFC125 is unusual in that the larger component in molecular weight has a lower critical temperature and vapor pressure than the smaller component. Up to the point B, the slope of the P–x diagram is positive. Above point B, we can predict that the azeotrope should appear in when it intersects the critical locus, although we were unable to distinguish it from our experimental techniques. Nagahama [10] reported interesting binary systems of HCFC22 (CHClF2 )–CFC115(C2 ClF5 ), HCFC22–propane and propane–CFC115 in which azeotrope appeared.
3. Polar parameters for equation of state 3.1. BWR equation of state The BWR equation of state is a virial type equation that was originally developed for the petrochemical industry [2]. The equation was generalized by Starling and Han [3] to have 11 constants and extended to the low temperature region by adding a total 15 generalized constants by Nishiumi [5], and Nishiumi and Saito [4]. To extend the equation to polar substances, Nishiumi added five polar parameters Ψ E , Ψ A , s3 , s2 and s1 [11]. C0 D0 E0 + ΨE d f e 2 P = ρRT+ B0 RT−(A0 +ΨA )− 2 + 3 − ρ ρ3 + bRT − a − − − T T T4 T T 4 T 23 d e c f g h 6 +α α + + 4 + 23 ρ + + + + T Ψs ρ 3 (1 + γρ 2 ) exp(−γρ 2 ) (1) T T T T 2 T 8 T 17
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Table 3 Fifteen generalized coefficients for non-polar contribution [3–5] B0 = (0.443690 + 0.115449ω)/ρc A0 = (1.28438 − 0.920731ω + 0.095ω2 )RTc /ρc C0 = (0.356306 + 1.70871ω)RT 3c /ρc D0 = (0.0307452 + 0.179433ω)RT 4c /ρc E0 = {0.006450 − 0.022143ω exp(−3.8ω)}RT 5c /ρc b = (0.528629 + 0.349261ω)/ρc2 a = (0.484011 + 0.754130ω)RT c /ρc2 c = (0.504087 + 1.32245ω)RT 3c /ρc2 d = (0.0732828 + 0.436492ω)RT 2c /ρc2 e = {4.65593 × 10−3 − 3.07393 × 10−2 ω + 5.58125 × 10−2 ω2 − 3.40721
(3) (4) (5) (6) (7) (8) (9) (10) (11)
×10−14 exp(−7.72753ω − 45.3152ω2 )}/(RTc24 /ρc2 ) f = {6.97 × 10−14 + 8.08 × 10−13 ω − 1.60 × 10−12 ω2 − 3.63078
(12)
×10−13 exp(−30.9009ω − 283.680ω2 )}RTc24 /ρc2 g = {2.20 × 10−5 − 1.065 × 10−4 ω + 1.09 × 10−5 ω exp(−26.024ω)}RT 9c /ρc2 2 h = {−2.40 × 10−11 + 11.8 × 10−11 ω − 2.05 × 10−11 ω exp(−21.52ω)}RT 18 c /ρc 3 α = (0.0705233 − 0.04448ω)/ρc γ = (0.544979 − 2.70896ω)/ρc2
(13) (14) (15) (16) (17)
where P, T, ρ and R are pressure, temperature, density and the gas constant, respectively. Moreover, s1 Ψs = s3 + s (2) T 2 The 15 generalized coefficients for non-polar contribution such as B0 , A0 and C0 were considered to be functions of critical temperature Tc , critical molar density ρ c and the acentric factor ω as shown in Table 3 (Eqs. (3)–(17)).Parameters for polar substances Ψ E , Ψ A , s3 , and s1 were related to five reduced quantities ΨE∗ , ΨA∗ , s3∗ , s1∗ and dimensionless parameter s2 , as follows: ΨA =
ΨA∗ RTc ρc
(18)
ΨE =
ΨE∗ RT5c ρc
(19)
s3 =
s3∗ R ρc2
(20)
s1 =
s1∗ RTsc2 ρc2
(21)
Values of ΨE∗ and ΨA∗ were obtained from the second virial coefficient data. The other three polar parameters were obtained by fitting to vapor pressure data. 3.2. Polar parameters Fig. 6 shows the deviation for HFC32 in calculated vapor pressure from experimental values as function of Ψ A . Two fixed points were observed as the value of Ψ A increased. For HFC32, the value of ΨA =
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R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
Fig. 6. Effect of Ψ A in optimum value determination for HFC32. Table 4 Critical properties and polar parameters Component
Pc (MPa)
Tc (K)
ρ c (mol/l)
ω
ΨA∗
ΨE∗
s3∗
s1∗
s2
HFC32 FC125
5.830 3.631
351.60 339.40
8.333 4.762
0.271 0.329
−0.58 −0.13
0.5991 0.1055
−0.5446 −0.1218
0.5058 0.0891
6.0310 5.824
0 minimized vapor pressure deviation. However, over the temperature of T r = 0.92, calculations were unstable and did not converge. In this work, we employed the value ΨA = −0.58 which allowed calculation up to the critical temperature. For the measured the critical loci and VLE near the critical points, we employed the following polar parameters which cover the range from T r = 0.7 to the critical points of the components listed in Table 4. Using the polar parameters in Table 4, correlation results of vapor pressures and calculated liquid densities of HFC32 and HFC125 were compared with the data as shown in Fig. 7. From the figure, correlation of the properties of HFC125 was within 1% deviation over most of the range of Tr . Higher deviation occurred near the critical point and at low Tr (HFC32). 4. Correlation of VLE 4.1. Mixing rules The second virial coefficient of Eq. (1), B is given by A0 + Ψ A C0 D0 E0 + ΨE B = B0 − (22) − 3+ 4− RT RT RT RT5 Applying statistical mechanics to the second virial coefficient of a mixture consisting of N components, B, we obtain;
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1003
Fig. 7. Correlated results of vapor pressures and calculated saturated liquid densities of HFC32 and HFC125 using polar parameters.
B=
N N xi xj Bij
(23)
i=1 j =1
Comparison of Eq. (22) with Eq. (23) gives the following relation: B0 =
N N i=1 j =1
xi xj B0ij
(24)
1004
A0 = C0 = D0 = E0 = ΨA = ΨE =
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
xi xj A0ij
(25)
xi xj C0ij
(26)
xi xj D0ij
(27)
xi xj E0ij
(28)
xi xj ΨAij
(29)
xi xj ΨEij
(30)
where the left side quantities such as A0 are the values for a mixture in Eq. (1), and xi and xj are mole fractions of components i and j, respectively. The cross coefficients in the above equations of Benedict et al. [2] and Starling and Han [3] seem to have little theoretical basis. Assuming that the corresponding state principle can apply to binary interaction, we obtain, A0ij = (1.28438 − 0.920731ωij + 0.095ωij2 )RTcij Vcij Tcij is defined by Tcij = mij Tci Tcj
(31)
(32)
where mij is a binary interaction parameter between component i and j. For systems consisting of non-polar components, Nishiumi and Saito [12] generalized mij as a function of critical molar volume ratio Vci /Vcj depending on family substances as predicted by Reed III [13] and Hudson and McCoubrey [14]. However, for systems consisting of polar components like in this work, a mij value could not help being correlated by fitting to VLE data as a function of temperature or both temperature and composition, because it is much sensitive to the choice of mij . For Vcij , rigid sphere approximation is employed: 1/3 3 Vci + Vcj 1/3 Vcij = (33) 2 Empirically, ωij =
ωi + ωj 2
(34)
Similarly, B0ij , A0ij , D0ij and E0ij are function of Tcij , Vcij and ωcij .The mixing rules for the cross coefficients of the polar parts, Ψ A , Ψ E were assumed to be: ∗ ΨAi + ΨA∗j RTcij ΨAij = (35) 2 ρcij ∗ ΨEi + ΨE∗j RT5cij ΨEij = (36) 2 ρcij
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These coefficients take into account the effect of orientation or induction forces. The third virial coefficient term b for a mixture was expressed by: N N N xi xj xk bijk
b=
(37)
i=1 j =1 k=1
The coefficients of a, d, e, f and the expanded exponential terms c, g and h for a mixture have the same triple summation of composition. The following assumption was employed according to Benedict et al. [2] bijk = (bi bj bk )1/3 Then,
(38)
(xi bi )1/3
b=
3 (39)
Finally, the following mixing rules for non-polar terms were assumed: 3 a= (xi ai )1/3 c=
(xi ci )1/3
d= e=
3 (41)
(xi di )1/3
f = g= h= α= γ =
(xi ei )
1/3
3 (42)
3
(43)
(xi fi )1/3
(40)
3 (44)
xi gi
(45)
xi hi
(46)
3 (xi αi )1/3
(xi γi )1/3
(47)
3 (48)
For polar terms, the following mixing rules were employed: s3 =
N xi s3i
(49)
i=1 N N s1i Ψs = xi s3i + xi s T 2i i=1 i=1
(50)
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Fugacity fi necessary to phase equilibrium calculation is calculated by the following expression:
n C0ij D0ij E0ij + ΨEij fi RTρ RT ln = RT ln + 2ρ xj B0ij RT − (A0ij + ΨAij ) − 2 + 3 − xi P P T T T4 j =1
3 (d 2 di )1/3 (e2 ei )1/3 (f 2 fi )1/3 + ρ 2 RT(b2 bi )1/3 − (a 2 ai )1/3 − − − 2 T T4 T 23 2 1/3 2 1/3 2 1/3
3 (e ei ) (d di ) (f fi ) + ρ 5 α (a 2 ai )1/3 + + + 4 5 T T T 23 e d f + (a 2 ai )1/3 a + + 4 + 23 T T T 2 1/3
2g + gi 2h + hi 2 3(c ci ) +ρ + + + T (2Ψs + Ψsi ) T2 T8 T 17
1 1 1 g h c 2 × − + + + exp(−γρ ) − 2 + T Ψs γρ 2 T 2 T 8 T 17 γρ 2 2
1 2 4 2 2 × 1 − 1 + γρ + γ ρ exp(−γρ ) 2
(51)
Fig. 8. Correlation of binary interaction parameter mij in Eq. (32) as a function of both composition and temperature for the system of HFC32 and HFC125: (䉱) 318.15 K; (䊊) 303.15 K; (䊏) 293.15 K; () 283.15 K; (䊉) 273.15 K.
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4.2. Correlation of binary interaction parameters mij From VLE data, the optimum mij values can determined by minimizing deviation between experimental and calculated vapor and liquid compositions at a fixed temperature and pressure. For systems composed of non-polar substances, appropriate mij values were obtained from correlations by Nishiumi and Saito [12]. For systems containing polar substances, the chosen mij values were sensitive and exhibited composition and temperature dependence. The optimum mij values for the system of HFC32 and HFC125 were found to be a linear function of composition and temperature (Fig. 8), although convergence was not obtained above 333.15 K. Regression of the values gave the following relation: m12 =
(0.87153 + 0.34599 × 10−3 T )x1 + (0.86117 + 0.39696 × 10−3 T )x2 x1 + x2
(52)
where suffix 1 and 2 are for HFC32 and HFC125, respectively. The above mathematical expression can be considered to contain the effect of “local-composition”. This means that it has a great potential to be applicable ternary or higher systems. The back-calculated results from solid lines in Fig. 2 showed excellent agreement with the experimental data. Moreover, VLE behavior above 318.15 K was well predicted by extrapolation of Eq. (52). 5. Conclusions We measured VLE at five isotherms ranging from 318.15 to 349.15 K for the system of HFC32and HFC125. From our measurements, it was not possible to distinguish whether a possible azeotrope existed or not at 318.15 K. The critical locus was found to belong to type I behavior according to the classification system of van Konynenburg [9]. When the critical locus crossed the vapor pressure line, an azeotrope should occur, although we were unable to measure it with our experimental technique. A modified form of the extended BWR equation of state could correlate the data with the introduction of polar parameters. List of symbols A0 , B0 , C0 , D0 , E0 , a, b, c, d, e, f, g, h, α, γ B Bij fi mij P Pc R s1 , s2 , s3 s1∗ , s3∗ T Tc Vc x
15 constants for non-polar parameters contribution in Eq. (1) second virial coefficient (m3 /mol) cross second virial coefficient (m3 /mol) fugacity of component i (Pa) binary interaction parameter defined by Eq. (32) pressure (Pa) critical pressure (Pa) gas constant (J/(mol K)) polar parameters defined by Eq. (2) reduced polar parameters defined by Eqs. (20) and (21) temperature (K) critical temperature (K) critical volume (m3 /mol) mole fraction
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R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
Greek letters ρ density (mol/m3 ) critical density (mol/m3 ) ρc ω Pitzer’s acentric factor Ψ A , Ψ E polar parameters due to second virial coefficient contribution in Eq. (1) ΨA∗ , ΨE∗ reduced polar parameters defined by Eqs. (18) and (19) Ψs quantity related to polar contribution defined by Eq. (2) Subscripts i component j component Acknowledgements The authors wish to thank Mr. Noriyuki Kasai, Mr. Keiji Ikemura, Mr. Ken-ichi Narizuka, Mr. Sin-ya Tsukamoto and Mr. Shuichi Okazaki, who assisted with the experiments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
M. Kobayashi, H. Nishiumi, Fluid Phase Equilib. 144 (1998) 191–202. M. Benedict, G.B. Webb, L.C. Rubin, J. Chem. Phys. 8 (1940) 334–345. K.E. Starling, M.S. Han, Hydrocarbon Process. 51 (1972) 129–132. H. Nishiumi, S. Saito, J. Chem. Eng. Jpn. 8 (1975) 356–360. H. Nishiumi, J. Chem. Eng. Jpn. 13 (1980) 74–76. H. Nishiumi, T. Ohno, Korean J. Chem. Eng. 17 (2000) 668–671. H. Kubota, 2000, personal communication. M. Nagel, K. Bier, Int. J. Refrig. 18 (1995) 534–543. P.H. van Konynenburg, Critical lines and phase equilibria in binary mixtures, PhD thesis, University of California, Los angels, California, 1968. K. Nagahama, Physico–Chemical Properties for Chemical Engineers, Vol. 15, Kagaku Kogyosha Co., Tokyo, 1993, pp. 31–77. H. Nishiumi, J. Chem. Eng. Jpn. 16 (1983) 449–453. H. Nishiumi, S. Saito, J. Chem. Eng. Jpn. 10 (1977) 176–180. T.M. Reed III, J. Phys. Chem. 59 (1955) 425–428. G.H. Hudson, J.C. McCoubrey, Trans. Faraday Soc. 5 (1960) 761–766.
Critical locus and vapor–liquid equilibria of HFC32–HFC125 system Ryo Kato, Katsushi Shirakawa, Hideo Nishiumi∗ Chemical Engineering Laboratory, Hosei University, Koganei, Tokyo 184-8584, Japan Received 21 March 2001; accepted 17 October 2001
Abstract We measured vapor–liquid equilibria (VLE) and critical locus for the system of difluoromethane (HFC32)– pentafluoroethane (HFC125) ranging from 318.15 to 349.15 K. Composition differences between vapor and liquid phases on the P–(x–y) diagram were very small. The critical locus can be classified as type I behavior according to the system of van Konynenburg–Scott. The system of HFC32 and HFC125 is unusual in that the larger component in molecular weight has a lower critical temperature and vapor pressure than the smaller component. Using binary interaction parameter mij expressed as a linear function of composition and temperature, we obtained excellent correlation of the experimental data with an extended BWR equation of state. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Vapor–liquid equilibria; Critical locus; Fluorocarbon; HFC32; HFC125; Mixture; Pure; BWR equation of state; Binary interaction parameter
1. Introduction Although chlorodifluoromethane (HCFC22) is a popular and effective refrigerant in air conditioner systems, it depletes the ozone layer and therefore, its production is scheduled for termination. As alternative refrigerants, fluorocarbon mixtures are expected to be used. Three types of fluorocarbons without chlorine atoms, HFC32, HFC125 and 1,1,1,2-tetrafluoroethane (HFC134a) were selected on the basis for their potential as future refrigerants. Kobayashi and Nishiumi [1] measured saturated vapor pressures of components and vapor–liquid equilibria (VLE) at 273.15, 283.05, 293.15, 303.15 and 318.15 K for the system of HFC32–HFC125 and ternary VLE at 333.15 K and 2.43 MPa. In this work, we tried to measure the critical locus of the system and VLE at higher temperatures than Kobayashi and Nishiumi [1]. For system correlation, we develop a method based on the BWR equation of state [2,3] as modified by Nishiumi [5], and Nishiumi and Saito [4]. ∗
Corresponding author. Tel.: +81-42-387-6142; fax: +81-42-387-6142. E-mail address: [email protected] (H. Nishiumi). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 7 8 8 - 9
996
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
2. Experimental 2.1. Materials HFC32 and HFC125 supplied by Showa Denko. and Daikin Kogyo had a purity of more than 99.9 and 99.8%, respectively. 2.2. Experimental apparatus Fig. 1 shows an apparatus for both critical locus and vapor–liquid equilibrium measurement in this work. System pressure was measured with a 10 MPa bourdon gauge that had a full scale accuracy of 0.15%. Temperature measurement had an accuracy of 0.02 K. The critical point was taken to the maximum in scattering light as observed with transmitted light. The composition was analyzed by gas chromatography. Details can be found in Nishiumi and Ohno [6]. 2.3. VLE measurement for HFC32–HFC125 system Experimental VLE results ranging from 318.15 to 349.15 K are listed in Table 1. Fig. 2 shows the VLE and the critical points data for the system of HFC32 and HFC125 together with VLE data from Kobayashi and Nishiumi [1] ranging from 273.15 to 303.15 K. The calculated results are shown in the figure. The calculations from an equation of state will be discussed later. Composition difference between liquid and vapor phases were very small. Fig. 3 compares some experimental results of VLE for the system of HFC32–HFC125 at 333.15 K. Kubota [7] reported an azeotrope, but we were unable to distinguish it with our measurements.
Fig. 1. Schematic diagram of experimental apparatus: sample cylinder; sample charging; equilibrium cell; thermometer; six-port valve; stirrer; heater; magnetic pump; gas chromatograph (GC); helium gas cylinder; vacuum pump; pressure gauge; air bath for equilibrium cell; air bath for conduction to GC.
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008 Table 1 Experimental VLE for the system of HFC32–HFC125 Pressure (MPa)
Mole fraction of HFC32 Liquid
Vapor
318.15 K 2.350 2.407 2.522 2.709 2.736 2.751
0.134 0.214 0.380 0.704 0.768 0.811
0.151 0.238 0.409 0.718 0.778 0.819
333.15 K 3.370 3.620 3.740 3.810 3.840 3.870 3.890 3.890 3.900 3.900 3.910
0.185 0.434 0.581 0.674 0.731 0.785 0.833 0.856 0.891 0.912 0.953
0.200 0.454 0.599 0.685 0.731 0.792 0.828 0.855 0.893 0.912 0.953
340.15 K 4.051 4.150 4.199 4.238 4.336 4.405 4.463 4.522 4.552 4.75 4.79 4.82 4.82 4.82 4.86
0.7135 0.6226 0.5857 0.5417 0.4486 0.3636 0.2953 0.1947 0.1108 0.6296 0.691 0.8193 0.726 0.7151 0.9481
0.2865 0.3774 0.4143 0.4583 0.5514 0.6364 0.7047 0.8053 0.8892 0.6356 0.709 0.8218 0.7296 0.7165 0.9482
345.15 K 5.005 5.035 5.045 5.055 5.060
0.783 0.892 0.857 0.922 0.945
0.782 0.892 0.858 0.922 0.943
349.15 K 5.267 5.269
0.939 0.952
0.940 0.952
997
998
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
Fig. 2. VLE and critical points data for HFC32 (1)–HFC125 (2) system in this work. Closed: liquid phase, open: vapor phase VLE data: (1) 349.15 K; (2) 345.15 K; (3) 343.15 K; (4) 340.15 K; (5) 333.15 K; (6) 318.15 K (see Fig. 3); (7) 303.15 K [1]; (8) 293.05 K [1]; (9) 283.05 K [1]; (10) 273.15 K [1]; square with crosshair: critical point data; solid line: calculated from an extended BWR equation of state in this work.
2.4. Critical locus for HFC32–HFC125 system Table 2 lists the experimental critical locus data in this work. The P–x diagram relation was shown in Fig. 2. Fig. 4 shows the P–T diagram of the critical locus, which agrees well with the data by Nagel and Bier [8]. The critical locus was found to belong to the type I behavior according to the classification system of Table 2 Critical locus data for the system of HFC32–HFC125 in this work Tc (K)
Pc (MPa)
Mole fraction of HFC32
339.50 340.15 341.74 344.39 346.74 349.15 349.60
3.757 3.993 4.395 4.880 5.214 5.513 5.576
0.109 0.252 0.470 0.693 0.828 0.925 0.946
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Fig. 3. Comparison in VLE for the system of HFC32–HFC125 at 333.15 K. Closed: liquid phase; open: vapor phase VLE data. (䊉䊊) This work; (䊏䊐) Kobayashi and Nishiumi [1]; (䉱) Kubota [7]; (䉲) vapor pressure of components.
Fig. 4. Critical locus of HFC32 (1)–HFC125 (2) system: (䊉) this work; (䊊) Nagel and Bier [8]; (—) vapor pressure of HFC125 and HFC32.
1000
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Fig. 5. Critical locus for the system of HFC32–HFC125: (䊐) critical points from data of Table 2.
van Konynenburg [9]. As shown in a left-hand side diagram of Fig. 5, the system of HFC32 and HFC125 is unusual in that the larger component in molecular weight has a lower critical temperature and vapor pressure than the smaller component. Up to the point B, the slope of the P–x diagram is positive. Above point B, we can predict that the azeotrope should appear in when it intersects the critical locus, although we were unable to distinguish it from our experimental techniques. Nagahama [10] reported interesting binary systems of HCFC22 (CHClF2 )–CFC115(C2 ClF5 ), HCFC22–propane and propane–CFC115 in which azeotrope appeared.
3. Polar parameters for equation of state 3.1. BWR equation of state The BWR equation of state is a virial type equation that was originally developed for the petrochemical industry [2]. The equation was generalized by Starling and Han [3] to have 11 constants and extended to the low temperature region by adding a total 15 generalized constants by Nishiumi [5], and Nishiumi and Saito [4]. To extend the equation to polar substances, Nishiumi added five polar parameters Ψ E , Ψ A , s3 , s2 and s1 [11]. C0 D0 E0 + ΨE d f e 2 P = ρRT+ B0 RT−(A0 +ΨA )− 2 + 3 − ρ ρ3 + bRT − a − − − T T T4 T T 4 T 23 d e c f g h 6 +α α + + 4 + 23 ρ + + + + T Ψs ρ 3 (1 + γρ 2 ) exp(−γρ 2 ) (1) T T T T 2 T 8 T 17
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Table 3 Fifteen generalized coefficients for non-polar contribution [3–5] B0 = (0.443690 + 0.115449ω)/ρc A0 = (1.28438 − 0.920731ω + 0.095ω2 )RTc /ρc C0 = (0.356306 + 1.70871ω)RT 3c /ρc D0 = (0.0307452 + 0.179433ω)RT 4c /ρc E0 = {0.006450 − 0.022143ω exp(−3.8ω)}RT 5c /ρc b = (0.528629 + 0.349261ω)/ρc2 a = (0.484011 + 0.754130ω)RT c /ρc2 c = (0.504087 + 1.32245ω)RT 3c /ρc2 d = (0.0732828 + 0.436492ω)RT 2c /ρc2 e = {4.65593 × 10−3 − 3.07393 × 10−2 ω + 5.58125 × 10−2 ω2 − 3.40721
(3) (4) (5) (6) (7) (8) (9) (10) (11)
×10−14 exp(−7.72753ω − 45.3152ω2 )}/(RTc24 /ρc2 ) f = {6.97 × 10−14 + 8.08 × 10−13 ω − 1.60 × 10−12 ω2 − 3.63078
(12)
×10−13 exp(−30.9009ω − 283.680ω2 )}RTc24 /ρc2 g = {2.20 × 10−5 − 1.065 × 10−4 ω + 1.09 × 10−5 ω exp(−26.024ω)}RT 9c /ρc2 2 h = {−2.40 × 10−11 + 11.8 × 10−11 ω − 2.05 × 10−11 ω exp(−21.52ω)}RT 18 c /ρc 3 α = (0.0705233 − 0.04448ω)/ρc γ = (0.544979 − 2.70896ω)/ρc2
(13) (14) (15) (16) (17)
where P, T, ρ and R are pressure, temperature, density and the gas constant, respectively. Moreover, s1 Ψs = s3 + s (2) T 2 The 15 generalized coefficients for non-polar contribution such as B0 , A0 and C0 were considered to be functions of critical temperature Tc , critical molar density ρ c and the acentric factor ω as shown in Table 3 (Eqs. (3)–(17)).Parameters for polar substances Ψ E , Ψ A , s3 , and s1 were related to five reduced quantities ΨE∗ , ΨA∗ , s3∗ , s1∗ and dimensionless parameter s2 , as follows: ΨA =
ΨA∗ RTc ρc
(18)
ΨE =
ΨE∗ RT5c ρc
(19)
s3 =
s3∗ R ρc2
(20)
s1 =
s1∗ RTsc2 ρc2
(21)
Values of ΨE∗ and ΨA∗ were obtained from the second virial coefficient data. The other three polar parameters were obtained by fitting to vapor pressure data. 3.2. Polar parameters Fig. 6 shows the deviation for HFC32 in calculated vapor pressure from experimental values as function of Ψ A . Two fixed points were observed as the value of Ψ A increased. For HFC32, the value of ΨA =
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Fig. 6. Effect of Ψ A in optimum value determination for HFC32. Table 4 Critical properties and polar parameters Component
Pc (MPa)
Tc (K)
ρ c (mol/l)
ω
ΨA∗
ΨE∗
s3∗
s1∗
s2
HFC32 FC125
5.830 3.631
351.60 339.40
8.333 4.762
0.271 0.329
−0.58 −0.13
0.5991 0.1055
−0.5446 −0.1218
0.5058 0.0891
6.0310 5.824
0 minimized vapor pressure deviation. However, over the temperature of T r = 0.92, calculations were unstable and did not converge. In this work, we employed the value ΨA = −0.58 which allowed calculation up to the critical temperature. For the measured the critical loci and VLE near the critical points, we employed the following polar parameters which cover the range from T r = 0.7 to the critical points of the components listed in Table 4. Using the polar parameters in Table 4, correlation results of vapor pressures and calculated liquid densities of HFC32 and HFC125 were compared with the data as shown in Fig. 7. From the figure, correlation of the properties of HFC125 was within 1% deviation over most of the range of Tr . Higher deviation occurred near the critical point and at low Tr (HFC32). 4. Correlation of VLE 4.1. Mixing rules The second virial coefficient of Eq. (1), B is given by A0 + Ψ A C0 D0 E0 + ΨE B = B0 − (22) − 3+ 4− RT RT RT RT5 Applying statistical mechanics to the second virial coefficient of a mixture consisting of N components, B, we obtain;
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Fig. 7. Correlated results of vapor pressures and calculated saturated liquid densities of HFC32 and HFC125 using polar parameters.
B=
N N xi xj Bij
(23)
i=1 j =1
Comparison of Eq. (22) with Eq. (23) gives the following relation: B0 =
N N i=1 j =1
xi xj B0ij
(24)
1004
A0 = C0 = D0 = E0 = ΨA = ΨE =
R. Kato et al. / Fluid Phase Equilibria 194–197 (2002) 995–1008
xi xj A0ij
(25)
xi xj C0ij
(26)
xi xj D0ij
(27)
xi xj E0ij
(28)
xi xj ΨAij
(29)
xi xj ΨEij
(30)
where the left side quantities such as A0 are the values for a mixture in Eq. (1), and xi and xj are mole fractions of components i and j, respectively. The cross coefficients in the above equations of Benedict et al. [2] and Starling and Han [3] seem to have little theoretical basis. Assuming that the corresponding state principle can apply to binary interaction, we obtain, A0ij = (1.28438 − 0.920731ωij + 0.095ωij2 )RTcij Vcij Tcij is defined by Tcij = mij Tci Tcj
(31)
(32)
where mij is a binary interaction parameter between component i and j. For systems consisting of non-polar components, Nishiumi and Saito [12] generalized mij as a function of critical molar volume ratio Vci /Vcj depending on family substances as predicted by Reed III [13] and Hudson and McCoubrey [14]. However, for systems consisting of polar components like in this work, a mij value could not help being correlated by fitting to VLE data as a function of temperature or both temperature and composition, because it is much sensitive to the choice of mij . For Vcij , rigid sphere approximation is employed: 1/3 3 Vci + Vcj 1/3 Vcij = (33) 2 Empirically, ωij =
ωi + ωj 2
(34)
Similarly, B0ij , A0ij , D0ij and E0ij are function of Tcij , Vcij and ωcij .The mixing rules for the cross coefficients of the polar parts, Ψ A , Ψ E were assumed to be: ∗ ΨAi + ΨA∗j RTcij ΨAij = (35) 2 ρcij ∗ ΨEi + ΨE∗j RT5cij ΨEij = (36) 2 ρcij
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These coefficients take into account the effect of orientation or induction forces. The third virial coefficient term b for a mixture was expressed by: N N N xi xj xk bijk
b=
(37)
i=1 j =1 k=1
The coefficients of a, d, e, f and the expanded exponential terms c, g and h for a mixture have the same triple summation of composition. The following assumption was employed according to Benedict et al. [2] bijk = (bi bj bk )1/3 Then,
(38)
(xi bi )1/3
b=
3 (39)
Finally, the following mixing rules for non-polar terms were assumed: 3 a= (xi ai )1/3 c=
(xi ci )1/3
d= e=
3 (41)
(xi di )1/3
f = g= h= α= γ =
(xi ei )
1/3
3 (42)
3
(43)
(xi fi )1/3
(40)
3 (44)
xi gi
(45)
xi hi
(46)
3 (xi αi )1/3
(xi γi )1/3
(47)
3 (48)
For polar terms, the following mixing rules were employed: s3 =
N xi s3i
(49)
i=1 N N s1i Ψs = xi s3i + xi s T 2i i=1 i=1
(50)
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Fugacity fi necessary to phase equilibrium calculation is calculated by the following expression:
n C0ij D0ij E0ij + ΨEij fi RTρ RT ln = RT ln + 2ρ xj B0ij RT − (A0ij + ΨAij ) − 2 + 3 − xi P P T T T4 j =1
3 (d 2 di )1/3 (e2 ei )1/3 (f 2 fi )1/3 + ρ 2 RT(b2 bi )1/3 − (a 2 ai )1/3 − − − 2 T T4 T 23 2 1/3 2 1/3 2 1/3
3 (e ei ) (d di ) (f fi ) + ρ 5 α (a 2 ai )1/3 + + + 4 5 T T T 23 e d f + (a 2 ai )1/3 a + + 4 + 23 T T T 2 1/3
2g + gi 2h + hi 2 3(c ci ) +ρ + + + T (2Ψs + Ψsi ) T2 T8 T 17
1 1 1 g h c 2 × − + + + exp(−γρ ) − 2 + T Ψs γρ 2 T 2 T 8 T 17 γρ 2 2
1 2 4 2 2 × 1 − 1 + γρ + γ ρ exp(−γρ ) 2
(51)
Fig. 8. Correlation of binary interaction parameter mij in Eq. (32) as a function of both composition and temperature for the system of HFC32 and HFC125: (䉱) 318.15 K; (䊊) 303.15 K; (䊏) 293.15 K; () 283.15 K; (䊉) 273.15 K.
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1007
4.2. Correlation of binary interaction parameters mij From VLE data, the optimum mij values can determined by minimizing deviation between experimental and calculated vapor and liquid compositions at a fixed temperature and pressure. For systems composed of non-polar substances, appropriate mij values were obtained from correlations by Nishiumi and Saito [12]. For systems containing polar substances, the chosen mij values were sensitive and exhibited composition and temperature dependence. The optimum mij values for the system of HFC32 and HFC125 were found to be a linear function of composition and temperature (Fig. 8), although convergence was not obtained above 333.15 K. Regression of the values gave the following relation: m12 =
(0.87153 + 0.34599 × 10−3 T )x1 + (0.86117 + 0.39696 × 10−3 T )x2 x1 + x2
(52)
where suffix 1 and 2 are for HFC32 and HFC125, respectively. The above mathematical expression can be considered to contain the effect of “local-composition”. This means that it has a great potential to be applicable ternary or higher systems. The back-calculated results from solid lines in Fig. 2 showed excellent agreement with the experimental data. Moreover, VLE behavior above 318.15 K was well predicted by extrapolation of Eq. (52). 5. Conclusions We measured VLE at five isotherms ranging from 318.15 to 349.15 K for the system of HFC32and HFC125. From our measurements, it was not possible to distinguish whether a possible azeotrope existed or not at 318.15 K. The critical locus was found to belong to type I behavior according to the classification system of van Konynenburg [9]. When the critical locus crossed the vapor pressure line, an azeotrope should occur, although we were unable to measure it with our experimental technique. A modified form of the extended BWR equation of state could correlate the data with the introduction of polar parameters. List of symbols A0 , B0 , C0 , D0 , E0 , a, b, c, d, e, f, g, h, α, γ B Bij fi mij P Pc R s1 , s2 , s3 s1∗ , s3∗ T Tc Vc x
15 constants for non-polar parameters contribution in Eq. (1) second virial coefficient (m3 /mol) cross second virial coefficient (m3 /mol) fugacity of component i (Pa) binary interaction parameter defined by Eq. (32) pressure (Pa) critical pressure (Pa) gas constant (J/(mol K)) polar parameters defined by Eq. (2) reduced polar parameters defined by Eqs. (20) and (21) temperature (K) critical temperature (K) critical volume (m3 /mol) mole fraction
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Greek letters ρ density (mol/m3 ) critical density (mol/m3 ) ρc ω Pitzer’s acentric factor Ψ A , Ψ E polar parameters due to second virial coefficient contribution in Eq. (1) ΨA∗ , ΨE∗ reduced polar parameters defined by Eqs. (18) and (19) Ψs quantity related to polar contribution defined by Eq. (2) Subscripts i component j component Acknowledgements The authors wish to thank Mr. Noriyuki Kasai, Mr. Keiji Ikemura, Mr. Ken-ichi Narizuka, Mr. Sin-ya Tsukamoto and Mr. Shuichi Okazaki, who assisted with the experiments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
M. Kobayashi, H. Nishiumi, Fluid Phase Equilib. 144 (1998) 191–202. M. Benedict, G.B. Webb, L.C. Rubin, J. Chem. Phys. 8 (1940) 334–345. K.E. Starling, M.S. Han, Hydrocarbon Process. 51 (1972) 129–132. H. Nishiumi, S. Saito, J. Chem. Eng. Jpn. 8 (1975) 356–360. H. Nishiumi, J. Chem. Eng. Jpn. 13 (1980) 74–76. H. Nishiumi, T. Ohno, Korean J. Chem. Eng. 17 (2000) 668–671. H. Kubota, 2000, personal communication. M. Nagel, K. Bier, Int. J. Refrig. 18 (1995) 534–543. P.H. van Konynenburg, Critical lines and phase equilibria in binary mixtures, PhD thesis, University of California, Los angels, California, 1968. K. Nagahama, Physico–Chemical Properties for Chemical Engineers, Vol. 15, Kagaku Kogyosha Co., Tokyo, 1993, pp. 31–77. H. Nishiumi, J. Chem. Eng. Jpn. 16 (1983) 449–453. H. Nishiumi, S. Saito, J. Chem. Eng. Jpn. 10 (1977) 176–180. T.M. Reed III, J. Phys. Chem. 59 (1955) 425–428. G.H. Hudson, J.C. McCoubrey, Trans. Faraday Soc. 5 (1960) 761–766.