Ind. Eng. Chem. Res. 1995,34, 4524-4530
4624
High-TemperaturePhase Equilibria for Asymmetric Mixtures of Helium m-Xylene and Nitrogen m-Xylene
+
+
Ho-MuLin,* Ming-Jer Lee, and Rong-Jwyn Lee Department
of
Chemical Engineering, National Taiwan Institute
of
Technology, Taipei, Taiwan 106, ROC
Equilibrium compositions of vapor and liquid phases were experimentally determined as a function of pressure for binary mixtures of helium m-xylene and nitrogen m-xylene at temperatures from 465 to 585 K. Five pressures from 50 to 150 bar were investigated at each temperature. A flow apparatus was developed for the measurement to minimize the thermal decomposition of m-xylene. The data were compared with calculated results from various equations of state. Several versions of mixing rules were also examined.
+
Introduction Phase equilibria were determined for two asymmetric mixtures of helium rn-xylene and nitrogen m-xylene at temperatures from 465 to 585 K over pressures of 50-150 bar. Equilibrium data of these types of mixtures are important, in addition to industrial applications, for development of theoretical methods for the calculation of mixture properties. These mixtures are characterized by interactions between molecules of significant dissimilarity in size and/or shape. For this reason, they are vital to the studies of mixing rules. On the other hand, equilibrium data at high values of reduced temperatures and pressures are sensitive to the repulsive forces for which they add a dimension t o the existing data base for evaluation of an equation of state and other correlation methods. Most of the equilibrium data are available at ambient temperatures. There is a dearth of information on the phase equilibrium behavior a t high temperatures. With the intensified development of alternate fossil fuel technologies, this information is in demand. Understanding of hightemperature phase behavior has also become increasingly important to a diversity of other processes. Five cubic equations of state were applied to correlate the new data. Various types of mixing rules which have been used for representation of asymmetric mixtures were also examined.
+
+
Experimental Section A flow apparatus was used in this work to reduce the possible thermal decomposition of rn-xylene a t high temperatures. Figure 1 shows a schematic diagram of the apparatus, which consists of three major sections: feed, equilibration, and sampling. Helium (or nitrogen) gas was supplied from a gas cylinder to the system through a Hofer compressor, while rn-xylene was delivered from a metering pump. Gas and liquid feeds were joined at a tee. The combined two-phase mixture was heated in a preheaterimixer to within 1 "C of the experimental temperature of interest before entering the equilibrium cell. The heart of the apparatus is the equilibrium cell, which is housed in a thermostated air bath. The cell provides the final equilibration between the gas and the liquid phases and also serves as a separator where the equilibrated gas and liquid are separated. The design of the cell was detailed by Lin and Lin (1990). The temperature was measured by a ~
~~~~~~
* Author to whom correspondence should be sent. E-mail:
[email protected]: 886-2-737-6644.
0888-5885i95~2634-4524$09.QQJQ0
m-xylene
+
qg7;
sampling system
N2 (or He) 2
1 liquid pump 2 coinpressor 3 preheatedmixer 4 thermostated bath
4
5 6 7 8
8
equilibrium cell pressure gauge metering valve (vapor sample) metering valve (liquid sample)
Figure 1. Schematic diagram of the flow apparatus.
calibrated type K chromel-alumel thermocouple inserted into the thermowell in the cell body t o an accuracy of 0.05 "C. Two Heise gauges (Model CMM) with maximum ranges of 1000 and 5000 psi were installed to read the pressure in the cell. The accuracy of the gauges is 0.1% of the maximum pressures. The cell effluents of both vapor and liquid phases were diverted to a sampling system (not shown in the figure) for the determination of phase compositions. This system is similar to that used by Simnick et al. (1977). The liquid stream from the bottom of the cell entered a separator after its pressure and temperature were reduced. rn-Xylene, which condensed as a liquid a t ambient conditions, was trapped in the separator and later weighed by an analytical balance. The quantity of liberated gas from the sample was determined volumetrically. The compositions of the vapor stream from the top of the cell were likewise measured. Due to the enormous differences in the volatilities of helium (or nitrogen) and m-xylene, quantitative separation was obtained at the liquid trap. Only minor corrections to the directly measured liquid weights and gas volumes were needed to obtain the final values of phase compositions in the samples. The compositions were estimated to within 1.5%accuracy under normal conditions. Helium and nitrogen were purchased from Matheson with a minimum purity of 99.9%. m-Xylene was supplied by Aldrich with a claimed purity of 99+% that was confirmed by gas chromatographic analysis in our research laboratory. Samples of rn-xylene were collected from effluents of the equilibrium cell during all of the experiments and analyzed by a Varian 3700 gas chromatograph for possible thermal decomposition. No significant quantity of impurities was detected at any of the experimental conditions.
1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4625 Table 1. Experimental Vapor-Liquid Equilibrium Data for Helium (1) rn-Xylene (2)
+
Phar
Y1
x1
Ki
Kz
41.2 29.1 22.0 18.2 15.3
0.0739 0.0534 0.0387 0.0322 0.0273
30.3 21.7 16.3 13.6 11.7
0.171 0.119 0.0894 0.0736 0.0617
T = 465.6 K 52.70 75.46 101.3 126.8 152.3
0.0225 0.0326 0.0438 0.0534 0.0637
50.92 75.25 101.7 126.8 152.5
0.0276 0.0409 0.0561 0.0686 0.0809
0.9278 0.9483 0.9630 0.9696 0.9744
0
I
Y
T = 504.9 K 0.8337 0.8856 0.9156 0.9315 0.9433
1:
> 10
-':
10 -
T = 546.3 K 51.05 75.73 101.5 126.9 151.9
0.0326 0.0519 0.0715 0.0891 0.1059
51.05 76.00 101.7 126.6 151.7
0.0358 0.0660 0.0940 0.1170 0.1439
0.6582 0.7593 0.8199 0.8528 0.8767
20.2 14.6 11.5 9.57 8.28
0.353 0.254 0.194 0.162 0.138
11.0 8.34 6.90 6.08 5.25
0.629 0.481 0.388 0.328 0.286
0
50
100
150
200
P/bar
+
Figure 2. K-values of helium (1) m-xylene (2) mixtures (0, 465.6 K 0,504.9 K A, 546.3 K 0, 584.3 K).
T = 584.3 K 0.3932 0.5504 0.6485 0.7107 0.7555
Table 2. Experimental Vapor-Liquid Equilibrium Data for Nitrogen (1) rn-Xylene (2)
+
Phar
x1
50.84 75.18 101.2 127.5 152.1
0.0495 0.0738 0.0992 0.1245 0.1503
51.32 75.39 101.0 126.1 152.2
0.0542 0.0842 0.1141 0.1415 0.1751
50.98 75.46 101.0 126.5 152.0
0.0576 0.0941 0.1331 0.1721 0.2099
50.98 75.80 103.2 125.8 135.5
0.0570 0.1099 0.1692 0.2341 0.2778
Y1
Ki
Kz
18.3 12.5 9.40 7.53 6.26
0.0985 0.0830 0.0753 0.0711 0.0703
14.8 10.0 7.59 6.19 5.04
0.209 0.170 0.151 0.144 0.142
11.2 7.67 5.62 4.47 3.71
0.375 0.308 0.291 0.279 0.281
6.62 4.35 3.10 2.27 1.89
0.661 0.586 0.573 0.611 0.659
T = 465.1 K 0.9064 0.9231 0.9322 0.9378 0.9403
T = 504.8 K 0.8024 0.8447 0.8660 0.8762 0.8826
T = 543.8 K 0.6459 0.7214 0.7475 0.7687 0.7782
T = 584.6 K 0.3771 0.4783 0.5244 0.5321 0.5244
Experimental Results Equilibrium compositions of vapor and liquid phases were experimentally determined for helium m-xylene and nitrogen m-xylene a t four temperatures from 465 to 585 K over pressures of 50-150 bar. The results are respectively presented in Tables 1 and 2. The mixtures of nitrogen m-xylene were measured to 135.5 bar at 584.6 K, because the equilibrium phases approach the critical region a t higher pressures for which the experiments become extremely difficult. The values of mole fraction in the tables represent the averages of multiple samples a t a fixed condition of temperature and pressure. Their reproducibility is generally well within 1% for both phases. Included in the tables are also the K-values of helium (or nitrogen) and m-xylene. Figures 2 and 3 show these values as a function of pressure at
+
+
+
-
10 -
2
0
50
100
150
200
P/bar Figure 3. K-values of nitrogen (1) + m-xylene (2) mixtures (0, 465.1 K, 0, 504.8 K, A, 543.8 K, 0, 584.6 K).
each temperature for both mixtures. Under the experimental conditions of this work, helium and nitrogen become more soluble in m-xylene a t higher temperatures, while the equilibrium compositions of light gases in vapor phase decrease with temperature. The solubility of helium appears to be much lower than that of nitrogen in m-xylene. The equilibrium data are available in the literature for both systems a t different conditions. Byrne et al. (1975) measured the solubility of helium in m-xylene at atmospheric pressure in the range of 283-313 K, and Richon et al. (1992) investigated the high-pressure phase equi€ibria for nitrogen m-xylene from 313 to 473 K. The present work extends the existing literature data to a significantly higher temperature range. A comparison of the results of Richon et al. (1992) with the interpolated values from this work at 472.6 K shows good agreement in y1 (vapor-phase composition of nitrogen). However, the interpolated values ofxl (liquidphase composition of nitrogen) from this work were found to be consistently higher than the data of Richon et al. (1992) by about 10%over 50-150 bar. The exact cause for such discrepancies is not known. Their data at 23.0 and 31.0 bar are, nevertheless, csincident with the extrapolated values of this work to lower pressures. The extrapolation was based on a smooth curve that connected the experimental XI (versus pressure) with the vapor pressure of m-xylene at x1 = 0. Furthermore, Richon et al. (1992) also determined the phase equilibria for nitrogen toluene by the same apparatus in the range of 313-473 K. The data appear to agree well with
+
+
4526 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 Table 3. Comparison of Calculated K-Values from Various Equations of State (EOSs) with Experimental Results
aij = (1- k, )(aiaj)0.5
bm = &bi i
SRKb PRc
PTd IMLe JTf
1.8909 1.3598 1.4151 0.9765 1.113
6.5 5.4 5.3 5.0 4.4
8.3 0.2486 5.8 .. 0.2211 5.4 0.1762 0.2781 2.0 0.2509 1.4
4.2 3.5 3.2 4.0 3.4
6.5 4.4 4.1 2.9 2.4
AAD K, = ( l O O / n ) ~ ~-=~ l ~ ~p ~l ~/ ~ ~SRK: p . Soave (1972). PR: Peng and Robinson (1976). h:patel and Teja (1982). & = 0.329, F = 0.450 751 for nitrogen (Georgeton et al., 1986); & = 0.301, F = 0.816 962 for m-xylene (Georgeton et al., 1986); tC= 0.338, F = -0.180 for helium (this work). e IML: Iwai et al. (1988). u for nitrogen and m-xylene were estimated from generalized correlation; u = 1.181 for helium was determined in this work. f JT: J a n and Tsai (1992).
where zi and zj are the mole fractions of vapor and liquid phases for components i andj, respectively. The mixing rules for other equation constants in the PT, IML, and JT equations are given in the cited references. The regressions were based on the following objective function:
c
the interpolated values from our previous work (Lin et al., 1995) at 472.6 K.
Data Correlation The experimental conditions are in the high region of reduced temperatures and pressures of the light gas. The conditions, for example, correspond to T, = 90113 and P, = 23 - 67 of helium in helium rn-xylene mixtures. Equilibrium data at these high T, and Pr are susceptible to repulsive contributions of intermolecular forces, and, as a consequence, they extend the existing data base to a new dimension for critical evaluation of an equation of state and other calculation methods. On the other hand, the equilibrium data of asymmetrical mixtures of dissimilar molecules are sensitive to the mixture parameters for which they provide a severe test of the mixing rules for representation of the mixture behavior. Various cubic equations of state, which have been found to be accurate for calculations of the phase equilibrium for a diversity of mixtures, are applied in this work to correlate the new data of both helium n-xylene and nitrogen rn-xylene. These equations include the Soave (SRK) (Soave, 1972), the PengRobinson (PR) (Peng and Robinson, 19761, the PatelTeja (PT)(Patel and Teja, 1982),the Iwai-MargerumLu (IML)(Iwai et al., 19881,and the Jan-Tsai (JT) (Jan and Tsai, 1992). Table 3 summarizes the calculated K-values in percent deviation (absolute average deviation, AAD) from experimental results. The critical temperature, critical pressure, and acentric factor used in the calculations were taken from Reid et al. (1987). tcand F in the PT equation and u in the IML equation for helium were obtained from fitting the equations to the vapor pressure data of Vargaftik (1975). The values are reported in Table 3. In the equilibrium calculations of mixtures, mixing rules are also needed for the prediction of mixture equation constants from the properties of constituent components. All five equations incorporated the traditional van der Waals one-fluid mixing rules:
+
+
+
i j
with
while the adjustable interaction constant k,,, was determined for each equation. The five equations of Table 3 are satisfactory for representing the phase equilibria of both systems to a rn-xylene reasonable accuracy. However, helium mixtures require an anomalous value of ka,,, ranging from about 1 to 1.9, to best fit the experimental data. The major reason is likely attributable to the inadequacy of the repulaive term of the equations. All five equations represent the repulsive contribution to pressure by the same form, RTI(V - b ) , which has been known to be theoretically erroneous. This term overestimates the repulsive pressures at high densities. The overestimation is compensated for in many instances by the attractive term in a sense of mutual cancellation of errors. The experimental conditions of helium n-xylene mixtures are within the region where the effect of repulsion is dominant to an extent that needs a sizable adjustment in attractive contribution to correct the total pressures. The constant k,, is the only adjustable parameter in the equation to perform this function. Each of the equations also couples with an a function to account for the temperature dependent equation constant a, a = aa,,where a = a, and a = 1 at the critical temperature of a compound. This a function is related to k,, through the mixing rule for am. In general, the expression of a with an equation of state is determined from the saturated phase properties of pure fluids by imposing the equality of the fugacities of vapor and liquid phases. The given a function is then extrapolated to T, > 1when the equation is applied at supercritical temperatures of a component in the mixtures. The extrapolation appears to be reliable at reduced temperatures that are not far apart from the critical temperature of the component (Han et al., 1988). However, its applicability to high T , has been in doubt. Soave (1972), for example, found the need for a refined expression of a to improve the accuracy of the Soave equation for the mixtures containing light compounds at high temperatures. An alternative is to use a different expression for a a t supercritical temperatures. Several common formulations of a are compared in Figures 4-6 for nitrogen, hydrogen, and helium, respectively. The symbolic points as indicated in the figures are used merely t o distinguish different a functions. They are not "data points". The calculated values are a continuous function. The value of a has also been suggested to set as 1 at T, > 1. Han et al. (1988), however, obtained better results with extrapolated a, rather than a = 1, at
+
+
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4527 o.P.?.P.P
SRK-original
?.!.?.!.t
?.?.e.?.!
SRK-GD SRK-EP
f.:.f.t.r
PT
.:
/,'
.:. _:.
3
I'.
a
,
$'
ts
..,. ./'
_, , ,'
2
1
0 0
10
20
30
40
Tr Figure 4. Variations of a with reduced temperature for nitrogen.
4'
I S RK - o r i g i n a i SRK-GO e.!.!.:.? SRK-EP ?.I.!.?.? SRK-Mothias t.!.?.?.? PR ......... P i o.o.P.P.?
?.?.?.P.P i
-
2-
..... .....
i
+
IML ..... ......... JT .........
........-...-..._.._ ...... ...-..... ....-.... *
an exponent form. Some of the functions appear to pass through a minimum at T,of about 10. The reduced temperatures of interest in engineering applications for nitrogen and its mixtures are well below 10 (the critical temperature of nitrogen: 126 K). The extrapolated values of a from the subcritical temperatures are often reliable at these temperatures and have insignificant effect on the phase equilibrium calculations with the equation of state. For hydrogen-containing mixtures, the reduced temperatures in practical calculations are extended to about 30 (T, of hydrogen: 33.2 K. GD and EP used an "effective" critical temperature: 41.7 K). At these high values of Tr,the equilibrium calculations become more sensitive to the a function. Various modifications have been developed for hydrogen to replace the original a function in the Soave equation, as compared in Figure 5 over T,= 1-150 of hydrogen. The discrepancy between these functions is evident. In fact, equilibrium calculations for hydrogen binaries with these modifications specifically for hydrogen at supercritical temperatures were not necessarily superior to the original equation with extrapolated a (Lin, 1980). The mixtures of helium m-xylene are at much higher values of T, than those of hydrogen (T,of helium: 5.19 K) for which the a function can be even more influential. A comparison of a values from different functions, including those specifically for hydrogen, is illustrated in Figure 6. The values of a are greater than 1 for any of the functions. For helium m-xylene, like other asymmetric mixtures (Han et al., 19881, setting a = 1 a t T, > 1is shown no better than the extrapolation. The AADs in K-values of helium and m-xylene with a = 1at supercritical temperatures from the Soave equation are 6.9 and 8.1%,respectively,which are about the same as the calculations by extrapolated a but with a noticeably larger k,, (=2.850). Additional results were also obtained with different setting a values to examine the response of k,, t o the magnitude of a. A larger k,, appears necessary from the implication of eq 1to compensate amfor a smaller a. By arbitrarily assignment of a constant value for a at Tr=- 1,the equilibrium calculations with the Soave equation for helium rn-xylene determined k,,, = 19.57 (AADs in K-values of helium and m-xylene: 6.9 and 8.0%, respectively) as setting a = 0.01; k,,J = 3.620 (6.9 and 8.0%) as a = 0.5; and k,,J = 1.556 (7.3 and 8.7%) as a = 10. The AADs in K-values of both components are comparable, regardless of the setting values of a,with the best-fitted results, indicating that the adjustment of k,, is sufficient to compromise the variations of a. However, when a is set larger than 10, the AADs begin to significantly deteriorate although the determined values of k,, continue to decrease. As a = 100, for example, k,,, is reduced to 1.093 with AADs of 11.4 and 18.5% in KIand K2, respectively. The value of kQ,Jand the subsequent calculated results with an equation of state are also dependent on the mixing rules used in the calculations. The results of Table 3 were based on the traditional rules of eqs 1and 2. These rules are reliable for the mixtures which contain the molecules of similar sizes. However, a significant adjustment in k,, is generally required for asymmetric mixtures, and, in some instances, the adjustment of only k,, is insufficient. Various studies (Graboski and Daubert, 1978; El-Twaty and Prausnitz, 1980; Mathias, 1983; Radosz et al., 1982; Mansoori, 1986) have found the needs for new mixing rules to represent the phase equilibria of hydrogen hydrocar-
*
+
0
150
100
50
Tr Figure 5. Variations of a with reduced temperature for hydrogen.
12 10
i
P.?.?.?.? !.!.?.?.!
SRK-orlglnai SRK-GD
?.e ?.r?SRK-EP ?.?.!.*.! t I.?.!.?
:.;.I.;;
SRK-Mathias PR PT IML
...... ..... ....... JT
.-5' ._-
_;a .
," ,I
_ . . ' e
+
0
......................... 100
50
150
Tr Figure 6. Variations of a with reduced temperature for helium.
supercritical temperatures from the Soave and the Peng-Robinson equations for a diversity of mixtures. All the results of Table 3 were calculated with the extrapolated a values at Tr > 1. Figure 4 shows the variations of a in five equations of state as they were extended to reduced temperatures Tr= 1-50 of nitrogen. Of these expressions, Jan and Tsai (1992) used a log form while all others are similar to the original Soave form. Iwai et al. (1988) determined an a function for the IML equation at Tr L 0.7 which slightly differs from its expression at Tr < 0.7. Included in the figure are also modified a functions to the Soave equation by Graboski and Daubert (GD)(1979), ElTwaty and Prausnitz (EP) (19801, and Mathias (1983). These modifications were developed specifically for hydrogen at supercritical temperatures, and all are with
+
4528 Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995
+
Table 4. Calculated K-Values of Helium rn-Xylene by Different Mixing Rules for the Soave Equation mixing rule vdWb
AAD*(%) K2
k*,,
kb,,
Ki
EF
1.2767 1.2268
Mathiase Mathias Radoszh Radosz
1.4864 1.3218 1.3156
-0.0989 13.66d 0.352@/1.203 -0.1001
9.1 8.9 4.4 9.2 2.0 2.1
-0.0019’
2.0 2.1 12.1 2.0 3.5 3.4
AAD K, = (lOO/n)X~&~ - e,tpI/K,ip. van der Waals onefluid mixing rules with kaUand kbv, eqs 1 and 4. El-Twaty and Prausnitz (1980). Binary interaction parameter: Eyi in eq 7. e Mathias (1983). f k ; in eq 6 . kl in eq 6. /I Radosz et al. (1982). kb,, in bi, = (1 - kb,)[(bi1’3 + bj1’3)/2]3. a
bon mixtures. They have developed new mixing rules to improve the accuracy of the Soave or the PengRobinson equation. An extensive comparison of different mixing rules for hydrogen-containing mixtures was presented by Laugier et al. (1986). Some of the rules were examined with the new equilibrium data of helium m-xylene, as demonstrated in Table 4. To account for the effect of molecular sizes in mixtures, many of the earlier studies have argued that the use of only k,, is unsatisfactory. El-Twaty and Prausnitz (1980)also showed that the equilibrium calculations for hydrogen-containing mixtures were much more sensitive to small changes in b, (eq 2) than to relatively large changes in a , (eq 1). The value of b m is more important than that of a m for asymmetric mixtures. An alternative is, therefore, t o replace eq 2 by introducing an additional interaction constant kbij for the covolume parameter bm:
tions for helium and m-xylene. In these calculations the modified a function by Mathias (1983) was used in the Soave equation. El-Twaty and Prausnitz (1980) suggested a quadratic equation for b, for hydrogen-containing mixtures:
(7) where subscript H stands for hydrogen. The binary parameter EHj has the dimension of volume and is adjusted directly to the equilibrium data at each temperature. However, the results, as reported in Table 4, were obtained by treating Eyi as a temperature independent parameter for four isotherms of the data. The grand AAD from individual fitting to each isotherm did not improve the results significantly. Radosz et al. (1982) applied a different approach to develop a set of conformal solution mixing rules:
+
b, = z&zjbu 1
(4)
J
+
with b, = (1- kb,)(b, bJ2. kg, can be treated as an adjustable parameter and determined simultaneously with k , by best-fitting to experimental equilibrium data. The calculated results by eq 4 in pair with eq 1 are presented in the first row of Table 4. Obviously, the addition of kg, improves the calculation for K-values of m-xylene. Gray et al. (19831, in their equilibrium calculations for hydrogen in mixtures with heavy hydrocarbons by the Redlich-Kwong-Zudkevitch-Joffe equation of state, found a strong temperature dependence of k,,, but the dependence can be eliminated through the use of two parameters k,, and kb,. Mathias (1983) applied eqs 1and 4 but with different expressions for a, and b,. He introduced two adjustable parameters for k,, and the other two for kb,: rn
k
= k: aii
1’ + ka-11000 m
Use of four parameters for a binary mixture is excessive. However, only two parameters k(j and k i were needed for hydrogen binaries which made the bo dependent on temperature. This covolume combining rule, eq 6, alone without k,, fails to accurately calculate the K-values of m-xylene, as shown in Table 4. The results are also compared in the table with those by adjustment of k: and k: in place of k(j and k i . Apparently, k,, and kb, are different in their influence on the K-value calcula-
i
j
with u~j.b~j.-O.~~ = (1 - k , , ) [ a ~ ~ j ( b ~ b j ) -The ~ ~ ~mixing ~I~~~ rule for b, is the same as eq 4 but with
+
b, = [(bili3 bj”3)/213
(9)
In Table 4, the results with addition of an adjustable parameter kb,, in eq 9 are also reported for comparison. No apparent improvement was found with introduction of this kb,,. Nevertheless, eqs 8 and 4 (with eq 9) appear to be the best of the mixing rules in Table 4 for representing the phase equilibria of helium m-xylene mixtures. Still an anomalous value of k,, was obtained to best fit the experimental data. Other varieties of conformal solution mixing rules were proposed by Mansoori (19861, who used different approximations for the mixture radial distribution functions to derive a series of sets of rules. Some are density and temperature dependent. The resulting mixing rules were applied to the van der Waals, the Redlich-Kwong, and the Peng-Robinson equations of state. For the Peng-Robinson equation, the energy constant “a”was expressed as
+
(10) where
A = a,(l
+ mI2
C = a,m2/RT, In accordance with the van der Waals theory, the conformal solution one-fluid mixing rules for Am, b,, and a , in the Peng-Robinson equation are reduced to a quadratic form:
i
j
where 8 represents the equation constant A, b, or C. The combining rules for 8, are given by
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4629
(12) (13)
These rules have been applied to describe the phase behavior involving the supercritical fluid extraction and retrograde condensation (Park et al., 1987). They are physically sound. However, the requirement of three adjustable parameters for a binary mixture has limited their applicability in engineering calculations. Furthermore, the rules of eqs 10-14 were also found to have no advantages over the mixing rules of Radosz et al. (1982), eqs 8 and 4 (with eq 91, with adjustment of only one yarameter k,, for representation of helium m-xy ene
+
n = number of data points
P = pressure (bar) R = gas constant (bar cm3 mol-I K-l) T = temperature (K) u = pure-component constant in the Iwai-Margerum-Lu equation V = molar volume (cm3 mol-1) x = mole fraction of liquid phase y = mole fraction of vapor phase z = mole fraction Greek Symbols
a = temperature dependent function in equation constant a 0 = constant as defined by eq 11
Ec = pure-component constant in the Patel-Teja equation n = objective function, eq 3 Superscripts
Conclusion Vapor-liquid equilibria were experimentally determined for the binary asymmetric mixtures of helium m-xylene and nitrogen m-xylene at high temperatures of 465-585 K. Five pressures from 50 to 150 bar were studied a t each temperature (except for nitrogen m-xylene at 584.6 K). A flow apparatus was used for the measurements to minimize the thermal decomposition of m-xylene. The new equilibrium data were compared with the calculated results from five cubic equations of state. The equations are satisfactory for representing the equilibrium conditions of nitrogen m-xylene mixtures. Good results were also obtained for helium m-xylene but with a peculiar value of k,, that requires it to be greater than unity (or equal t o 1 for the IML equation). The reason for this anomalous behavior of the equation is likely attributable to the erroneousness of its van der Waals excluded volume expression for the repulsive pressure. The experimental conditions of helium m-xylene in terms of reduced temperatures and reduced pressures are in the region where the repulsive contribution comes to dominate. A sizable adjustment in k,, for the attractive contribution is necessary t o correct the total pressures. Various mixing rules that have been developed specifically for such asymmetric mixtures as hydrogen hydrocarbon binaries were examined with the equilibrium data of helium m-xylene. None of the mixing rules is able to fit the experimental data without a k,,, of greater than unity, although the conformal solution mixing rules of Radosz et al. (1982) are accurate in view of AAD.
+
+
+
+
+
+
+
+
Acknowledgment Financial support from the National Science Council, ROC, through Grant No. NSC84-2214-EOll-012 is gratefully acknowledged.
Nomenclature A, C = constants in eq 10 a, b = equation constants Em = binary interaction parameter in eq 7 F = pure-component constant in the Patel-Teja equation K = equilibrium ratio k,, = binary interaction parameter in a, kb,,, k i , k i = binary interaction parameter in b , m = function of acentric factor in the Peng-Robinson equation
cal = calculated value exp = experimental value Subscripts c = critical property i = component z j= i-j pair interaction j = componentj m = mixture
r = reduced property 1 = component 1 2 = component 2
Literature Cited Byme, J . E.; Battino, R.; Wilhelm, E. The Solubility of Gases in Liquids. 8. Solubility of He, Ne, Ar, Kr, C02, CHI, CF4, and SFe in 0-,m-, and p-Xylene at 283 to 313 K. J. Chem. Thermodyn. 1975,7,515-522. El-Twaty, A. I.; Prausnitz, J. M. Correlation of K-Factors for Mixtures of Hydrogen and Heavy Hydrocarbons. Chem. Eng. Sci. 1980,35,1765-1768. Georgeton, G. K.; Smith, R. L., Jr.; Teja, A. S. Application of Cubic Equations of State to Polar Fluids and Fluid Mixtures. In Equations of State Theories and Applications; Chao, K. C., Robinson, R. L., Jr., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986; pp 434-451. Graboski, M. S.; Daubert, T. E. A Modified Soave Equation of State for Phase Equilibrium Calculations. 3. Systems Containing Hydrogen. Ind. Eng. Chem. Process Des. Dev. 1979,18,300306. Gray, R. D.; Heidman, J. L.; Hwang, S. C.; Tsonopoulos, C. Industrial Applications of Cubic Equations of State for VLE Calculations with Emphasis of Hz Systems. Fluid Phase Equilib. 1983,13,59-76. Han, S. J.; Lin, H. M.; Chao, K. C. Vapor-Liquid Equilibrium of Molecular Fluid Mixtures by Equations of State. Chem. Eng. Sci. 1988,43,2327-2367. Iwai, Y.;Margerum, M. R.; Lu, B. C.-Y. A New Three-Parameter Cubic Equation of State for Polar Fluids and Fluid Mixtures. Fluid Phase Equilib. 1988,42,21-41. Jan, D. S.; Tsai, F. N. A New Four-Parameter Cubic Equation of State for Mixtures. Vapor-Liquid Equilibrium Calculations. Can. J . Chem. Eng. 1992,70, 320-329. Laugier, S.; Richon, D.; Renon, H. Representation of HydrogenHydrocarbon Vapor-Liquid Equilibria and Saturated Densities at High Pressures and Temperatures. Chem. Eng. Sci. 1986, 41,2407-2417. Lin, H. M. Modified Soave Equation of State for Phase Equilibrium 501Calculations. Znd. Eng. Chem. Process Des. Dev. 1980,19, 505. Lin, H. M.; Lin, Y. R. Flow Apparatus for Phase Equilibrium Measurement. AIChE J . 1990,36,1597-1599.
4530 Ind.Eng. Chem. Res., Vol. 34, No. 12, 1995 Lin, H. M.; Lee, M. J.; Lee, R. J. Phase Equilibria of Toluene in Mixtures with Helium or Nitrogen a t High Temperatures. J . Chem. Eng. Data 1995,40,653-656. Mansoori, G.A. Mixing Rules for Cubic Equations of State. In Equations of State Theories and Applications; Chao, K. C., Robinson R. L., Jr., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986; pp 314-330. Mathias, P. M. A Versatile Phase Equilibrium Equation of State. Ind. Eng. Chem. Process Des. Dev. 1983,22,385-391. Park, S.J.; Kwak, T. Y.; Mansoori, G . A. Statistical Mechanical Description of Supercritical Fluid Extraction and Retrograde Condensation. Int. J . Thermophys. 1987,8 , 449-471. Patel, N. C.; Teja, A. S. A New Cubic Equation of State for Fluids and Fluid Mixtures. Chem. Eng. Sci. 1982,37,463-473. Peng, D.Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976,15,59-64. Radosz, M.; Lin, H. M.; Chao, K. C. High-pressure Vapor-Liquid Equilibria in Asymmetric Mixtures Using New Mixing Rules. Ind. Eng. Chem. Process Des. Dev. 1982,21,653-658. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987.
Richon, D.; Laugier, S.; Renon, H. High-pressure Vapor-Liquid Equilibrium Data for Binary Mixtures Containing Nz, COz, HzS, and an Aromatic Hydrocarbon or Propylcyclohexane in the Range of 313-473 K. J . Chem. Eng. Data 1992,37,264-268. Simnick, J. J.; Lawson, C. C.; Lin, H. M.; Chao, K. C. VaporLiquid Equilibrium of the Hydrogefletralin System a t Elevated Temperatures and Pressures. M C h E J . 1977,23,469476. Soave, G. Equilibrium Constants form a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27,1197-1203. Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases, 2nd ed.; Wiley: New York, 1975.
Received for review December 16, 1994 Revised manuscript received J u n e 13, 1995 Accepted J u n e 15, 1995@ IE940744J Abstract published i n Advance A C S Abstracts, September 15, 1995. @
