An equation of state for pentafluoroethane (HFC-125)

ml ELSEVIER

Fluid PhaseEquilibria 125(1996)45-54

An equation of state for pentafluoroethane (HFC- 125) Chun-cheng Piao ", Masahiro Noguchi Mechanical Engineering Laboratory, Daikin Industries, Ltd., 1304 Kanaoka-cho, Sakai, Osaka 591, Japan

Abstract

An 18-coefficient modified Benedict-Webb-Rubin equation of state of HFC-125 (pentafluoroethane) has been developed. Correlations of vapor pressure and saturated liquid density are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, isochoric heat capacities, and speeds of sound by using a least squares fitting. This equation of state is effective in both the superheated gaseous phase and the compressed liquid phase at pressures up to 68 MPa, densities to 1700 kg m -3, and temperatures from 170 to 475 K, respectively. Keywords: HFC-125; Pentafluoroethane; Equation of state; Thermophysical properties; Heat capacity; Vapor pressure

I. Introduction

HCFC-22 (chlorodifluoromethane) is one of the most widely used working fluids in air-conditioning systems. Because concern about environmental issues is increasing, HCFC-22 is scheduled to be phased out before 2030 due to the possibility of ozone depletion and the impact of global warming. There is no single-component refrigerant to replace HCFC-22 at present, and some binary and ternary mixtures have been proposed, e.g., HFC-32/134a, HFC-32/125 binary systems and HFC3 2 / 1 2 5 / 1 3 4 a ternary system are considered as the most probable substitutes to replace HCFC-22. We have reported equations of state for HFC-134a [1], HCFC-123 [2], HFC-32 [3], HFC-125 [4], H F C - 3 2 / 1 3 4 a [5], and H F C - 3 2 / 1 2 5 / 1 3 4 a [6] based on the available thermodynamic property measurements. Since we want to apply the pure fluid equations of state for mixtures also, all these equations of state were developed in a similar functional form: the 18-coefficient modified BenedictWebb-Rubin equation of state. Many experimental studies of the thermodynamic properties of HFC-125, i.e., P V T properties, saturation properties, critical parameters, heat capacities, speed of sound, 2nd and 3rd virial coefficients, and ideal gas heat capacity, have been reported during recent years. In this study, a new equation of state for HFC-125 is proposed using the most recent information. • Corresponding author. 0378-3812/96/$15.00 Copyright© 1996ElsevierScienceB.V. All fights reserved. PII S0378-3812(96)03087-7

46

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996)45-54

2. Experimental data There are 14 experimental studies [7-20] available, reporting more than 500 points of vapor pressure for HFC-125. On the basis of these vapor pressure measurements [7-20], a new vapor pressure correlation for HFC-125 has been developed. The developed vapor pressure correlation is ln(Pr) =

1/Tr[a,(1- Tr) + a 2 ( l -

Tr) '2' + a 3 ( l -

Tr) 2 + a 4 ( 1 -

Tr) 3]

(1)

where Pr = P/Pc, Tr= T/T~, and the coefficients of Eq. (1) are listed in Table 1. The critical temperature of Tc = 339.165 K according to ITS-90, adopted in Eq. (1), was reported by Kuwabara et al. [21]. The critical pressure of Pc = 3617.5 kPa was then determined from the selected vapor pressure measurements [7,10,14,15,17,18,20] at the critical temperature of 339.165 K. Eq. (1) is considered to be effective from 170 K to the critical temperature, and represents almost all the selected measurements [7,10,14,15,17,18,20] within 1 kPa. Seven studies [8,12,15,22-25] for the saturated liquid densities of HFC-125 have reported more than 180 saturated liquid densities. Based on these measurements, a new correlation of the saturated liquid density has been developed as follows Pr = 1 + b,(1 - T~)°325 + b2(1 -- Tr) °'6 + b3(1 - Tr) + b4(1 - Tr) 3

(2)

where Pr = P/&, Tr = T/T¢, Tc = 339.165 K is the critical temperature and Pc = 568 kg m -3 is the critical density of HFC-125 reported by Kuwabara et al. [21]. The coefficients axe listed in Table 2. This correlation is applicable for temperatures from 170 K to the critical temperature. Eq. (2) represents almost all the available saturated liquid densities within 0.2%, expect those in the vicinity to the critical point. More than 1410 experimental data points representing PVT properties have been reported by Defibaugh and Morrison [8], Wilson et al. [9], Holste [11], Magee and Howley [12], Boyes and Weber [14], Luddecke and Magee [15], Oguchi et al. [17], Ye et al. [19], de Vries [20], and Sagawa et al. [26]. The available experimental data cover a wide range of temperatures from 178 to 474 K, densities up to 1700 kg m-3, and pressures up to 68 MPa, respectively. Luddecke and Magee [15] reported 97 points of isochoric heat capacity for the liquid phase, Gillis and Moldover [27] reported 149 points on speed of sound data in the vapor phase, and Takagi [28] and

Table I Coeffien~ of Eq. (I) i

ai

1 2 3 4

-7.75445235783 !.24476106475 0.434510973356 -3.43557217428

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54

Table 2 Coefficients of Eq. (2) i 1 2 3 4

47

bi 1.77740963498 0.56693411478 0.333737378064 0.262031546374

Grebenkov et al. [29] reported 135 points and 30 points of speed of sound data in the liquid phase, respectively.

3. Modified BWR equation of state In 1994, we reported an 18-coefficient MBWR equation of state for HFC-125 [4] on the basis of the experimental thermodynamic property data available at that time. Since then, further measurements have been reported, and the range of measurements has become much wider. In this study, we revise our equation of state using the updated measurements. The input data of the least square fitting procedures include P V T data, saturation data, Maxwell's equal-area construct, thermodynamic restrictions at the critical point, isochoric heat capacities, and speed of sound data. The saturation data, namely, the vapor pressures coupled with the saturated vapor/liquid densities, and the Maxwell's equal-area construct, i.e., the thermodynamic restriction of Gibbs free energy of the saturated vapor and the saturated liquid being equal at the same temperatures, were calculated from Eq. (1) and Eq. (2) and a supplementary correlation of the saturated vapor density developed in the present study, since it is difficult to obtain pairs of vapor pressure data and saturated vapor/liquid data measured exactly at the same temperatures. The thermodynamic constraints at the critical point include the conditions that the pressure be exactly consistent with the critical pressure, and that the first and second density differentials of pressure be zero at the critical point, respectively. After trial and error changing of the weighting factors of each data point, the formulation in a non-dimensional form of an 18-coefficient MBWR equation of state has finally been developed as follows

Pr = T r P J Z ¢ + B, " p~ + B2P 3 + Bap 4 +B4p~5 + B s p 6 + BrP~7 + (B 7 + B s p 2 ) p i ~ e x p ( - p r 2)

(3) where Pr = P / P c , Pr = P/Pc, Tr = T/Tc, Zc = Pc/(RxTc Pc), Rx = R / m ; R = 8.314471 kJ kmol -I K - J, m = 120.022 kg kmol- i B l = c I T r -~- c 2 -I-- c 3 / T r 2 -]- c 4 / T r 3 B 2 = c5Tr + c 6 + c7/Tr 2

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54

48 Table 3 Coeffients o f Eq. (3) i

ci 1 2 3 4 5 6 7 8 9

0.808566655441 - 2.51780953929 - 2.94597557896 - 0.0760276076613 2.96477516838 - 4.83671254055 4.72188690811 1-220500A'A'A'89 -- 1.13148249658 -- 0 . 1 3 9 8 4 8 2 0 8 6 8 6 -- 1.19005656049 0.292385852249 0.325447083246 -- 0 . 0 4 6 5 0 4 ! 609061 3.79541158133 -- 4 . 5 0 7 2 9 9 7 3 4 5 9 -- 3 . 0 0 0 5 9 2 0 6 2 0 5 3.33598009967

10

11 12 13 14 15 16 17 18

B3 = c8 + c9/T, 2 B 4 - - Clo + C l l / / T r e 5 = ¢12 "~ C l 3 / T r B6 ~ c14 B 7 - - c i 5 -~- C l 6 / T r

Bs = ct7 + c~s/T,

The coefficients are listed in Table 3. The correlation of ideal gas heat capacity reported by Hozumi et al. [30] was adopted in this study C ~ / R x = d t + d2T + d3T 2 Cp/kJkg -1K -I

The coefficients of Eq. (4) are given in Table 4. Table 4 Coeffients o f Eq. (4) i

di

I 2 3

4.3987 0.0242728 - 4.099 X 10 - 6

C.-c, Piao. M. Noguchi / Fluid Phase Equilibria 125 (1996)45-54

49

The Helmholtz free energy derived from Eq. (3) and Eq. (4) is given below a r = nl Pr + n 2 / 2 P $ + B 3 / 3 P 3 + n a / a P 4 + B s / 5 P 5 + B 6 / 6 P 6 - n v / 2 [ e x p ( - P 2 r ) - 1] -B8/2[(1 + p$)exp(-p$)-

1] + T J Z ~ . In(p,) + a °

(5)

where A° is the Helmholtz free energy at the ideal gas state which is expressed as follows

A°= l/Z¢{(d,-

1)[T r -

T~° - Trln(Tr/T~°)] - d2/2(T r - Tr°) 2

- d a / 6 ( T r 3 - 3T~T~°2 + 2T~°3) + A I - A2Tr}

(6)

where T r ° = 2 7 3 . 1 5 / T ¢ . The numerical constants, A I = 325.238156988/(TcR~) and A 2 = 1.325387302930/R x, are assigned so as to provide the specific enthalpy and entropy values as 200 kJ kg -I and 1 kJ kg -1 K -t at the saturated liquid state of 273.15 K, respectively.

4. D i s c u s s i o n

Fig. 1 shows the comparison of the measured PVT property data and the present equation of state, Eq. (3), in the pressure deviation for the superheated gaseous phase and the supercritical region. The present equation of state represents almost all of the measurements reported by Defibaugh and Morrison [8], Holste et al. [11], Boyes and Weber [14], Oguchi et al. [17], Sagawa et al. [26], Ye et al. [19], and de Vries [20] within 0.5%. For the compressed liquid phase, as shown in Fig. 2 in density deviation, almost all of the available measurements reported by Defibaugh and Morrison [8], Holste et al. [l 1], Luddecke and Magee [15], Magee and Howley [12], Oguchi et al. [17], Sagawa et al. [26], and de Vries [20] are shown within 0.5%, except for measurements close to the supercritical region. 2 O O

x

HFC-~25

/oc

7

I 0

E &

A

0

-20

160 260 360p/~Om_a~60. 600

~ Oefibaugh & M0rrls0n (!9921 O 0guchi e t a ] . 1994) U ¥e et ai.[1994) Helste et ai.(!993) ~ Sagawae t a ] 1994J ~ Be°rd de Vries (1995) Bores & Weber (1994)

Fig. l. Comparisonof Pl/Tmeasummen~andF_,q.(3) in theg~eouspha~ andsupe~fificalmgion.

50

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54 2

:2:

HFC-~25

k;

;°

2L v'

- o0

700

9do

l bo

p~

13bo 5bo

7oo

kg.m -°

~Oefibaugq g Merr]son (1992) Magee g Howley (1993) Sa§awaeL a: :19941 4clste eL a1.(:993) ~) OguchL eL al {1994) ~> Bernd de Vries (19951 <~ Luddecke g Magee (1993)

Fig. 2. Comparison of P V T measurements and Eq. (3) in the liquid phase and supercritical region.

HFC-125

3

2

Tc <

2

i m u

o -1

I

77

-2 180

2oo

220

240

260 T

2ao 3o 320 / K L

E Nonluc eL a1.(t9911 Q Boyes and Weber 119941 ~ Weber and Silva 1t994) Baroncini et al. 11993{ A Nagee and Howley 11994) Bernd de Vries [1995) b Luddecke and Nagee (t993) <] Oguchi et a].1t994)

Fig. 3. Comparison of measured vapor pressures and Eq. (3).

Tc

HFC-125 5 -

L;kg~ 3

I

0 ~V ~7E7

-'5 [ -- I

I

160

vvvv~ i

v .

iBO

.

.

200

.

v .

.

220

.

.

240

.

.

.

260

©~fibaugh and flirt]son(19921@Widiatmo et al. 199] ~Oiller et a1.(19931 Aluddecke and N~gee 11993 E] Ripple eL a]. (19931

.

280

T/K

.

.

300

~j V

.

320

~1

340

~Nagee and HowleT (t993) ~Hlgashi 119941

Fig. 4. Comparison of measured saturated liquid densities and Eq. (3).

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996)45-54

51

HFC-t25 I

0

"J~

-i ~

I

-2 2 0

0

~

0

~,.0

O ~ ~ ' ~ ' 0 0

,0

25o '

0o0

O0

0

aoo '

'

3so

'

T/K O kuddecke and gagee (tgg3)

Fig. 5. Comparison of measured C'~ data and Eq. (3).

Fig. 3 is the comparison of measured vapor pressures with Eq. (3). Eq. (3) represents the selected measurements [7,10,14,15,17,18,20] within 2 kPa, except for several points above 300 K. The curve indicates the vapor pressure correlation, Eq. (1). Fig. 4 shows the comparison of saturated liquid densities with Eq. (3). The broken lines indicate absolute deviations with 2 kg m -3 and - 2 kg m -3, and the solid curve is the saturated liquid correlation, Eq. (2). The saturated liquid densities are represented by the present equation of state, Eq. (3), within 2 kg m -3, except for several data in the vicinity of the critical point. The present equation of state also represents the C v data reported in the liquid phase by Luddecke and Magee [15] with a maximum deviation of - 1.7% and a standard deviation of 0.57%, as shown in Fig. 5. Fig. 6 shows the comparison of the speed of sound data with the equation of state, Eq. (3). The speed of sound reported in the superheated gaseous phase by Gillis et al. [27] is represented with a maximum deviation of 0.2%, and a standard deviation of 0.06%. The speeds of sound in the liquid

HFC-125

o

x

.2

°'-ii -'2

o

T/K

0 6illis et O 0 X

ai.(1993} HFC-125

2

) ll), !

'1 240

2 0

280

t

8, 8 i

i

300

320

T/K Takagl Hgg4)

~ Grebenkov et a1.(t994)

Fig. 6. Comparison of measured speed of sound data and Eq. (3).

340

52

o

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54

-iO0

-

-

This

------

-200

"7 o

HFC-t25 work

Hazumi

et

a l . (1994)

-300

E

¢J

-400

//

Cfl

-500

-600 /[ 250

i

I

i

•

I

300

I

350

i

450

400

T/K Fig. 7. Temperature dependence of 2nd virial coefficient.

phase reported by Takagi [28] and Grebenkov et al. [29] are represented with maximum deviations of 1.3% and -0.7%, and standard deviations of 0.7% and 0.3%, respectively. Fig. 7 compares the behavior of the temperature dependence of the second virial coefficients calculated from the present equation of state, with the reported data of Ye et al. [19] and Hozumi et al. [30]. These results show good agreement.

HFC-125

.

Iso~arsl

0 ! 0 5 t 0

MPa WPa WPa MPa WPa WPa WPa WPa '~Pa WPa WPa WPa WPa

I 5

2 3 4 5 6 8 tO t5

0 0 0 0 O 0 0 O ~C 0

T. / I

sat

l:q.

~

~

+

O

"

I

.

I

.

i

.

i

.

I

•

I

I

I

I

I

.

I

.

i

.

I

.

i

.

J

.

1

.

I

.

t60 t80 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480

T/K Fig. 8. Temperature dependence of

Cp.

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54

1.2

. . . . . . . . . . . .

.

. . . . . . .

•

HFC-125 . . . . .

•

53

. . . .

!

v.

t.O

I

0.8

•

io 6o

0.6

~ ~ 0 o 4

.

,

Mp~

80

/i.

.

i

.

,

.

i

.

,

.

i

.

i

.

i

.

i

.

i

.

i

.

i

.

,

.

10.0

WPa wPa

15.0

MPa

20.0

WPa

,

.

i

.

160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 /'/K

0 Luddecke and Wagee (19931

Fig. 9. Temperature dependence of Cv. Figs. 8 and 9 show the behavior of the temperature dependence of the isobaric heat capacity and isochoric heat capacity calculated from the present equation of state, respectively. These isobars show reasonable behavior from the thermodynamic point of view.

5. Conclusion A new 18-coefficient M B W R equation of state for HFC-125 has been developed. New correlations of vapor pressures and of saturated liquid densities are also presented. This equation of state is considered to be effective in the range of temperatures from 170 to 475 K, densities up to 1700 kg m -3 and pressures up to 68 MPa. The temperature scale throughout this study is in the new temperature scale of ITS-90.

6. List of symbols A C m P R Rx T p

Helmholtz free energy heat capacity/kJ k g - ~ K - J molar mass pressure/kPa universal gas constant/kJ kmol-m K gas constant/kJ k g - t K temperature/K density/kg m - 3

54

C.-c. Piao, M. Noguchi / Fluid Phase Equilibria 125 (1996) 45-54

6.1. Subscripts c p r v

critical parameter isobaric reduced parameter isochoric

6.2. Superscript o

ideal gas state

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [! l] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

C.-C. Piao, M. Noguchi, H. Sato and K. Watanabe, ASHRAE Trans., 100 (1994) Pt. 1. C.-C. Piao, M. Noguchi, H. Sato and K. Watanabe, Final Report to the lEA-Annex 18, 1993. C.-C. Piao, M. Noguchi, H. Sato and K. Watanabe, Proc. 1993 JAR Annual Conf., 1993, pp. 13-16. C.-C. Piao and M. Noguchi, Proc. 15th Japan Syrup. on Thermophysical Properties, 1994, pp. 9-13. C.-C. Piao, M. Noguchi, H. Sato and K. Watanabe, Proc. 1994 Int. Refrigeration Conf. Purdue, 1994, pp. 37-42. C.-C. Piao, I. Iwata, K. Fujiwara and M. Noguchi, Proc. 19th Int Congress of Refrigeration, IVa (1995) 488-495 Y. Monluc, T. Sagawa, H. Sato and K. Watanabe, Proc. 12th Japan Syrup. on Tbermophysical Properties, 1991, pp. 65-68. D.R. Defibaugh and G. Morrison, Fluid Phase Equilibria, 80 (1992) 157-166. L.C. Wilson, W.V. Wilding, G.M. Wilson, R.L. Rowley, V.M. Felix and T. Chisolm-Carter, Fluid Phase Equilibria, 80 (1992) 167-177. C. Baroncini, G. Giuliani and F. Polonara, 3rd World Conf. on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, Oct.30-Nov.5, 1993. J.C. Holste, Final Report to ASHRAE on Project RP-654, 1993. J.W. Magee and J.B. Howley, to be submitted to Int. J. Thermophys. Nagel, DKV-Tagungsbericht 20, Band II.l (1993) 39-59. S.J. Boyes and L.A. Weber, J. Chem. Thermodyn., 27 (1995) 163-174. T.O.D. Luddecke and J.W. Magee, to be submitted to Int. J. Thermophys. LW. Magee and J.B. Howley, to be submitted to Int. J. Thermophys. K. Oguchi, A. Murano, K. Omata and N. Yada, 12th Symp. Thermophys. Prop., Boulder, June, 1994. L.A. Weber and A.M. Silva, J. Chem. Eng. Data, 39(4) (1994) 808-812. F. Ye, H. Sato and K. Watanabe, J. Chem. Eng. Data, 400) (1994) 148-152. Bemd de Vries, University of Hannover, data from IEA-Annex-18 database, 1995. S. Kuwabara, H. Sato and K. Watanabe, J. Chem. Eng. Data, 39 (1994) 304-308. E. Diller and S.M. Peterson, Int. J. Thermophys., 14 (1993) 55. D. Ripple and O. Matar, letter from Dr. Moldover at NIST, 1993. VJ. Widiaano, H. Sato and K. Watanabe, J. Chem. Eng. Data, 39(2) (1994) 304-308. Y. Higashi, Int. J. Refrig., 17(8) (1994) 524-531. T. Sagawa, H. Sato and K. Watanabe, High Temp.-High Press., 26 (1994) 193-201. K.A. Gillis and M.R. Moldover, Int. J. Thermophys., 17 (1996), in press. T. Takagi, private communication, 1994. Grenbenkov, Proc. CFC's: The Day After, IIR Comm B1, B2, El, E2, Padova, Italy, Sept.21-23, 1994. T. Hozumi, H. Sato and K. Watanabe, J. Chem. Eng. Data, 39(4) (1994) 493-495.