Ind. Eng. Chem. Res. 1989, 28, 1913-1917
1913
Application of the PFGC-MES Equation of State to Refrigerants The Parameters from Group Contribution (PFGC) equation of state, as used by Moshfeghian, Erbar, and Shariat (PFGC-MES), is used to describe the thermodynamic behavior of 20 refrigerants. These refrigerants include pure halogenated compounds, azotropic mixtures of halogenated compounds, and ammonia. The parameters were determined by simultaneously fitting data for vapor pressure, saturated vapor and liquid volumes, and heats of vaporization using a standard nonlinear analysis program. All parameters for the 20 refrigerants are reported, as are the deviations between predicted and experimental data. These deviations are compared to those from the Soave-Redlich-Kwong equation of state. The predicted and experimental K values for two binary mixtures of the pure halogenated compounds are also compared. The need for methods of accurately describing the thermodynamic properties of halogenated compounds such as chloro, fluoro, and chlorofluoro derivatives of methane and ethane has been well established. The halogenated compounds have been extensively applied as refrigerants and heat-transfer agents. This paper provides a method for calculation of the thermodynamic properties of the halogenated compounds. For pure compounds, vapor pressure, saturated vapor and liquid volumes, and heat of vaporization are calculated. The azeotropic mixtures are treated as pure compounds, and the same thermodynamic properties are calculated. For binary mixtures, K values are calculated. In all cases, the calculated results are compared with experimental values. The calculation method is based on the Parameters From Group Contribution (PFGC) equation of state, which has been presented by Cunningham and Wilson (1974). In their original publication, Cunningham and Wilson (1974) showed the distinct advantage of the PFGC system of equations for hydrocarbons. They showed that the PFGC predicted K values for typical hydrocarbon systems that were equivalent to the results predicted by the Mark V equation of state and were in good agreement with experimental data. Moshfeghian et al. (1979) have developed an improved and extended set of parameters for various groups used in the PFGC equation of state. Moshfeghian et al. (1980) and Shariat et al. (1979) also successfully applied their version of the PFGC, called PFGC-MES, to polar and diverse systems such as the hydrocarbon-water-methanol system. Majeed (1983, 1985) successfully applied the PFGC to glycol-water-hydrocarbon systems. In addition, the PFGC has also been successfully applied to hydrocarbon systems with COP freezeout and with hydrate formation (Majeed, 1983; Majeed et al., 1984; Wagner et al., 1985; Majeed and Wagner, 1985),to coal-derived compounds (Moshfeghian et al., 1985), and to ionic systems (Friedemann, 1987).
I )
0.901
-80
I
-60
-40 TEMPERATURE, OC
-20
I
Figure 1. Effect of temperature on liquid-phase interaction between CHF, and CCIFB.
namic properties (chemical potential and isothermal effect of pressure on enthalpy) are more complex than those based on the more standard cubic equations of state. In no case are calculations as complex as those required to solve the Benedict-Webb-Rubin-Starling (BWRS) equation of state. Determination of Parameters
Determination of the various parameters for each group involved is a fairly complex and tedious fitting procedure. Attempts to determine a common set of group parameters to describe the thermodynamic behavior of all the refrigerants failed. Therefore, all of the molecules treated in this study were fitted as individual groups. The basic fitting procedure consisted of assembling the best available data for vapor pressure, saturated vapor and liquid volumes, and heat of vaporization. These data were fitted simultaneously by using a standard nonlinear analysis program. The values determined were the group parameters bk, sk, Ek(O),Ek('), and E,". The parameters for the refrigerants fitted in this study are shown in Table 11. PFGC-MES Equation of State The mixing rules of the PFGC-MES equation of state The basic PFGC-MES equations used to predict the had to be modified to predict the phase behavior of binary thermodynamic properties of systems are given in Table systems of refrigerants. This modification consisted priI. As can be seen, the PFGC-MES equation of state relies marily of defining different binary interaction parameters only on group contributions-critical properties, etc., are for each phase present-i.e., one interaction parameter per not required. All Redlich-Kwong-based equations of state binary pair for the vapor phase (equal to one for all of the such as Soave-Redlich-Kwong (SRK) (Soave, 1972) or binary systems studied); another binary interaction parameter was defined for the liquid phase. In addition, the Peng-Robinson (PR) (Peng and Robinson, 1976) rely on using the critical properties to estimate the parameters for liquid-phase binary interaction parameter usually had to solution. be temperature dependent to achieve good agreement The PFGC-MES equation itself is basically cubic. Unbetween predicted and experimental K values. The liqfortunately, however, it requires more complex calculation uid-phase binary interaction parameter appears to be nearly linear with temperature for most systems. The for solution than the standard cubic equations of state. In addition, the various functions for the other thermodytypical temperature dependence of the liquid-phase in0888-5885/89/2628-1913$01.50/0 0 1989 American Chemical Society
1914 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 Table I. PFGC-MES Equationsa
B
41
X
compressibility:
-Pu= z =
RT
-41
E
-6
e chemical potential:
1
d
g
-8
E
,
,
0.8
0.9
S A T U R T VAPOR,VOLUME
A SATURATED LIQUID VOLUME 3 HEAT
OF
VAPORIZATION
-10
(y)
0.6
0.5
0.7
1.0
REDUCED TEMPERATURE, Tr
-
In
1
0 VAPOR PRESSURE
A
mikbk
Figure 2. Ability of PFGC-MES to predict the P-V-T of pure CF,.
bf
ethalpy departure:
mixing rules:
2
C
b = &bi
mixture volume
A SATURATED LIQUID VOLUME
-8
0 HEAT OF VAPORIZATION
a -10 0 4
L
0.5
8
bi = Zmikbk
component i volume
0.6 0.7 0.8 REDUCED TEMPERATURE, Tr
I
0.9
1.0
Figure 3. Ability of PFGC-MES to predict the P-V-T of pure NH,.
k
8
Cximikbk
:tC/k
k group fraction in mixture 7
=
0
C
s = &si
5!
proportional t o mixture degrees of freedom
k
=
e-EkJT
2-
a
AAA AA
X
proportional to component degrees of freedom (8)
Tkn
A A A ~ ~ A A
X
8
si = xmiksk
4-
interaction energy parameter between groups k and n (9)
where interaction energy between Ekn = Kkn[Ek + EnJ/2.0 groups k and n (10) Ek = E,(O) - E k (1)( 2 8 3 . 2 / T - 1) + Ek'"[(283.2/7')' - 11 energy term for group k (11)
" i is the ith component of c total components; c is the total number of components; k is the kth group of g total groups; n is the nth group of g total groups; g is the total number of groups; c/bH is the Universal constant, 12.0; mik is the number of groups k in component i; u is the molar volume; P is the absolute pressure; R is the Universal gas constant; T is the absolute temperature; &('), &(", and E,(z) are the energy coefficients for group k ; bk is the molar volume of group k; sk is the group k degrees of freedom; and Kkn is the binary interaction coefficient between groups k and n.
teraction parameter for the system CHF,-CClF, is shown i n Figure 1.
Results
Tables I11 and IV summarize the results of the fitting process and show some predicted d e v i a t i o n s for the
-w i! J
' 0
AA
w
oc
25
a: 0
opoo 0 A
-2-
A A
-4 -
-6-
c
5
A
00
X
I
A
n o_c_o a --A---mn5L-
A
Bo
A
C - 8 - 0 VAPOR PRESSURE D SATURATED VAPOR VOLUME
0
a
W
a -10- A SATURATED LlOUlD VOLUME 0 HEAT OF VAPORIZATION -12
o
n
PFGC-MES equation of state. The absolute average deviations between the predicted a n d the e x p e r i m e n t a l values for pure and azeotropic m i x t u r e s of refrigerants fitted in this s t u d y are shown i n Table 111. The experimental data are those published in the A S H R A E Handbook of Fundamentals (1977). The predicted values appear to be in excellent agreement with the experimental data. To further define the power of the PFGC-MES equation of state, we compared the accuracy of p r e d i c t e d results w i t h those predicted b y the Soave-
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1915 Table 11. P F W - M E S Parameters for Refrigerants refrigerant compd b, ft3/lb-mol 11 CClqF 0.9940 0.8530 12 CC1;Fz 0.8472 13 CClF3 0.8472 14 CF, 0.8454 21 CHC12F 0.6723 22 CHClFz 0.5764 23 CHF3 0.6606 40 CH3Cl 0.5660 50 CHI 1.4009 CClzFCClFz 113 1.2747 CClFzCClFz 114 1.0955 CZClFj 115 0.8834 CH3CClFZ 142b 0.7705 CHSCHF2 152a 0.6495 170 CZH6 CClZFz-CH3CHF2 0.8200 500" CHzFz-CzClF5 0.7264 502" CClFq-CHFq 0.5905 503" 0.6305 504" 0.2749 717
E(O)/R,O -453.33 -404.87 -253.46 -203.10 -464.19 -446.54 -365.24 -445.93 -137.03 -344.77 -323.63 -293.88 -440.33 -419.36 -320.81 -400.32 -455.71 -394.93 -428.95 -997.01
s 6.5677 6.0670 4.0990 3.500 5.2309 4.8861 3.9402 3.4159 1.8488 6.3884 6.7136 6.0522 6.4543 4.7970 3.8604 5.6308 6.6788 5.2765 4.8257 2.7722
R
E("/R, O
R
-47.09 -41.44 -70.78 -69.76 -110.10 -135.12 -153.16 -137.70 -53.04 -64.46 -53.89 -68.15 -164.25 -209.43 -72.26 -88.60 -57.14 -57.88 -172.13 -618.67
E @ ) / RO, R 2.88 1.17 9.00 8.44 12.09 22.57 23.20 13.01 5.93 8.03 7.39 12.00 60.00 60.00 10.00 16.30 7.51 2.25 36.47 115.73
" Azeotropic mixtures are treated as pure compounds. Table 111. Summary of Deviations between Predicted and Experimental Pure Refrigerant Properties av abs % dev reduced temp vapor saturated saturated saturated refrigerant compd no. of points range pressure vapor vol liquid vol vapor 2 11 CC13F 47" 0.44-0.98 0.67 1.02 5.46 1.11 0.55-0.98 0.64 1.35 5.53 12 CClzFz 38 1.85 0.48-0.97 2.19 2.20 13 CClF, 28 0.68 2.36 14 CFI 18 0.56-0.98 0.47 1.20 1.77 1.42 21 1.81 0.44-0.96 0.48 1.37 3.25 CHClzF 31 0.67 1.57 22 CHClFz 35 2.12 0.47-0.98 4.06 2.71 23 CHF, 26 3.13 0.50-0.96 0.58 1.57 CH&l 22 0.51-0.83 0.22 1.44 0.42 40 1.63 CH; 16 1.12 50 1.73 0.52-0.96 1.09 1.64 113 CClZFCClFz 37 2.17 2.31 0.49-0.98 0.30 4.55 114 CClFXClF, 41 0.48 0.44-0.97 0.32 0.69 4.90 C~CI@~ 27 2.48 0.53-0.96 0.69 115 3.21 4.53 0.49-0.96 CH3CClFZ 36 142b 3.06 2.94 0.57 3.89 CHICHF, 36 152a 2.75 2.71 0.44-0.95 1.08 1.42 170 1.04 1.42 0.44-0.96 0.76 3.99 cZH6 30 1.44 0.53-0.95 0.52 500 1.89 3.85 CClzFZ-CH3CHFz 30 0.27 CHzFZ-CzClF5 32 502 0.67 0.50 0.48-0.97 6.13 CClF3-CHS 26 0.87 0.49-0.97 0.20 6.19 503 0.98 3.64 0.55-0.96 0.26 CHzFz-CClF, 26 504 3.73 3.19 NH3 27 717 0.61 0.55 0.46 0.48-0.92 0.90
saturated heat of liquid 2 vaporization 5.74 1.16 5.56 1.55 2.27 2.33 2.15 1.03 3.31 1.68 2.18 4.04 3.12 1.73 0.93 0.58 2.52 2.10 2.31 4.36 0.71 5.07 2.82 4.54 3.56 3.92 3.13 1.55 1.46 4.03 1.53 3.77 0.89 6.23 0.71 6.20 3.77 3.23 0.43 0.87
" An increment of 10 "F was chosen between the points. 5.0
- V A EXPERIMENTAL 4.0 - - CALCULATED - T 32OF
EXPERIMEN'A' n 31.9OF
-
3.0
2.01
'
1
0 -100.05oF -PREDICTED
0
w
3
i$ 2.0Y
o* 0.40.0
0.2
0.4
0.6
0.8
1.0
MOL FRACTION OF LIGHTER COMPONENT, C2H4F2
Figure 5. PFGC-MES binary K-value predictions of CzH4F2CF&
1.0 -
0.90.80.71
0.0
I
0.2
0.4
0.6
0.8
1.0
1
MOL FRACTION OF LffiHTER COMPONENT, CHF3
Redlich-Kwong equation of state. This comparison, which is in terms of the standard deviation for various thermodynamic properties, is shown in Table IV. It should be noted that the SRK prediction has been reported by As-
Figure 6. PFGC-MES binary K-value predictions of CHF3-CC1F3
selineau et al. (1978). Even though PFGC-MES covers a wider range for reduced temperature, overall PFGC-MES
1916 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989
V B
0 g
vs
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1917
+
Table VI. Binary Interaction Coefficient for CHFS CClFj" binary interaction, Kbn system vap phase liq phase temp, "F CHF:, + CClF:, 1.000 0.925 31.9 1.000 1.000 1.000
0.920 0.910 0.905
-0.1 -55.1 -100.05
For the liquid phase, the correlation equation is Kkn = 0.8584 + 1.29T/10000, where Tis in OR.
gives better results. As can be seen, tjpr and 6," for PFGC-MES are much smaller than those of SRK; however, 6, and 6m for SRK are almost equal or somewhat smaller than those of PFGC-MES. It should also be noted that the number of points are not the same in both methods. We used an upper reduced temperature limit for the pure component fitting process of approximately 0.97. This upper limit was used to avoid problems in the fitting process around the critical point of the component. The PFGC-MES equation is not applicable in the region of the critical point. The difficulty stems mainly from not satisfying the usual critical point requirements, i.e., Consequently, we do not recommend using this approach with a system in the critical region. Figures 2, 3, and 4 show the percent error for CF4,NH,, and Refrigerant 504 as a function of reduced temperature. The breakdown near the critical region clearly shows. After the pure component parameters had been determined, an extensive evaluation of the ability of the PFGC-MES equation to predict the thermodynamic properties of mixtures was made. A number of different binary systems were considered. The ability of PFGCMES to predict K values for two of these systems is summarized in Table V and shown graphically in Figures 5 and 6. Table VI shows the variation with temperature of the binary interaction coefficient for CHF, with CC1F3. The average absolute deviations between the predicted and the experimental K values are shown in Table V. As can be seen, the predicted K values are in good agreement with the experimental values.
Summary
A calculation method based on the PFGC-MES equation of state to describe the thermodynamic behavior of halogenated compounds has been presented. Parameters for 20 refrigerants have been determined and are listed. This study and a comparative analysis of the results of the PFGC-MES equation of state with the SRK equation of state have shown that the PFGC-MES can provide a reasonable tool to describe the thermodynamic behavior of refrigerant systems. Literature Cited ASHRAE Handbook of Fundamentals; American Society of Heating, Refrigerant and Air-conditioning Engineers: New York, 1977.
Asselineau, L.; Bogdanic, G.; Vidal, J. Calculation of Thermodynamic Properties and Vapor-Liquid Equilibria of Refrigerants. Chem. Eng. Sci. 1978, 33, 1269-1276. Cunningham, John R.; Wilson, Grant, M. Equation of State Analogy to an Activity Coefficient Equation-Calculation of Parameters
from Group Contributions. In Proceedings of the 54th GPA Annual Convention, Denver, CO, Gas Processors Association, Tulsa, OK 1974; pp 77-86. Friedemann, John D. Simulation of Vapor-Liquid Equilibria in Ionic Systems. Doctoral Dissertation, School of Chemical Engineering, Oklahoma State University, Stillwater, 1987. Majeed, Ali I. Prediction of Inhibition of Hydrate Formation Using the PFGC Equation of State. Doctoral Dissertation, School of Chemical Engineering, Oklahoma State University, Stillwater, 1983.
Majeed, Ali I. VLE Predictions for Hydrocarbon Systems Containing Methanol and Glycols Using the PFGC Equation of State. Presented at the Ninth Annual Symposium on Thermophysical Properties, Boulder, CO, June 23-27, 1985. Majeed, Ali I.; Wagner, Jan The PFGC Equation and Phase Equilibria in Light Hydrocarbon Systems. In Equations of StateTheories and Applications; Robinson, Robert L., Jr., Chao, K. C., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1985. Majeed, Ali I.; Wagner, Jan; Erbar, John H. Prediction of Thermodynamic Properties Using the PFGC Equation of State. Proceedings of the 1984 Summer Computer Simulation Conference, Boston, Society for Computer Simulation, July 23-25, 1984; pp 537-542.
Moshfeghian, Mahmood; Shariat, Ahmed; Erbar, John H. Application of the PFGC Equation of State to Gas Processing Systems. Presented at the National AIChE Meeting, Houston, April 5, 1979.
Moshfeghian, Mahmood; Shariat, Ahmed; Erbar, John H. Application of the PFGC-MES Equation of State to Synthetic and Natural Gas Systems. In Thermodynamics of Aqueous Systems with Industrial Applications, Presented at the NBS/NSF Symposium on Thermodynamics of Aqueous Systems with Industrial Applications, Airlie House, VA, Oct 22,1979; Newman, Steven A., Ed.; ACS Symposium Series 133; American Chemical Society: Washington, DC, 1980. Moshfeghian, Mahmood; Taheri, M.; Shariat, Ahmed Application of PFGC-MES Equation of State to Coal Derived Compounds. Presented at 40th Annual Calorimetry Conference, Asilomar, CA, Aug 25-30, 1985. Peng, Ding-Yu; Robinson, Donald B. Two and Three Phase Equilibrium Calculations for Systems Containing Water. Can. J . Chem. Eng. 1976,54, 595-599. Pennington, W. A.; Reed, W. H. Azeotrope of 1,l-Difluoroethane and Dichlorodifluoromethane as a Refrigerant. Chem. Eng. Prog. 1950, 46(9), 464-466.
Shariat, Ahmed; Moshfeghian, Mahmood; Erbar, John H. Predicting Water Knockout in Gas Lines. Oil Gas J. 1979, 77(47), 126-133. Soave, Giorgio Equilibrium Constants From a Modified RedlichKwong Equation of State. Chem. Eng. Sci. 1972,27,1197-1203. Stein, Fred P.; Proust, Patricio C. Vapor-Liquid Equilibria of the Trifluoromethane-trifluorochloromethane System. J . Chem. Eng. Data 1971, 16(4), 389-392. Wagner, Jan; Erbar, Ruth C,; Majeed, Ali I. AQUA*SIM-Phase Equilibrium and Hydrate Inhibition Using the PFGC Equation of State. Proceedings of the 64th GPA Annual Convention, Houston, March 18-20, 1985.
* Corresponding author. t Deceased.
Mahmood Moshfeghian, A h m e d Shariat
Department of Chemical Engineering Shiraz University Shiraz, Iran John
H.Erbar: Ruth C.E r b a r *
School of Chemical Engineering Oklahoma State university Stillwater, Oklahoma 74078-0537 Received for review April 20, 1988 Accepted November 4, 1988
