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Correlation of excess enthalpies and prediction of vapor—liquid equilibria from excess enthalpies by means of an equation of state
Fluid Phase Equilibria, 65 (1991) 145-157 Elsevier Science Publishers B.V., Amsterdam
145
Correlation of excess enthalpies and prediction of vapor-liquid equilibria from excess enthalpies by means of an equation of state Guangshun
Chen, Zhaoli Wu, Zhongxiu Chen and Yujun Hou
Department of Chemical Engineering, Zhejiang University, Hangzhou, (People’s Republic of China) (Received February 12, 1990; accepted in final form January 3, 1991)
ABSTRACT Chen, G.S., Wu, Z.L., Chen, Z.X. and Hou, Y.J., 1991. Correlation of excess enthalpies and prediction of vapor-liquid equilibria from excess enthalpies by means of an equation of state. Fluid Phase Equilibria, 65: 145-157. The Martin-Hou (M-H) equation of state with the modification by Hou was applied to correlate the excess enthalpy of binary gaseous or liquid systems. 144 sets of data for the excess enthalpy of 19 binary gaseous systems and 39 sets of data for the excess enthalpy of 22 binary liquid systems were correlated. The results were satisfactory. In this work, the M-H equation was also applied to predict isothermal binary vapor-liquid equilibrium data from the excess enthalpy data.
INTRODUCTION
When two or more pure compounds mix, the excess enthalpy will be produced owing to molecular interaction. Mixing or separation of substances is very common in chemical production and scientific experiments; in all such processes, the excess enthalpies are involved, and therefore the correlation of excess enthalpies is of fundamental importance in process design. The correlation methods for the excess enthalpy are as follows: (i) Empirical or semi-empirical methods. In general, the excess enthalpy is correlated by a function of composition or temperature (e.g. Redlich and Rister, 1948; Mrazek and Van Ness, 1961; Brandrech et al., 1966; Morris et al., 1975; Rogalski and Malanovski, 1977; Trezo, 1982). Some of these correlation formulae are empirical and others are derived from certain 0378-3812/91/$03.50
0 1991 Elsevier Science Publishers B.V.
146
models of solution. These are the most common correlation methods for the excess enthalpy of liquid mixtures. (ii) The equation of state method. The excess enthalpies of gaseous mixtures are commonly correlated by means of equations of state (e.g. Sctonder, 1972; Ba et al., 1977, 1978; Ashton and Haselden, 1980; Jadot, 1980). In the critical region, it is usual to explore the changes of HE for binary mixtures using Van der Waals-like equations of state (Wormald, 1986; Christensen et al., 1987). Recently, equations of state have also been used to correlate HE in the liquid region. For instance, Ada&i and Sugie (1988) correlated HE of the water-acetone system by means of a cubic equation of state; Casielles et al. (1989) predicted HE of a ternary system from binary experimental data using the Peng-Robinson (P-R) equation. In addition to these methods, approaches based on the “graph” theory and Monte Carlo simulation (Prochazka, 1976; Enciso, 1981; Sir@ et al., 1982) have also been tried. The Martin-Hou (M-H) equation is an accurate equation of state. The original equation proposed by Martin and Hou (1955) is applicable only to the gaseous phase; however, the equation modified by Hou et al. (1981a) is applicable to both gaseous and liquid phases. Hou et al. (1981b) and Hu (1984) have successfully applied this equation to calculate vapor-liquid and liquid-liquid equilibria for binary and ternary mixtures. Therefore, it is to be hoped that the M-H equation can be applied to correlate the excess enthalpies of both gaseous and liquid mixtures, and to predict isothermal vapor-liquid equilibria from the excess enthalpies of liquid systems.
THE CORRELATION
METHOD FOR EXCESS ENTHALPY
According to the definition of excess enthalpy, with the standard state at zero pressure, the excess enthalpy for binary mixture can be expressed
0) For pure compounds
P=
the M-H
equation
is
; FL/(vw# L=l
F,=RT F2= A, + B,T+ C, exp(-5.475T/T,) F3=A, + B,T+ C, exp( -5.475T/T,)
(5)
F4=A4+B4T
(6)
F,=B,T
(7)
147
By thermodynamic
derivation, ( H - H * ) for pure compounds
(H-H*)=PV-RT+
;
is
(FL-TdFL/dT),‘[(L-l)(V-b)L-l]
(8)
L=2
For mixtures, mixing rules for temperature functions of the M-H equation (Hou et al., 1981b) can be expressed as follows: F,, = RT
(9)
F,,=C~~1;;,-CC(l-Q,,,~X,~~
(10)
(id
Fm,=[~x,I~~11~3]3
01)
Fm4=
(12)
-[xqI&11/4]4
l1’5]5
Fm,=[~W~
(13)
b, = c X,b,
(14)
Thus the M-H equation for mixtures is P=
?
F,,/(v,-4,,)L
(15)
L=l
Similarly, for mixtures (H-H*),=PV-,,-RT+
;
(FmL-TdFmL/dT)
L=2 /[U
-
w,
- &I”-‘1
06)
where dF,,/dT=
xX2
dI;;:,/dT-
xX(1
- Q,,)Xx,
d,/lF;,F,,
I
/dT
(izj) (17)
dF,3/dT=[~XJIc;31’/3]2[~X,I~3l-2’3dE;3/dTSGN(F;3)]
(18)
dF,,/dT=
-[cXi
(19)
dF,,/dT=
[~&I&, -1
SGN( X) =
0 1
1~4 ~l’~]~[ Cxi 11’14l-3’4 d~,/dTSGN(EJ.,)] I’“l*[~XJ& XC0 x=0 x>o
l-4’5 dE;.,,‘dTSGN(&)]
(20) (21)
148 TABLE 1 Comparison of results calculated by means of the M-H equation with literature data at different temperatures and pressures for gaseous excess enthalpy P (atm)
AH:%
AH:=%
N,+CH,” Q, = 0.05076 21.02 6.8 40.96 1.6 60.99 3.7 81.02 5.6
298 K 11.5 3.4 - 8.3 -11.4
Qi, = 0.0426 4.1 30.10 3.8 39.87 6.5 50.82 4.8 54.87 10.1 64.94 70.46 9.7 8.1 80.43
201 K -9.2 -8.8 - 13.8 - 17.5 28.8 12.9 11.1
Ar+CH,
a
Qi, = 0.03793 20.13 1.0 3.4 40.26 60.50 2.6 80.04 2.6 8.3 100.7 Q,, = 0.027 50.33 3.9 60.00 1.1 8.8 65.13 8.0 70.07 5.7 85.07 CH,+H,
298 K 1.7 6.4 - 6.1 - 5.5 - 13.4 201 K 17.0 2.8 13.6 12.9 - 13.1
=
Q, = 0.05447 10.95 3.2 21.01 3.9 31.38 3.8 3.5 41.15 50.63 4.4 60.69 13.7 6.6 70.96 80.43 5.3 90.20 5.8 Qi, = 1.459 5.9 15.99
201 K - 5.2 5.6 4.2 -9.3 7.3 - 17.8 -11.3 -7.7 11.0 298 K - 10.1
P (atm)
AH:‘%
30.99 45.99 60.99 75.99 100.96
2.4 3.6 2.0 2.0 2.4
AH&.$ 4.3 5.2 - 4.2 - 4.0 -4.5
CH, + H,S b Qij = 0.2454 5.00 8.0 9.97 6.3 15.00 4.9
293 K 14.6 - 10.7 17.4
Q, j = 0.2538 5.00 10.3 9.97 3.0 15.00 6.4
305 K - 22.1 9.4 9.5
Qij = 0.2641 5.00 6.1 9.97 5.2 15.00 2.3
313 K 7.8 10.6 3.3
N,+Hza Qij =1.486 21.02 40.76 60.99 81.02 101.06
8.4 7.2 2.5 2.5 2.9
298 K - 18.0 - 14.0 6.4 3.9 - 8.2
Qij = 0.03164 30.99 5.2 50.92 2.8 70.96 1.4 90.99 1.4 110.92 3.5
201 K 7.6 -3.7 -3.9 -4.6 4.4
CH, + CO, ’ Q, = 0.13686 10 7.8 20 29 30 1.7 40 1.1 50 4.7 60 2.3
305 K - 19.9 6.0 2.8 7.6 12.4 9.4
P (atm) 70 80
AHE%
AH:=,%
5.7 6.0
- 18.0
Qij = 0.12515 10 8.6 20 5.3 30 1.5 4.6 40 3.0 50 5.1 60 70 6.7 1.9 80
313 K - 17.1 6.8 - 3.7 - 9.4 7.7 10.0 - 13.8 -7.8
Qij = 0.11575 10 10.9 20 4.0 4.9 30 40 4.3 50 2.1 2.1 60 2.7 70 80 1.2 6.0 90 100 8.6
333 K - 20.7 - 10.7 -9.3 7.0 -5.1 -3.2 3.9 - 2.2 - 17.7 -40.3
Q, = 0.11485 9.6 10 20 3.5 30 2.5 40 2.5 50 2.0 2.5 60 2.0 70 80 2.0 90 3.9 100 4.8
343 K - 29.6 6.7 5.4 3.7 - 3.3 - 3.5 - 6.4 - 8.0 - 16.3 - 27.1
Q,j = 0.11812 10 10.6 20 3.1 30 1.7 2.6 40 50 2.4 60 1.4 70 2.3 80 5.2 90 4.7 100 4.0
353 K - 26.3 -9.7 -4.6 3.5 3.3 3.1 3.8 21.1 - 15.0 -5.7
a Wormald et al., 1977. b Alpha et al., 1982. ’ Lee and Mather, 1972.
- 13.8
149 TABLE 2 Comparison of results calculated by means of the M-H equation with literature data at 1 atm and different temperatures for gaseous excess enthalpy
T WI
CH, +C,H, 363.2 373.2 383.2 393.2 403.2 413.2
AHE%
Qii
AH:ax%
0.68 0.63 0.68 0.73 0.70 0.62
1.3 -1.8 -1.8 -1.7 1.3 - 2.2
1.00650 0.93120 0.86990 0.82042 0.80752 0.73978
383.2 403.2 413.2
0.60 0.63 0.64 0.87 1.2 1.1
-1.0 - 1.1 - 1.8 1.8 - 3.1 -2.1
C,H, + n-C,H,, b 0.189480 304.5 0.146600 333.2 0.095840 363.2
1.37 2.25 5.16
- 3.5 - 5.0 14.7
C,H, + n-C,H,, b 0.50200 372.2 0.45560 383.2 0.39440 403.2
1.45 1.10 0.62
6.5 2.6 1.6
C,H, +n-CsH,, b 1.19920 403.2 1.11960 413.2
1.14 1.07
2.7 -2.5
n-C,H, + n-C,H,, b 0.35100 344.2 0.27800 363.2 0.22330 396.9
1.06 0.56 0.85
-2.2 1.7 -2.2
AH,F;%
AH;=%
b
0.49800 0.38640 0.39460
1.24 0.89 2.35
3.8 -2.4 -4.7
1.22 1.14 1.40
- 2.5 3.0 -2.9
4.35 4.07 5.76 7.86
-8.8 - 7.8 - 8.7 - 18.4
1.33 1.62 1.71
2.7 - 3.6 5.0
5.54 6.13 6.16
- 9.7 11.8 - 14.5
2.61 2.01
- 5.3 5.0
2.91 5.14
6.8 -8.6
n-C,H, + n-CsH,, b 403.2 410.2 413.2
CH, +C6H,* a 363.2 373.2 383.2 393.2 403.2 413.2
Qij
n-C,H, + n-C,H,,
a
1.22990 1.05300 0.97960 0.90250 0.86060 0.83140
T W)
n-C,H,, 363.2 373.2 383.2 393.2
0.74301 0.71000 0.69264 + n-C,H,,
b
0.12748 0.11865 0.11412 0.09705
n-C,H,, + n-CsH,, b 403.2 410.5 413.2
0.46050 0.41280 0.41120
n-C,H,, + n-&H,, 393.2 403.2 413.2 n-C,H,, 403.2 413.2
b
0.10962 0.09369 0.08882 + n-CsH,s b 0.24270 0.22030
n-C,H,, + n-CsH,, b
a Wormald, 1977. b Wormald et al., 1979.
403.2 413.2
0.10550 0.09436
150
Qi,. is a binary interaction parameter. The average percentage deviation of the calculated results for excess enthalpy from experimental values is selected as the objective function for the optimization.
RESULTS AND DISCUSSION
Correlation of the gaseous excess enthalpy
144 sets of data for the excess enthalpy of 19 binary gas systems were correlated, and the correlated results compared with published data. The results of the comparisons are given in Tables 1 and 2, and typical results are illustrated in Figs. l-4. In Figs. l-4, the ordinate is HE(J mol-‘) and the abscissa is the mole fraction X,. Each curve represents the values calculated by the M-H equation, and points represent the published data. Tables 1 and 2 and Figs. l-4 show that the correlation results from the M-H equation are very satisfactory. The average percentage deviation (AH%).. of each set for the system CH, + C,H, is less than 1.2%, both being within the accuracy of experiment. Wormald (1977) used the corre-
100
ah
c” 1%
70
f 2ec "r 2" m 5
40
& zm : lzl:?o
10
C 0.0
0.2
Mole
0.4
fraction
0.6
0.E
Y,
1.0
I.0
0.2
Mole
0.4
fraction
0.6
0.6
1.0
Y,
Fig. 1. Comparison of calculated and published data (Wormald et al., 1977) at 298 K for the N,(l)+H,(2) system. Fig. 2. Comparison of calculated and published data (Lee and Mather, 1972) at 343.15 K for the CH,(l) + CO,(2) system.
151
I
100.37
atm
I
20
0
Mole
fraction
y1
0 0.0
0.2 Mole
Fig. 3. Comparison of calculated and published data (Wonnald Ar(1) + CH,(2) system. Fig. 4. Comparison H,S(2) system.
0.4 fraction
0.6
0.6
1.0
Yl
et al., 1977) at 298 K for the
of calculated and published data (Alpha et al., 1982) for the CH,(l)+
sponding states to correlate the excess enthalpies for these two systems, but the correlation results were not as good as the above. Thirty-one sets of the excess enthalpy data of 11 alkane systems in Table 2, such as C,H, + n-C,H,,, are accurate to 2%. Comparison with the experimental data shows that the average deviations of 22 data sets are less than 2%, and those of the rest are about 5%, the maximum being 7.86%. We can draw three conclusions from Table 1 and Table 2 about the variation of interaction parameter Q,,: (1) For the systems CH, + N,, +Ar, +H,, + H,S and H, + N,, Qij rises as the temperature is increased; for the systems containing hydrogen it is especially sensitive to the temperature; (2) For alkane + alkane systems, as shown in Table 2, Qij reduces as the temperature is increased; (3) For n-alkane + n-alkane systems containing the same component, Qjj increases with the number of carbon atoms in the other component. Correlation of the liquid excess enthalpy Thirty-nine sets of data for the excess enthalpy of 22 binary liquid systems are also correlated by means of the above correlation method. Temperature, pressure, interaction parameter Qij and average and maxi-
152 TABLE 3 Comparison of results calculated by means of the M-H equation different temperatures and pressures for liquid excess enthalpy
Q,
P (atm) C-C,H,,
AHE%
+ n-C,H,,
288.15 K 0.9869 148.0
AH&.$
T(K) 348.1 373.1 393.1
a
- 0.00084 - 0.00084
’ 1.83 1.60
-4.3 2.7
-
0.00024 0.00024 0.00024 0.00024 0.00024
1.78 2.05 0.98 1.47 1.17
- 3.0 - 3.4 2.4 2.3 3.1
AHE%
Qij 0.00723 0.00753 0.00766
2.84 2.61 2.78
C,H, +n-CNH,,+2 N
298.15 K 0.9869 1.0 68.9 136.9 148.0
with literature
6 8 10 12 14
323.15 K
H,O+
0.00035 0.00035 0.00035
CH,OH
2.85 2.10 3.67
-6.3 -4.2 6.8
b
298.15 K 0.9869 493.5
- 0.021412 - 0.021412
5.58 6.61
10.6 14.9
383 K 9.869
- 0.002970
9.61
16.5
413 K 9.869
- 0.00044
5.21
13.4
C,H,
T (K) 280.1 298.1 323.1 a b ’ d ’
+ C-C,H,,
1 atmC
0.00646 0.00687 0.00703
2.44 3.53 3.04
5.7 7.8 6.1
N 8 10 11 13 14 17 c-C,H,,
0.00366 0.00857 0.00842 0.00605 0.00036
5.92 2.33 0.65 1.16 1.20
- 16.8 - 8.10 - 3.40 - 4.00 5.60
’
298.15 K 1 atm 0.00307 4.40 0.00130 3.17 - 0.00177 2.26 - 0.00501 3.98 - 0.01169 8.47 0.04100 10.3 +n-CNHIN+*
14.2 - 8.4 7.6 16.0 26.1 - 40.0
’
288.2 K 1 atm - 0.00087 6.54 0.00111 5.28 0.00001 6.16 - 0.01337 8.57
N
298.2 K - 0.00051 0.00102 0.00004 - 0.01258
5.3 5.0 -5.1
1 atm
N 6 7 8 12
6 7 8 12
AH&%
d
C,Hrz +n-CNHz,+, 313.15 K 0.9869 148.0 296.1
data
13.4 11.2 14.3 25.5
1 atm 5.99 7.07 6.62 10.5
Siddiqi and Lucas, 1982; Christensen et al., 1978. Heintz and Lichtenthaler, 1979; Christensen et al., 1981. Elliott and Wormald, 1976 Pena and Menduina, 1974. Arenosa et al., 1979. ’ Letcher et al., 1983; N represents the number in the formula n-C,H,,+2.
13.4 27.2 14.2 30.1
at
153 450
0.0
0.2 Mole
D.6
0.4 fraction
0.8
0 0.0
1.0
0.2
Mole
Xl
0.4 fraction
0.6
0.e
Fig. 5. Comparison of calculated H@(l) + CH,OH(Z) system.
and published
data (Heintz and Lichtenthaler,
Fig. 6. Comparison of calculated CWHZN+Z (2) system.
and published
data (Arenosa
-0.0
0.2
Mole
0.4
0.6
frrction
1.0
X1
1979) for the
et al., 1979) for the &H,,(l)
+
0.1) Mote
XI
fraction
%I
Fig. 7. Comparison C,H,(l)+C,H,,(2)
of calculated system.
and published
data (Elliott
and Wormald,
1976) for the
Fig. 8. Comparison
of calculated
and published
data (Pena and Menduina,
1974) for the
C,H,(L)+C,H,,+,(2)
system.
154
mum deviations of correlation for each set of data are given in Table 3 and typical results are illustrated in Figs. 5-8. Because the application of an equation of state is limited in the liquid region, it is difficult to obtain accurate values of HE by means of an equation of state. Ada&i and Sugie (1988), and Casielles et al. (1989) used two adjustable parameters in the mixing rule for their calculation. In this work, we use only one binary interaction parameter. Table 3 and Figs. 5-8 show that the correlation results for the excess enthalpy data of these 22 liquid systems by the M-H equation are acceptable. The average deviations for 21 data sets are less than 4%, those for 2 data sets are 10% and those for the rest vary from 4-10%. The pressure for the system C-C,H,, + n-C,H,, varies up to about 300 atm, and for the system H,O + CH,OH reaches 493 atm. From Table 3, we can see that the interaction parameter Qii rises with the temperature, but since it is very small, its variation is not obvious. Prediction
of vapor-liquid
equilibrium from the excess enthalpy data
Fifteen isothermal vapor-liquid equilibrium data sets for four binary mixtures (C,H,, + C,H,, C,H,, + C,H,,, C,H, + C,H,, and CH,OH + TABLE 4 Comparison of vapor-liquid equilibrium predicted by means of the M-H excess enthalpy with literature data at different temperatures
equation from
343.15 0.001527 CH,OH + Ha0 b 308.15 - 0.01496 322.91 - 0.01260 323.15 - 0.01256 333.15 - 0.01096 335.65 - 0.01056 338.15 - 0.01016 373.15 - 0.00457
0.0167 0.0144 0.0017 0.0075 0.0177 0.0095 0.0340
0.152 0.046 0.005 0.022 0.058 0.030 0.108
8.71 2.06 4.50 0.98 1.01 0.87 11.41
22.30 4.02 5.60 1.64 4.70 1.60 18.90
C&f,, +C,H, 293.15 343.15
0.00366 0.00366
0.0119 0.0123
0.027 0.021
2.19 1.87
4.11 2.98
C,H, + C,H,, a 283.15 0.00653 313.15 0.00697 333.15 0.00711 343.15 0.00719 392.45 0.00766
0.0099 0.0035 0.0068 0.0097 0.0041
0.0144 0.0053 0.0330 0.0145 0.0077
3.77 1.28 0.32 2.32 7.30
5.08 1.57 0.96 2.93 7.80
a
a Gmehling et al., 1980. b Gmehling and Onken, 1977.
155
H,O) are predicted by means of the M-H equation. The mixing rules for the M-H equation are the same as above, and the numerical value of the binary interaction parameter Qij, determined by correlating the excess enthalpy of binary liquid mixtures, is given in Table 3. The method requires no VLE data; only excess enthalpy data and the M-H equation of state constants for pure compounds. The predicted results are shown in Table 4. The binary interaction parameter Qjj for the system C6H,, + C,H,, at 343.15 K is obtained from the Qij data at 288.15, 298.15 and 313.15 K given in Table 3. Seven Qij data at seven temperatures from 308.15 to 373.15 K for CH,OH + H,O are interpolated from three Qij data at 298.15, 383.15 and 413 K in Table 3. Owing to the large deviation of the correlation for excess enthalpy at 383.15 K, the predicted deviation of VLE at 373.15 K is also larger than for the other temperatures. The Qij value at 323.15 K in Table 3 is selected as the Qij data at 293.15 K and 343.15 K for C,H, + C,H,,. For the C,H, + C,H,, system, five Qij data at 283.15-392.15 K are calculated by linear interpolation of data from Table 3. Generally, it is possible to predict VLE data from the excess enthalpy data using the M-H equation, provided that the correlation result for the excess enthalpy of the liquid mixture is acceptable.
CONCLUSIONS
As shown above, the Martin-Hou equation of state modified by Hou (1981), can be applied to correlate the excess enthalpy of binary gaseous mixtures at pressures up to 100 atm. For the excess enthalpy of 22 binary liquid mixtures at pressures up to 493 atm, the results of correlation by the M-H equation are satisfactory. The present study also shows that the M-H equation can be applied to predict VLE data from the excess enthalpy data, provided that the correlation result for the excess enthalpy of the liquid mixture is acceptable.
LIST OF SYMBOLS
A,, A,, A,, b, B,, B3, B4, B,, C,, C, constants in the M-H equation F,, F2, I;;, F4, F5 temperature functions in the M-H equation H enthalpy (J mol-‘) H* enthalpy at zero pressure (J mol-‘) HE excess enthalpy (J mol-‘) R gas constant P pressure
156
V T 6P%
AHE%
Qij X Y AY
molar volume temperature (‘lit
-
( H,ii-
Pcal )/‘lit
’ loos
Hi, )/Hft x 100%
interaction parameter liquid molar concentration gaseous molar concentration ‘*it
-
Ycal
Subscripts
m av max C
4 .i lit cal
property of mixture average value maximum value critical state property of pure component literature calculation
i and j
REFERENCES Ada&i, Y. and Sugie, H., 1988. J. Chem. Eng. Jpn., 21(l): 57-63. Alpha, O.B., Kaliaguine, SC. and Ramalho, RX, 1982. J. Chem. Eng. Data, 27: 436-439. Arenosa, R.L., Menduina, C., Tardajos, G. and Diaz, P.M., 1979. J. Chem. Thermodyn., 11: 159-166. Ashton, G.J. and Haselden, G.G., 1980. Cryogenics, 20(l): 41. Ba, L.B., Nain, V.P.S., Kaliaguine, S.C. and RamaIho, R.S., 1977. J. Chem. Eng. Data, 22(2): 171. Ba, L.B., Kaliaguine, S.C. and Rarnalho, R.S., 1978. J. Chem. Thermodyn., 10: 603-12. Brandrech, D.A., G’Neill, S.P. and Missen, R.W., 1966. Trans. Faraday Sot., 62: 2355. Casielles, A.G., Pando, C., Renuncio, J.A.R., Christensen, J.J. and Izatt, R.M., 1989. Thermochim. Acta, 154: 57-69. Christensen, J.J. Izatt, R.M., Eatough, D.J. and Hansen, L.D., 1978. J. Chem. Thermodyn., 10: 25-34. Christensen, J.J., 1981. Rev. Sci. Instrum., 52: 1226. Christensen, J.J., Izatt, R.M. and Zebolsky, D.M., 1987. Fluid Phase Equilibria, 38: 163-193. Elliott, K. and Wormald, C.J., 1976. J. Chem. Thermodyn., 8: 881-893. Enciso, E., 1981. Mol. Phys., 44(3): 725-32. Gmehling, J. and Onken, U., 1977. Vapor-liquid equilibrium data collection. AqueousOrganic Systems. DECHEMA, Chemistry Data Series, Vol. 1, Part 1. Frankfurt. Gmehling, J., Onken, U. and Arlt, W., 1980. Vapor-liquid equilibrium data collection. Aliphatic Hydrocarbons: C,-C,. DECHEMA, Chemistry Data Series, Vol. 1, Part 6a. Frankfurt. Heintz, A. and Lichtenthaler, R.N., 1979. Ber. Ben. Phys. Chem., 83: 853.
157 Hou, Y.J., Zhang, B. and Tong, H.Q., 1981a. Huagong Xuebao (in Chinese with English abstract), 1: 1. Hou, Y.J., Wu, G.H. and Tang, J.H., 1981b. Symposium of Chem. Eng. Exchange between China and USA in Bejing. Hu, W.M., 1984. Master’s thesis, Zhejiang University, People’s Republic of China. Jadot, R., 1980. Sci. Tech. Froid., 1: 35-44. Lee, J.I. and Mather, A.E., 1972. Can. J. Chem. Eng., 50 (5): 95. Letcher, T.M., Heyward, C. and Spiteri, W.L., 1983. J. Chem. Thermodyn., 15: 395-396. Martin, J.J. and Hou, Y.C., 1955. AIChE J., 1: 142. Mrazek, R.V. and Van Ness, H.C., 1961. AIChE J., 7: 190. Morris, J.W., Mulvey, P.J., Abbott, M.M. and Van Ness, H.C., 1975. J. Chem. Eng. Data, 20: 403. Pena, M.D. and Menduina, C., 1974. J. Chem. Thermodyn., 6: 1097. Prochazka, K., 1976. Collect. Czech. Chem. Commun., 41(5): 1273. Redlich, 0. and Kister, A.T., 1948. Ind. Eng. Chem., 40: 341. Rogalski, M. and Malanovski, S., 1977. Fluid Phase Equilibria, 1: 137. Sctonder, K., 1972. AIChE J., 18(5): 999. Siddiqi, M.A. and Lucas, K., 1982. J. Chem. Thermodyn., 14: 1183. Sir@, P.P. Nigam, R.K., Sharma, V., Sharma, S. and Sir@, K.C., 1982. Thermochim. Acta, 52(1-3): 87-102. Trezo, R., 1982. J. Chem. Sot. Faraday Trans., 78(3), 501. Wormald, C.J., 1977. J. Chem. Thermodyn., 9: 901-910. Wormald, C.J., Lewis, K.L. and Mosedale, S., 1977. J. Chem. Thermodyn., 9: 27-42. Wormald, C.J., Lewis, E.J. and Hutchings, D.J., 1979. J. Chem. Thermodyn, 11: 1-12. Wormald, C.J., 1986. Fluid Phase Equilibria, 28: 137-153.
145
Correlation of excess enthalpies and prediction of vapor-liquid equilibria from excess enthalpies by means of an equation of state Guangshun
Chen, Zhaoli Wu, Zhongxiu Chen and Yujun Hou
Department of Chemical Engineering, Zhejiang University, Hangzhou, (People’s Republic of China) (Received February 12, 1990; accepted in final form January 3, 1991)
ABSTRACT Chen, G.S., Wu, Z.L., Chen, Z.X. and Hou, Y.J., 1991. Correlation of excess enthalpies and prediction of vapor-liquid equilibria from excess enthalpies by means of an equation of state. Fluid Phase Equilibria, 65: 145-157. The Martin-Hou (M-H) equation of state with the modification by Hou was applied to correlate the excess enthalpy of binary gaseous or liquid systems. 144 sets of data for the excess enthalpy of 19 binary gaseous systems and 39 sets of data for the excess enthalpy of 22 binary liquid systems were correlated. The results were satisfactory. In this work, the M-H equation was also applied to predict isothermal binary vapor-liquid equilibrium data from the excess enthalpy data.
INTRODUCTION
When two or more pure compounds mix, the excess enthalpy will be produced owing to molecular interaction. Mixing or separation of substances is very common in chemical production and scientific experiments; in all such processes, the excess enthalpies are involved, and therefore the correlation of excess enthalpies is of fundamental importance in process design. The correlation methods for the excess enthalpy are as follows: (i) Empirical or semi-empirical methods. In general, the excess enthalpy is correlated by a function of composition or temperature (e.g. Redlich and Rister, 1948; Mrazek and Van Ness, 1961; Brandrech et al., 1966; Morris et al., 1975; Rogalski and Malanovski, 1977; Trezo, 1982). Some of these correlation formulae are empirical and others are derived from certain 0378-3812/91/$03.50
0 1991 Elsevier Science Publishers B.V.
146
models of solution. These are the most common correlation methods for the excess enthalpy of liquid mixtures. (ii) The equation of state method. The excess enthalpies of gaseous mixtures are commonly correlated by means of equations of state (e.g. Sctonder, 1972; Ba et al., 1977, 1978; Ashton and Haselden, 1980; Jadot, 1980). In the critical region, it is usual to explore the changes of HE for binary mixtures using Van der Waals-like equations of state (Wormald, 1986; Christensen et al., 1987). Recently, equations of state have also been used to correlate HE in the liquid region. For instance, Ada&i and Sugie (1988) correlated HE of the water-acetone system by means of a cubic equation of state; Casielles et al. (1989) predicted HE of a ternary system from binary experimental data using the Peng-Robinson (P-R) equation. In addition to these methods, approaches based on the “graph” theory and Monte Carlo simulation (Prochazka, 1976; Enciso, 1981; Sir@ et al., 1982) have also been tried. The Martin-Hou (M-H) equation is an accurate equation of state. The original equation proposed by Martin and Hou (1955) is applicable only to the gaseous phase; however, the equation modified by Hou et al. (1981a) is applicable to both gaseous and liquid phases. Hou et al. (1981b) and Hu (1984) have successfully applied this equation to calculate vapor-liquid and liquid-liquid equilibria for binary and ternary mixtures. Therefore, it is to be hoped that the M-H equation can be applied to correlate the excess enthalpies of both gaseous and liquid mixtures, and to predict isothermal vapor-liquid equilibria from the excess enthalpies of liquid systems.
THE CORRELATION
METHOD FOR EXCESS ENTHALPY
According to the definition of excess enthalpy, with the standard state at zero pressure, the excess enthalpy for binary mixture can be expressed
0) For pure compounds
P=
the M-H
equation
is
; FL/(vw# L=l
F,=RT F2= A, + B,T+ C, exp(-5.475T/T,) F3=A, + B,T+ C, exp( -5.475T/T,)
(5)
F4=A4+B4T
(6)
F,=B,T
(7)
147
By thermodynamic
derivation, ( H - H * ) for pure compounds
(H-H*)=PV-RT+
;
is
(FL-TdFL/dT),‘[(L-l)(V-b)L-l]
(8)
L=2
For mixtures, mixing rules for temperature functions of the M-H equation (Hou et al., 1981b) can be expressed as follows: F,, = RT
(9)
F,,=C~~1;;,-CC(l-Q,,,~X,~~
(10)
(id
Fm,=[~x,I~~11~3]3
01)
Fm4=
(12)
-[xqI&11/4]4
l1’5]5
Fm,=[~W~
(13)
b, = c X,b,
(14)
Thus the M-H equation for mixtures is P=
?
F,,/(v,-4,,)L
(15)
L=l
Similarly, for mixtures (H-H*),=PV-,,-RT+
;
(FmL-TdFmL/dT)
L=2 /[U
-
w,
- &I”-‘1
06)
where dF,,/dT=
xX2
dI;;:,/dT-
xX(1
- Q,,)Xx,
d,/lF;,F,,
I
/dT
(izj) (17)
dF,3/dT=[~XJIc;31’/3]2[~X,I~3l-2’3dE;3/dTSGN(F;3)]
(18)
dF,,/dT=
-[cXi
(19)
dF,,/dT=
[~&I&, -1
SGN( X) =
0 1
1~4 ~l’~]~[ Cxi 11’14l-3’4 d~,/dTSGN(EJ.,)] I’“l*[~XJ& XC0 x=0 x>o
l-4’5 dE;.,,‘dTSGN(&)]
(20) (21)
148 TABLE 1 Comparison of results calculated by means of the M-H equation with literature data at different temperatures and pressures for gaseous excess enthalpy P (atm)
AH:%
AH:=%
N,+CH,” Q, = 0.05076 21.02 6.8 40.96 1.6 60.99 3.7 81.02 5.6
298 K 11.5 3.4 - 8.3 -11.4
Qi, = 0.0426 4.1 30.10 3.8 39.87 6.5 50.82 4.8 54.87 10.1 64.94 70.46 9.7 8.1 80.43
201 K -9.2 -8.8 - 13.8 - 17.5 28.8 12.9 11.1
Ar+CH,
a
Qi, = 0.03793 20.13 1.0 3.4 40.26 60.50 2.6 80.04 2.6 8.3 100.7 Q,, = 0.027 50.33 3.9 60.00 1.1 8.8 65.13 8.0 70.07 5.7 85.07 CH,+H,
298 K 1.7 6.4 - 6.1 - 5.5 - 13.4 201 K 17.0 2.8 13.6 12.9 - 13.1
=
Q, = 0.05447 10.95 3.2 21.01 3.9 31.38 3.8 3.5 41.15 50.63 4.4 60.69 13.7 6.6 70.96 80.43 5.3 90.20 5.8 Qi, = 1.459 5.9 15.99
201 K - 5.2 5.6 4.2 -9.3 7.3 - 17.8 -11.3 -7.7 11.0 298 K - 10.1
P (atm)
AH:‘%
30.99 45.99 60.99 75.99 100.96
2.4 3.6 2.0 2.0 2.4
AH&.$ 4.3 5.2 - 4.2 - 4.0 -4.5
CH, + H,S b Qij = 0.2454 5.00 8.0 9.97 6.3 15.00 4.9
293 K 14.6 - 10.7 17.4
Q, j = 0.2538 5.00 10.3 9.97 3.0 15.00 6.4
305 K - 22.1 9.4 9.5
Qij = 0.2641 5.00 6.1 9.97 5.2 15.00 2.3
313 K 7.8 10.6 3.3
N,+Hza Qij =1.486 21.02 40.76 60.99 81.02 101.06
8.4 7.2 2.5 2.5 2.9
298 K - 18.0 - 14.0 6.4 3.9 - 8.2
Qij = 0.03164 30.99 5.2 50.92 2.8 70.96 1.4 90.99 1.4 110.92 3.5
201 K 7.6 -3.7 -3.9 -4.6 4.4
CH, + CO, ’ Q, = 0.13686 10 7.8 20 29 30 1.7 40 1.1 50 4.7 60 2.3
305 K - 19.9 6.0 2.8 7.6 12.4 9.4
P (atm) 70 80
AHE%
AH:=,%
5.7 6.0
- 18.0
Qij = 0.12515 10 8.6 20 5.3 30 1.5 4.6 40 3.0 50 5.1 60 70 6.7 1.9 80
313 K - 17.1 6.8 - 3.7 - 9.4 7.7 10.0 - 13.8 -7.8
Qij = 0.11575 10 10.9 20 4.0 4.9 30 40 4.3 50 2.1 2.1 60 2.7 70 80 1.2 6.0 90 100 8.6
333 K - 20.7 - 10.7 -9.3 7.0 -5.1 -3.2 3.9 - 2.2 - 17.7 -40.3
Q, = 0.11485 9.6 10 20 3.5 30 2.5 40 2.5 50 2.0 2.5 60 2.0 70 80 2.0 90 3.9 100 4.8
343 K - 29.6 6.7 5.4 3.7 - 3.3 - 3.5 - 6.4 - 8.0 - 16.3 - 27.1
Q,j = 0.11812 10 10.6 20 3.1 30 1.7 2.6 40 50 2.4 60 1.4 70 2.3 80 5.2 90 4.7 100 4.0
353 K - 26.3 -9.7 -4.6 3.5 3.3 3.1 3.8 21.1 - 15.0 -5.7
a Wormald et al., 1977. b Alpha et al., 1982. ’ Lee and Mather, 1972.
- 13.8
149 TABLE 2 Comparison of results calculated by means of the M-H equation with literature data at 1 atm and different temperatures for gaseous excess enthalpy
T WI
CH, +C,H, 363.2 373.2 383.2 393.2 403.2 413.2
AHE%
Qii
AH:ax%
0.68 0.63 0.68 0.73 0.70 0.62
1.3 -1.8 -1.8 -1.7 1.3 - 2.2
1.00650 0.93120 0.86990 0.82042 0.80752 0.73978
383.2 403.2 413.2
0.60 0.63 0.64 0.87 1.2 1.1
-1.0 - 1.1 - 1.8 1.8 - 3.1 -2.1
C,H, + n-C,H,, b 0.189480 304.5 0.146600 333.2 0.095840 363.2
1.37 2.25 5.16
- 3.5 - 5.0 14.7
C,H, + n-C,H,, b 0.50200 372.2 0.45560 383.2 0.39440 403.2
1.45 1.10 0.62
6.5 2.6 1.6
C,H, +n-CsH,, b 1.19920 403.2 1.11960 413.2
1.14 1.07
2.7 -2.5
n-C,H, + n-C,H,, b 0.35100 344.2 0.27800 363.2 0.22330 396.9
1.06 0.56 0.85
-2.2 1.7 -2.2
AH,F;%
AH;=%
b
0.49800 0.38640 0.39460
1.24 0.89 2.35
3.8 -2.4 -4.7
1.22 1.14 1.40
- 2.5 3.0 -2.9
4.35 4.07 5.76 7.86
-8.8 - 7.8 - 8.7 - 18.4
1.33 1.62 1.71
2.7 - 3.6 5.0
5.54 6.13 6.16
- 9.7 11.8 - 14.5
2.61 2.01
- 5.3 5.0
2.91 5.14
6.8 -8.6
n-C,H, + n-CsH,, b 403.2 410.2 413.2
CH, +C6H,* a 363.2 373.2 383.2 393.2 403.2 413.2
Qij
n-C,H, + n-C,H,,
a
1.22990 1.05300 0.97960 0.90250 0.86060 0.83140
T W)
n-C,H,, 363.2 373.2 383.2 393.2
0.74301 0.71000 0.69264 + n-C,H,,
b
0.12748 0.11865 0.11412 0.09705
n-C,H,, + n-CsH,, b 403.2 410.5 413.2
0.46050 0.41280 0.41120
n-C,H,, + n-&H,, 393.2 403.2 413.2 n-C,H,, 403.2 413.2
b
0.10962 0.09369 0.08882 + n-CsH,s b 0.24270 0.22030
n-C,H,, + n-CsH,, b
a Wormald, 1977. b Wormald et al., 1979.
403.2 413.2
0.10550 0.09436
150
Qi,. is a binary interaction parameter. The average percentage deviation of the calculated results for excess enthalpy from experimental values is selected as the objective function for the optimization.
RESULTS AND DISCUSSION
Correlation of the gaseous excess enthalpy
144 sets of data for the excess enthalpy of 19 binary gas systems were correlated, and the correlated results compared with published data. The results of the comparisons are given in Tables 1 and 2, and typical results are illustrated in Figs. l-4. In Figs. l-4, the ordinate is HE(J mol-‘) and the abscissa is the mole fraction X,. Each curve represents the values calculated by the M-H equation, and points represent the published data. Tables 1 and 2 and Figs. l-4 show that the correlation results from the M-H equation are very satisfactory. The average percentage deviation (AH%).. of each set for the system CH, + C,H, is less than 1.2%, both being within the accuracy of experiment. Wormald (1977) used the corre-
100
ah
c” 1%
70
f 2ec "r 2" m 5
40
& zm : lzl:?o
10
C 0.0
0.2
Mole
0.4
fraction
0.6
0.E
Y,
1.0
I.0
0.2
Mole
0.4
fraction
0.6
0.6
1.0
Y,
Fig. 1. Comparison of calculated and published data (Wormald et al., 1977) at 298 K for the N,(l)+H,(2) system. Fig. 2. Comparison of calculated and published data (Lee and Mather, 1972) at 343.15 K for the CH,(l) + CO,(2) system.
151
I
100.37
atm
I
20
0
Mole
fraction
y1
0 0.0
0.2 Mole
Fig. 3. Comparison of calculated and published data (Wonnald Ar(1) + CH,(2) system. Fig. 4. Comparison H,S(2) system.
0.4 fraction
0.6
0.6
1.0
Yl
et al., 1977) at 298 K for the
of calculated and published data (Alpha et al., 1982) for the CH,(l)+
sponding states to correlate the excess enthalpies for these two systems, but the correlation results were not as good as the above. Thirty-one sets of the excess enthalpy data of 11 alkane systems in Table 2, such as C,H, + n-C,H,,, are accurate to 2%. Comparison with the experimental data shows that the average deviations of 22 data sets are less than 2%, and those of the rest are about 5%, the maximum being 7.86%. We can draw three conclusions from Table 1 and Table 2 about the variation of interaction parameter Q,,: (1) For the systems CH, + N,, +Ar, +H,, + H,S and H, + N,, Qij rises as the temperature is increased; for the systems containing hydrogen it is especially sensitive to the temperature; (2) For alkane + alkane systems, as shown in Table 2, Qij reduces as the temperature is increased; (3) For n-alkane + n-alkane systems containing the same component, Qjj increases with the number of carbon atoms in the other component. Correlation of the liquid excess enthalpy Thirty-nine sets of data for the excess enthalpy of 22 binary liquid systems are also correlated by means of the above correlation method. Temperature, pressure, interaction parameter Qij and average and maxi-
152 TABLE 3 Comparison of results calculated by means of the M-H equation different temperatures and pressures for liquid excess enthalpy
Q,
P (atm) C-C,H,,
AHE%
+ n-C,H,,
288.15 K 0.9869 148.0
AH&.$
T(K) 348.1 373.1 393.1
a
- 0.00084 - 0.00084
’ 1.83 1.60
-4.3 2.7
-
0.00024 0.00024 0.00024 0.00024 0.00024
1.78 2.05 0.98 1.47 1.17
- 3.0 - 3.4 2.4 2.3 3.1
AHE%
Qij 0.00723 0.00753 0.00766
2.84 2.61 2.78
C,H, +n-CNH,,+2 N
298.15 K 0.9869 1.0 68.9 136.9 148.0
with literature
6 8 10 12 14
323.15 K
H,O+
0.00035 0.00035 0.00035
CH,OH
2.85 2.10 3.67
-6.3 -4.2 6.8
b
298.15 K 0.9869 493.5
- 0.021412 - 0.021412
5.58 6.61
10.6 14.9
383 K 9.869
- 0.002970
9.61
16.5
413 K 9.869
- 0.00044
5.21
13.4
C,H,
T (K) 280.1 298.1 323.1 a b ’ d ’
+ C-C,H,,
1 atmC
0.00646 0.00687 0.00703
2.44 3.53 3.04
5.7 7.8 6.1
N 8 10 11 13 14 17 c-C,H,,
0.00366 0.00857 0.00842 0.00605 0.00036
5.92 2.33 0.65 1.16 1.20
- 16.8 - 8.10 - 3.40 - 4.00 5.60
’
298.15 K 1 atm 0.00307 4.40 0.00130 3.17 - 0.00177 2.26 - 0.00501 3.98 - 0.01169 8.47 0.04100 10.3 +n-CNHIN+*
14.2 - 8.4 7.6 16.0 26.1 - 40.0
’
288.2 K 1 atm - 0.00087 6.54 0.00111 5.28 0.00001 6.16 - 0.01337 8.57
N
298.2 K - 0.00051 0.00102 0.00004 - 0.01258
5.3 5.0 -5.1
1 atm
N 6 7 8 12
6 7 8 12
AH&%
d
C,Hrz +n-CNHz,+, 313.15 K 0.9869 148.0 296.1
data
13.4 11.2 14.3 25.5
1 atm 5.99 7.07 6.62 10.5
Siddiqi and Lucas, 1982; Christensen et al., 1978. Heintz and Lichtenthaler, 1979; Christensen et al., 1981. Elliott and Wormald, 1976 Pena and Menduina, 1974. Arenosa et al., 1979. ’ Letcher et al., 1983; N represents the number in the formula n-C,H,,+2.
13.4 27.2 14.2 30.1
at
153 450
0.0
0.2 Mole
D.6
0.4 fraction
0.8
0 0.0
1.0
0.2
Mole
Xl
0.4 fraction
0.6
0.e
Fig. 5. Comparison of calculated H@(l) + CH,OH(Z) system.
and published
data (Heintz and Lichtenthaler,
Fig. 6. Comparison of calculated CWHZN+Z (2) system.
and published
data (Arenosa
-0.0
0.2
Mole
0.4
0.6
frrction
1.0
X1
1979) for the
et al., 1979) for the &H,,(l)
+
0.1) Mote
XI
fraction
%I
Fig. 7. Comparison C,H,(l)+C,H,,(2)
of calculated system.
and published
data (Elliott
and Wormald,
1976) for the
Fig. 8. Comparison
of calculated
and published
data (Pena and Menduina,
1974) for the
C,H,(L)+C,H,,+,(2)
system.
154
mum deviations of correlation for each set of data are given in Table 3 and typical results are illustrated in Figs. 5-8. Because the application of an equation of state is limited in the liquid region, it is difficult to obtain accurate values of HE by means of an equation of state. Ada&i and Sugie (1988), and Casielles et al. (1989) used two adjustable parameters in the mixing rule for their calculation. In this work, we use only one binary interaction parameter. Table 3 and Figs. 5-8 show that the correlation results for the excess enthalpy data of these 22 liquid systems by the M-H equation are acceptable. The average deviations for 21 data sets are less than 4%, those for 2 data sets are 10% and those for the rest vary from 4-10%. The pressure for the system C-C,H,, + n-C,H,, varies up to about 300 atm, and for the system H,O + CH,OH reaches 493 atm. From Table 3, we can see that the interaction parameter Qii rises with the temperature, but since it is very small, its variation is not obvious. Prediction
of vapor-liquid
equilibrium from the excess enthalpy data
Fifteen isothermal vapor-liquid equilibrium data sets for four binary mixtures (C,H,, + C,H,, C,H,, + C,H,,, C,H, + C,H,, and CH,OH + TABLE 4 Comparison of vapor-liquid equilibrium predicted by means of the M-H excess enthalpy with literature data at different temperatures
equation from
343.15 0.001527 CH,OH + Ha0 b 308.15 - 0.01496 322.91 - 0.01260 323.15 - 0.01256 333.15 - 0.01096 335.65 - 0.01056 338.15 - 0.01016 373.15 - 0.00457
0.0167 0.0144 0.0017 0.0075 0.0177 0.0095 0.0340
0.152 0.046 0.005 0.022 0.058 0.030 0.108
8.71 2.06 4.50 0.98 1.01 0.87 11.41
22.30 4.02 5.60 1.64 4.70 1.60 18.90
C&f,, +C,H, 293.15 343.15
0.00366 0.00366
0.0119 0.0123
0.027 0.021
2.19 1.87
4.11 2.98
C,H, + C,H,, a 283.15 0.00653 313.15 0.00697 333.15 0.00711 343.15 0.00719 392.45 0.00766
0.0099 0.0035 0.0068 0.0097 0.0041
0.0144 0.0053 0.0330 0.0145 0.0077
3.77 1.28 0.32 2.32 7.30
5.08 1.57 0.96 2.93 7.80
a
a Gmehling et al., 1980. b Gmehling and Onken, 1977.
155
H,O) are predicted by means of the M-H equation. The mixing rules for the M-H equation are the same as above, and the numerical value of the binary interaction parameter Qij, determined by correlating the excess enthalpy of binary liquid mixtures, is given in Table 3. The method requires no VLE data; only excess enthalpy data and the M-H equation of state constants for pure compounds. The predicted results are shown in Table 4. The binary interaction parameter Qjj for the system C6H,, + C,H,, at 343.15 K is obtained from the Qij data at 288.15, 298.15 and 313.15 K given in Table 3. Seven Qij data at seven temperatures from 308.15 to 373.15 K for CH,OH + H,O are interpolated from three Qij data at 298.15, 383.15 and 413 K in Table 3. Owing to the large deviation of the correlation for excess enthalpy at 383.15 K, the predicted deviation of VLE at 373.15 K is also larger than for the other temperatures. The Qij value at 323.15 K in Table 3 is selected as the Qij data at 293.15 K and 343.15 K for C,H, + C,H,,. For the C,H, + C,H,, system, five Qij data at 283.15-392.15 K are calculated by linear interpolation of data from Table 3. Generally, it is possible to predict VLE data from the excess enthalpy data using the M-H equation, provided that the correlation result for the excess enthalpy of the liquid mixture is acceptable.
CONCLUSIONS
As shown above, the Martin-Hou equation of state modified by Hou (1981), can be applied to correlate the excess enthalpy of binary gaseous mixtures at pressures up to 100 atm. For the excess enthalpy of 22 binary liquid mixtures at pressures up to 493 atm, the results of correlation by the M-H equation are satisfactory. The present study also shows that the M-H equation can be applied to predict VLE data from the excess enthalpy data, provided that the correlation result for the excess enthalpy of the liquid mixture is acceptable.
LIST OF SYMBOLS
A,, A,, A,, b, B,, B3, B4, B,, C,, C, constants in the M-H equation F,, F2, I;;, F4, F5 temperature functions in the M-H equation H enthalpy (J mol-‘) H* enthalpy at zero pressure (J mol-‘) HE excess enthalpy (J mol-‘) R gas constant P pressure
156
V T 6P%
AHE%
Qij X Y AY
molar volume temperature (‘lit
-
( H,ii-
Pcal )/‘lit
’ loos
Hi, )/Hft x 100%
interaction parameter liquid molar concentration gaseous molar concentration ‘*it
-
Ycal
Subscripts
m av max C
4 .i lit cal
property of mixture average value maximum value critical state property of pure component literature calculation
i and j
REFERENCES Ada&i, Y. and Sugie, H., 1988. J. Chem. Eng. Jpn., 21(l): 57-63. Alpha, O.B., Kaliaguine, SC. and Ramalho, RX, 1982. J. Chem. Eng. Data, 27: 436-439. Arenosa, R.L., Menduina, C., Tardajos, G. and Diaz, P.M., 1979. J. Chem. Thermodyn., 11: 159-166. Ashton, G.J. and Haselden, G.G., 1980. Cryogenics, 20(l): 41. Ba, L.B., Nain, V.P.S., Kaliaguine, S.C. and RamaIho, R.S., 1977. J. Chem. Eng. Data, 22(2): 171. Ba, L.B., Kaliaguine, S.C. and Rarnalho, R.S., 1978. J. Chem. Thermodyn., 10: 603-12. Brandrech, D.A., G’Neill, S.P. and Missen, R.W., 1966. Trans. Faraday Sot., 62: 2355. Casielles, A.G., Pando, C., Renuncio, J.A.R., Christensen, J.J. and Izatt, R.M., 1989. Thermochim. Acta, 154: 57-69. Christensen, J.J. Izatt, R.M., Eatough, D.J. and Hansen, L.D., 1978. J. Chem. Thermodyn., 10: 25-34. Christensen, J.J., 1981. Rev. Sci. Instrum., 52: 1226. Christensen, J.J., Izatt, R.M. and Zebolsky, D.M., 1987. Fluid Phase Equilibria, 38: 163-193. Elliott, K. and Wormald, C.J., 1976. J. Chem. Thermodyn., 8: 881-893. Enciso, E., 1981. Mol. Phys., 44(3): 725-32. Gmehling, J. and Onken, U., 1977. Vapor-liquid equilibrium data collection. AqueousOrganic Systems. DECHEMA, Chemistry Data Series, Vol. 1, Part 1. Frankfurt. Gmehling, J., Onken, U. and Arlt, W., 1980. Vapor-liquid equilibrium data collection. Aliphatic Hydrocarbons: C,-C,. DECHEMA, Chemistry Data Series, Vol. 1, Part 6a. Frankfurt. Heintz, A. and Lichtenthaler, R.N., 1979. Ber. Ben. Phys. Chem., 83: 853.
157 Hou, Y.J., Zhang, B. and Tong, H.Q., 1981a. Huagong Xuebao (in Chinese with English abstract), 1: 1. Hou, Y.J., Wu, G.H. and Tang, J.H., 1981b. Symposium of Chem. Eng. Exchange between China and USA in Bejing. Hu, W.M., 1984. Master’s thesis, Zhejiang University, People’s Republic of China. Jadot, R., 1980. Sci. Tech. Froid., 1: 35-44. Lee, J.I. and Mather, A.E., 1972. Can. J. Chem. Eng., 50 (5): 95. Letcher, T.M., Heyward, C. and Spiteri, W.L., 1983. J. Chem. Thermodyn., 15: 395-396. Martin, J.J. and Hou, Y.C., 1955. AIChE J., 1: 142. Mrazek, R.V. and Van Ness, H.C., 1961. AIChE J., 7: 190. Morris, J.W., Mulvey, P.J., Abbott, M.M. and Van Ness, H.C., 1975. J. Chem. Eng. Data, 20: 403. Pena, M.D. and Menduina, C., 1974. J. Chem. Thermodyn., 6: 1097. Prochazka, K., 1976. Collect. Czech. Chem. Commun., 41(5): 1273. Redlich, 0. and Kister, A.T., 1948. Ind. Eng. Chem., 40: 341. Rogalski, M. and Malanovski, S., 1977. Fluid Phase Equilibria, 1: 137. Sctonder, K., 1972. AIChE J., 18(5): 999. Siddiqi, M.A. and Lucas, K., 1982. J. Chem. Thermodyn., 14: 1183. Sir@, P.P. Nigam, R.K., Sharma, V., Sharma, S. and Sir@, K.C., 1982. Thermochim. Acta, 52(1-3): 87-102. Trezo, R., 1982. J. Chem. Sot. Faraday Trans., 78(3), 501. Wormald, C.J., 1977. J. Chem. Thermodyn., 9: 901-910. Wormald, C.J., Lewis, K.L. and Mosedale, S., 1977. J. Chem. Thermodyn., 9: 27-42. Wormald, C.J., Lewis, E.J. and Hutchings, D.J., 1979. J. Chem. Thermodyn, 11: 1-12. Wormald, C.J., 1986. Fluid Phase Equilibria, 28: 137-153.