Thermodynamic properties of HFC-32, HFC-125, and HFC-134a mixtures

Fluid Phase Equilibria 150–151 Ž1998. 313–322

Thermodynamic properties of HFC-32, HFC-125, and HFC-134a mixtures Chun-cheng Piao a

a, )

, Ikuhiro Iwata a , Masahiro Noguchi

b

Mechanical Engineering Laboratory, Daikin Industries, 1304 Kanaoka-cho, Sakai, Osaka 591, Japan b Chemical DiÕision, Daikin Industries, 1-1 Nishi Hitotsuya, Settsu, Osaka 566, Japan

Abstract This study presents an equation of state for mixtures of HFC-32, HFC-125, and HFC-134a based on available PVTx , VLE, heat capacity and speed of sound measurements. The equation of state is valid for VLE and superheated gaseous and compressed liquid phases from 200 to 470 K and pressures up to 20 MPa. The equation is also valid for ternary mixtures of HFC-32, HFC-125, and HFC-134a. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Critical parameters; Equation of state; HFC-125; HFC-134a; HFC-32; Mixtures; PVTx ; VLE

1. Introduction HCFC-22, which is one of the most widely used working fluids in air-conditioning systems, is scheduled to be phased out before 2030 by international agreement. Binary mixtures of HFC-32r134a and HFC-32r125 and ternary mixtures of HFC-32r125r134a are considered as candidates to replace HCFC-22. There is a strong demand for reliable thermodynamic properties of these alternative working fluids. Many experimental studies have been reported for these mixtures in an extensive range of pressure, temperature and composition. This study presents an equation of state for these mixtures based on these available PVTx , VLE, heat capacity and speed of sound measurements. The equation of state covers all compositions of the ternary mixture and the entire fluid phase.

)

Corresponding author. Tel.: q81-772-57-8517; fax: q81-722-52-8255; e-mail: [email protected]

0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 8 . 0 0 3 3 1 - 8

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

314

2. Equations of state for the pure fluids We have developed equations of state for HFC-32 w1x, HFC-125 w2x, and HFC-134a w3x based on experimental measurements with the same functional form. The 18-coefficient modified BWR equation of state is given below: Pr s Tr P rrrZc q B1 P rr2 q B2 P rr3 q B3 P rr4 q B4 P rr5 q B5 P rr6 q B6 P rr7 q Ž B7 P rr3 q B8 P rr5 . P exp Ž yrr2 . B1 s a1Tr q a 2 q a 3rTr2 q a 4rTr3 B2 s a5Tr q a6 q a 7rTr

2

B3 s a8 q a9rTr2 B4 s a10 q a11rTr

Ž1. B5 s a12 q a13rTr B6 s a14 B7 s a15 q a16rTr B8 s a17 q a18rTr

where Pr s PrPc , rr s rrrc , Tr s TrTc , Zc s PcrŽ R P Tc P rc ., and R s 8.314471 JrŽmol K.. These equations represent almost all of the PVT data within "0.5% for HFC-32, HFC-125, and HFC-134a. These equations of state also represent the vapor pressures, saturated vapor and liquid densities, and heat capacities with high accuracy. The coefficients of Eq. Ž 1. and other details of these equations are presented in Refs. w1–3x.

3. Critical parameters of the mixture There are two sets of measurements of the critical parameters available from Higashi w4x and Nagel and Bier w5x. Between these only Nagel and Bier w5x reported critical pressures. From these measurements, the following correlations were developed to represent the critical locus for this ternary mixture. Pcm s x 12 P Pc1 q x 22 P Pc2 q x 32 P Pc3 q PcE

rcm s x 12 P rc1 q x 22 P rc2 q x 32 P rc3 q rcE Tcm s x 12 P Tc1 q x 22 P Tc2 q x 32 P Tc3 q TcE

Ž2. Ž3. Ž4.

where PcE s 8845 P x 1 P x 21.040 q 7825 P x 2 P x 30.994 q 10035P x 3 P x 11.009 q 700 P x 1 P x 2 P x 3

r

E 1.030 q 9.73 P x 2 P x 30.992 q 11.25 P x 3 P x 10.980 q 0.8 P x 1 P x 2 P x 3 c s 11.25 P x 1 P x 2

TcE s 682 P x 1 P x 21.007 q 712.5 P x 2 P x 30.999 q 729 P x 3 P x 1 q 5 P x 1 P x 2 P x 3

Ž5. Ž6. Ž7.

The subscripts 1, 2 and 3 indicate HFC-32, HFC-125 and HFC-134a, respectively, and x i indicates the mole fraction of component i. These correlations represent the critical pressures of Nagel and Bier

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

315

w5x with a standard deviation of 0.12% and a maximum deviation of y0.31%, critical densities of Higashi w4x and Nagel and Bier w5x with standard deviations of 2.00 and 0.23% and maximum deviations of 2.83 and y0.41%, and critical temperatures of Higashi w4x and Nagel and Bier w5x with standard deviations of 0.058% and 0.033% and maximum deviations of 0.13 and y0.069%, respectively. 4. Equation of state for the mixture There are 15 publications w6–20x reporting more than 5000 PVTx measurements, covering a wide range of compositions, pressures and temperatures. Fig. 1 shows the distribution of the available PVTx measurements over all compositions. There are 10 reports w7,9,12,13,16,18–22x available which report more than 1400 VLE data points. For the derived properties, Magee w23x reported 131 C v data points for HFC-32r134a at 30r70 wt.%, and Nakamura w24x reported 6 C v data points for different compositions in the compressed liquid phase. Hozumi et al. w25x reported 530 speed of sound points in superheated gaseous phase for various compositions. Based on these reported thermodynamic properties, an equation of state for this mixture was developed. The thermodynamic properties of the mixture are given by the following equation of state: Pr s x 1 P Pr1 q x 2 P Pr2 q x 3 P Pr3 q k mix P PrE

Ž8.

where Pr s P r Pcm . Pr1, Pr2 and Pr3 are the equations of state for the pure fluids, Eq. Ž 1., and

Fig. 1. Distribution of PVTx measurements.

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

316

Table 1 Coefficients of Eq. Ž10. i

ei

i

ei

1 2 3 4 5 6 7 8 9 10

y8.38590513903 22.6414027058 y10.9061853330 2.68881393381 10.8254585604 y25.9383399640 y2.01463864000 y1.33726095393 y2.22827937095 27.0080950488

11 12 13 14 15 16 17 18 19 20

y0.925158415527 12.1455193420 y28.8129287538 3.20170773648 y8.69391897029 12.7401947550 y0.659998176269 1.42317484331 y2.28049865531 0.123216354628

k mix P PrE is the residual part. PrE is an equation for the residual part. A new mixing rule k mix for this mixture was proposed as follows: k mix s d12 P x 1 P x 21.10 q d 23 P x 2 P x 3 q d 31 P x 3 P x 11.10 q d123 P x 10.9 P x 21.2 P x 30.6 d12 s 0.247470 q 1.47647rr y 2.16869rr2 q 1.77969rr3 y 0.465584 rr4 d 23 s 0.107712 q 0.271327rr y 0.593654 rr2 q 0.418627rr3 y 0.0383766 rr4 d 31 s 0.286548 q 1.958887rr y 2.19654 rr2 q 2.08583 rr3 y 0.635465 rr4 d123 s y0.05 where rr s rrrcm .

Fig. 2. Behavior of mixing rule, k mix .

Ž9.

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

317

Fig. 3. Comparison of PVTx data of HFC-32r125.

The equation of state for the residual part is given as: PrE s E1 P rr2 q E2 P rr3 q E3 P rr4 q E4 P rr5 q E5 P rr6 q E6 P rr7 q E7 P rr8 E1 s e1 P Tr2 q e 2 q e 3rTr2 q e 4rTr3

E5 s e14 q e15rTr q e16rTr2

E2 s e5 P Tr2 q e6 q e 7rTr3

E6 s e17 q e18rTr q e19rTr2

E3 s e8 P Tr2 q e9rTr q e10rTr2

E7 s e 20rTr2

Ž 10.

E4 s e11 P Tr2 q e12rTr q e13rTr2 PrE s P ErPcm , rr s rrrcm , Tr s TrTcm The coefficients of Eq. Ž 10. are listed in Table 1. Fig. 2 shows the behavior of the mixing rule k mix at rr s 1. The HFC-32r134a binary pair shows a large mixing effect, and the HFC-125r134a binary pare shows a small effect. The k mix function gives a smooth values over all compositions. To avoid complexity, we selected the Peng–Robinson equation of state w26x to represent the VLE, for the two phase region, for the P–T–x–y properties. Densities are still calculated using Eq. Ž8.. The Peng–Robinson equation is P s R P Tr Ž V y bm . y amr Ž V 2 q 2 P bm P V y bm2 .

Ž 11.

318

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

Fig. 4. Comparison of PVTx data of HFC-32r134a.

Fig. 5. Comparison of PVTx data of HFC-125r134a.

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

Fig. 6. Comparison of PVTx data of HFC-32r125r134a.

Fig. 7. Comparison of bubblerdew point pressures.

319

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

320

The mixing rules for the Peng–Robinson equation are given as: a m s x 12 P Ž a a . 1 q x 22 P Ž a a . 2 q x 32 P Ž a a . 3 q 2 P k 12 P x 1 P x 2 P Ž a a . 1 P Ž a a . 2 q 2 P k 13 P x 1 P x 3 P Ž a a . 1 P Ž a a . 3

0.5

q 2 P k 23 P x 2 P x 3 P Ž a a . 2 P Ž a a . 3

q 3 P k 123 P x 1 P x 2 P x 3 P Ž a a . 1 P Ž a a . 2 P Ž a a . 3 bm s x 1 P b 1 q x 2 P b 2 q x 3 P b 3

1r3

0.5 0.5

Ž 12. Ž 13.

where k 12 s 1.00000 y 0.00004 P Ž T y 273.15 .

Ž 14 . Ž 15 . Ž 16 . Ž 17 . Ž 18. Ž 19.

k 13 s 1.00000 q 0.00003 P Ž T y 273.15 . k 23 s 0.99750 y 0.00009 P Ž T y 273.15 . k 123 s 0.00000 y 0.00013 P Ž T y 273.15 . a i s 0.45724 R 2 Tci2rPci bi s 0.07780 RTcirPci

a i s 1 q Ž 0.37464 q 1.54226 v i y 0.26992 v i2 .Ž 1 y Tr0.5 .

2

Ž 20.

The parameters k 12 , k 13 , k 23 , and k 123 are the mixing parameters for the HFC-32r125, 32r134a, and 125r134a binary mixtures, and the HFC-32r125r134a ternary mixture, respectively. These

Fig. 8. Comparison of bubblerdew point pressures.

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

321

Fig. 9. Comparison of isochoric heat capacity measurements.

parameters, which depend on the temperature, were determined from available VLE data w7,9,12,13,16,18–22x. The adopted ideal gas heat capacities are the correlations reported by McLinden w27x for HFC-134a and Hozumi et al. w28x for HFC-32 and HFC-125, respectively. 5. Discussion Figs. 3–6 show the comparisons of the PVTx data and the present equation of state for the HFC-32r125, HFC-32r134a and HFC-125r134a binary mixtures and the HFC-32r125r134a ternary mixture. The present equation of state represents most of the PVTx data within "0.5–1.0% in pressurerdensity deviations for the superheated gaseous and compressed liquid phases. Some of the measurements exceed "1.0%, this is considered to be the uncertainty of the measurements. On the other hand, as shown in Figs. 7 and 8, the bubble and dew-point pressure measurements show a rather large scatter as compared to the PVTx measurements. In Figs. 7 and 8, the single symbols indicate the dew point data, and the double symbols indicate the bubble point data. The present mixing rule for the Peng–Robinson equation w26x represents almost all of the measurements within "1.0–2.0%, however, some of the measurements exceed "2.0%.

Fig. 10. Comparison of speed of sound measurements.

C.-c. Piao et al.r Fluid Phase Equilibria 150–151 (1998) 313–322

322

Fig. 9 shows the comparison of the present equation of state with C v data. The present equation of state represents the C v data by Magee w23x with a standard deviation of 0.74% and a maximum deviation of 1.78%, and by Nakamura w24x with a standard deviation of 1.14% and a maximum deviation of y3.25%. As shown in Fig. 10, the present equation of state also represents the speed of sound data by Hozumi et al. w25x with a standard deviation of 0.036% and a maximum deviation of y0.18%.

6. Conclusions The equations presented here are valid not only for the ternary mixture over all compositions but also for the HFC-32r125, HFC-32r134a, and HFC-125r134a binary mixtures. The equation of state is valid for VLE and superheated gaseous and compressed liquid phases of temperatures from 200 to 470 K and pressures up to 20 MPa.

References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x w23x w24x w25x w26x w27x w28x

C.-C. Piao, M. Noguchi, submitted to Int. J. Refrig. Ž1996.. C.-C. Piao, M. Noguchi, Fluid Phase Equilibria 125 Ž1996. 45–54. C.-C. Piao, M. Noguchi, H. Sato, K. Watanabe, ASHRAE Transactions 100 Ž1. Ž1994. 358–366. Y. Higashi, Int. J. Thermophys. 16 Ž5. Ž1995. 1175–1184. M. Nagel, K. Bier, Int. J. Refrig. 18 Ž8. Ž1995. 534–543. I. Iwata, C.-C. Piao, M. Noguchi, 29th Japanese Joint Conf. Air-conditioning and Refrigeration, April 18–20, 1995, Tokyo, Japan. I. Iwata, C.-C. Piao, M. Noguchi, to be submitted to J. Chem. Eng. Data Ž1998.. S. Nakamura, K. Fujiwara, M. Noguchi, J. Chem. Eng. Data 42 Ž2. Ž1997. 334–338. J.V. Widiatmo, H. Sato, K. Watanabe, High Temperatures–High Pressures 25 Ž1993. 677–683. H. Kiyoura, J. Takebe, H. Uchida, H. Sato, K. Watanabe, J. Chem. Eng. Data 41 Ž1996. 1409–1413. H.-L. Zhang, H. Sato, K. Watanabe, J. Chem. Eng. Data 41 Ž1996. 1401–1408. J.V. Widiatmo, H. Sato, K. Watanabe, Fluid Phase Equilibria 99 Ž1994. 199–207. J.V. Widiatmo, H. Sato, K. Watanabe, submitted to J. Chem. Eng. Data Ž1997.. J.V. Widiatmo, H. Sato, K. Watanabe, private communication, data from IEA-Annex18 Database Ž1996.. T. Sato, H. Kiyoura, H. Sato, K. Watanabe, J. Chem. Eng. Data 39 Ž4. Ž1994. 855–858. C.D. Holcomb, National Institute of Standard and Technology, Boulder, Colorado, Final Report for ARTI MCLR Project 660 Ž1996. 660–50800. J.W. Magee, private communication, data from IEA-Annex18 Database Ž1996.. L.A. Weber, D.R. Defibaugh, Int. J Thermophys. 15 Ž5. Ž1994. 863–880. D.R. Defibaugh, G. Morrison, Int. J. Refrig. 18 Ž8. Ž1995. 518–523. M. Kleemiss, Fortschr.-Ber. VDI Reihe 19, No.98, VDI-Verlag Duesseldorf Ž1997.. L.A. Weber, A.M. Silva, private communication, data from IEA-Annex18 Database Ž1994.. D. Gorenflo, R. Koester, G. Herres, data from IEA-Annex18 Database Ž1995.. J.W. Magee, private communication, data from IEA-Annex-18 Database Ž1996.. S. Nakamura, Daikin Industries, private communication Ž1996.. Hozumi, T., H. Sato, K. Watanabe, Proceedings of 4th Asian Thermophysical Properties Conference, Japan Ž1995. 307–310. D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 Ž1. Ž1976. 59–64. M.O. McLinden, Int. J. Refrig. 13 Ž1990. 149–162. T. Hozumi, H. Sato, K. Watanabe, private communication, data from IEA-Annex-18 Database Ž1996..