Ind. Eng. Chem.
1234
Res. 1987, 26, 1234-1238
In conclusion, it appears that none of the ferrous nitrosyl chelates we studied exist as dinitrosyls under the conditions reported. The Fe^IDA and Fen-citrate systems are complicated by the multiple charge states of the chelates and the formation of hydroxyl complexes in addition to nitrosyl complexes.
Acknowledgment We appreciate the support and encouragement of Michael Persweig, Joseph Strakey, and John Williams. This work was supported by the Assistant Secretary for Fossil Energy, Office of Coal Research, Advanced Environment Control Division of the U.S. Department of Energy under Contract DE-AC03-76SF00098 through the Pittsburgh
Energy Technology Center, Pittsburgh. Registry No. Fen(H20)6N0, 29966-86-7.
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Literature Cited Armor, J. N. J. Chem. Eng. Data 1974, 19, 82-84. Chang, S. G.; Littlejohn, D.; Lin, N. H. ACS Symp. Ser. 1982,188, 127-152.
Griffiths, E. A.; Chang,
S. G.
Ind. Eng. Chem. Fundam. 1986, 25,
356-359. Equivalents
Figure
3.
Titration
Hamm, R. E.; Shull, C. M.; Grant, D. M. J. Am. Chem. Soc. 1954,
of base added
76, 2111-2114. Hishinuma, U.; Kaji, R.; Akimoto, H.; Nakajima, F.; Mori, T.; Kamo, T.; Arikawa, Y.; Nozawa, S. Bull. Chem. Soc. Jpn. 1979, 52,
of Fe(II) + citric acid.
curve
between 4 and 5 equiv of base, which could be attributed to the process
Fen(cit3_)(OH~) + OH"
=
2863-2865.
Kustin, K.; Taub, I. A.; Weinstock, E. Inorg. Chem. 1966,
5,
1079-1082. Lin, N. H.; Littlejohn, D.; Chang, S.-G. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 725-728. Littlejohn, D.; Chang, S. G. J. Phys. Chem. 1982, 86, 537-540. McDonald, C. C.; Phillips, W. D.; Mower, H. F. J. Am. Chem. Soc. 1965, 87, 3319-3326. Ogura, K.; Ishikawa, H. Electrochim. Acta 1983, 28, 167-170. Ogura, K.; Watanabe, M. Electrochim. Acta 1982, 27, 111-114. Pearsall, K. A.; Bonner, F. T. Inorg. Chem. 1982, 21, 1978-1985.
Fen(cit3-)(OH-)2
Color changes also occured during the titration after 3 equiv of base was added. The solution turned from pale yellow to yellow-green and then to dark green as more base was added. This could also be due to the formation of the mono- and dihydroxy Fen(cit3_) complexes. The color was different from that obtained in titrations of ferrous solutions without citrate, indicating that the Fen(OH)2 complex is responsible for it.
Received for review November 4, 1985 Accepted February 20, 1987
Application to Mixtures of the Peng-Robinson Equation of State with Fluid-Specific Parameters Zhong Xu* and Stanley I. Sandler* Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
The vapor-liquid equilibria and volumetric behavior of mixtures have been calculated by using the Peng-Robinson equation of state with fluid-specific temperature-dependent parameters proposed earlier. Illustrative calculations show that this modification of the Peng-Robinson equation of state results in a great improvement in the simultaneous correlation of phase compositions and phase densities and excellent predictions of molar volumes in the one-phase region. The Peng-Robinson (1976) equation of state is v
-
( +
b
b) + b(v
-
b
=
\paR2T2/Pc
(2)
and Author to whom correspondence should be addressed. Permanent address: Jiao Tong University, Sian, People’s Republic of China. *
f
0888-5885/87/2626-1234801.50/0
tbRTJPc
(3)
In a previous paper (Xu and Sandler, 1987), we developed fluid-specific, temperature-dependent expressions for and \pb from vapor pressures, saturated liquid volume, and supercritical volumetric data. The form of these expressions satisfies the classical critical conditions and, unlike the equations used by others (Yarborough, 1979; Morris and Turek, 1986) leads to and ipb and their first derivatives, which are continuous in the critical region. Futher, the predictions for pure component molar volumes and vapor pressures obtained with these parameters were found
b)
with a
=
©
1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
O
100
200
300 P.
400
500
600
1235
700
bar
2. Comparison of predicted molar volume for the argon + methane system at 113.70 K.
Figure
P.
bar
consistent, method in which a cubic equation of state is used to predict the compositions of the coexisting phases and then separate correlations are used to compute the phase densities based on these equilibrium compositions. We show here that using the equation of state parameters we have proposed, this is not necessary in that both the densities and compositions of the coexisting phases can be accurately and simultaneously predicted using the Peng-Robinson equation of state. Further, for reservoir simulations, the additional slight complexity of temperature-dependent parameters is unimportant since petroleum reservoirs remain at constant temperature, so that the equation of state parameters need be calculated only once. to Mixtures In applying the Peng-Robinson (P-R) equation of state to mixtures, we used the van der Waals one-fluid combining rules (1980)
Application
am
Comparison of predicted molar volume for the nitrogen + ethane system at (a, top) 311.1 K, (b, middle) 411.1 K, and (c, bottom) 511.1 K.
Figure
(4)
=
i=lj=l
1.
bm
(5)
=
1=1
to be much better than those obtained with the standard, generalized parameters. Here we study the use of this temperature-dependent parameter Peng-Robinson equation of state for mixtures by considering the vapor-liquid equilibria (VLE) and volumetric behavior of a number of binary mixtures. We find that using our fluid-specific, temperature-dependent parameters, there is a slight improvement in the phase equilibrium (bubble point P and y) predictions using the Peng-Robinson equation of state and a great improvement in the saturated volumes of the coexisting phases. Obviously, there are numerous advantages to the accurate prediction of both phase compositions and densities with a simple equation of state. For example, one important potential application of this work is to petroleum reservoir simulation. There not only are accurate phase compositions required, but so are the phase densities in order to predict the interfacial tensions and viscosities needed in the fluid dynamic part of the simulation. Since reservoir simulations are very computer intensive, it is not uncommon to use a hybrid, but thermodynamically in-
with =
(1
-
k^iafl^!2
(6)
is the binary interaction coefficient with the where temperature-dependent fluid specific \pa and 1pb parameters we have proposed earlier (Xu and Sandler, 1987). First we considered the applicability of this modification of the P-R equation to the volumetric behavior of binary mixtures in the single-phase region. Here four systems were considered, covering a wide range of temperatures and pressures. In all cases, the binary interaction coefficient was set equal to zero, as volumetric predictions are Since no binary rather insensitive to the value of parameter was used, the results are true predictions rather than correlations. A summary comparison of the volumetric predictions for the P-R equation with both original and temperature-dependent, fluid-specific parameters is given in Table I. There we see that the P-R equation with two temperature-dependent parameters results in an average absolute
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
1236
Table I. Summary of Deviations between Calculated and Experimental Volumes in the Single-Phase Region A.A.D.," %
mixture
T, K
argon + methane
113.7 120.0 311.1
nitrogen + ethane
377.8 411.1 444.4 477.8 511.1 311.1 377.8 444.4 511.1 377.8 411.1 477.8 511.1
methane + carbon dioxide
methane + propane
overall
av
P range, bar 19-1370 15-1378 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689 14-689
no.
of points 67 69 66 66 66 66 66 66 80 80 80 80 198 198 198 198
orig."
prop.6
11.48 11.51 4.30 3.27 2.94 2.62 2.28 2.17 5.40 3.28 2.36 1.82 3.39 2.87 2.23 2.02
1.83 2.64 3.15 1.60 1.08
4.00
dev.
data ref
Ponte et al., 1981 Reamer et al., 1952
0.66 0.42 0.46 2.60
Reamer et al., 1944
1.42 0.95 0.72 2.37 1.74 1.12 0.94
Reamer et al., 1950
1.48
"Original parameters. 6Proposed parameters. "Average absolute deviation. Values of Bubble Point Pressure and Mole Fraction in Vapor
Table II. Summary of Deviations of Calculated and Literature Phase
proposed parameters kn |Ay|av |AP/P|av, % 0.0031 0.0525 0.56 0.69 0.0048 0.055 0.0038 0.046 1.51 0.045 0.19 0.0033 0.0027 0.055 0.23 1.12 0.0002 0.008 0.0006 0.008 0.42 0.011 0.0019 0.93 0.0105 0.004 0.99 0.0030 0.008 0.63 0.0028 0.010 0.28 0.40 0.0021 0.012 0.0111 0.016 0.42 0.0010 0.060 3.26 0.0022 0.010 0.19 0.07 0.0008 0.008 0.0091 0.064 2.09 0.0112 0.100 1.51 2.40 0.0093 0.123 0.0074 0.145 0.73 0.0063 0.135 1.47 0.0055 0.68 0.184 0.0044 0.127 5.64 0.0242 0.155 2.18 0.0040 0.112 4.98 0.0105 0.102 4.27 0.77 0.0035 0.110 1.04 0.0333 0.094 0.015 2.54
original parameters
mixture +
nitrogen methane
methane + ethane ethane + propane ethane + propylene ethane + benzene propylene + propane carbon dioxide + propylene carbon dioxide + propane carbon dioxide + n-butane carbon dioxide + n-pentane carbon dioxide + n-hexane carbon dioxide + n-heptane ethane +
methanol overall
av
T, K
max
113 122 138 150 172 130 144 172 255 283 261 278 311 298 261 311 253 273 278 344 311 411 278 378 298 313 353 477 348 373
P, bar
|AP/P|av, %
|Ay|av
k12
0.50 0.69 0.81 1.65 0.44 1.22 0.52
0.0043 0.0081 0.0052 0.0066 0.0033 0.0002 0.0005 0.0025 0.0135 0.0034 0.0069 0.0040 0.0129 0.0004 0.0056 0.0013 0.0084 0.0115 0.0093 0.0129 0.0063 0.0224 0.0047 0.0245 0.0035 0.0104 0.0033 0.0421
0.035 0.0375 0.0263 0.040 0.040 0.011 0.007
17
28 34 41 41 3.4
6.8
1.07 1.01 0.61 0.64 0.45
23 14
28 17
24 45 38
0.80 3.35 0.54 0.20 2.40
4
16 18
1.52 1.81 0.84 1.13 0.89 5.12 2.65 4.74 4.47 0.87 1.38 4.99 8.68
34 31 55 62
48 38 96 52 77 106 97
60 60
1.87
dev.
-0.001 -0.006 0.001 0.003 0.005 0.018 0.048 0.011 0.008 0.068 0.104 0.120 0.150 0.133 0.210 0.125 0.140 0.112 0.102 0.099 0.097 0.084 0.124
Wichterle and Kobayashi, 1972
Matschke and Thodos, 1962 Mckay et al., 1951
Ohgaki et al., 1976 Reamer and Sage, 1951
Nagahama et al., 1974
Reamer et al., 1951
Olds et al., 1949
Besserer and
Robinson, 1973 Ohgaki and Katayama, 1976
Kalra et al., 1978
Ma and Kohn, 1964
0.0061
1.61
proposed parameters
original parameters mixture ethane + propylene
carbon dioxide + propane carbon dioxide + n-butane propylene + propane ethane + methanol av
1974
Summary of Deviations between Calculated and Experimental Values of Saturated Liquid and Vapor Volume
Table III.
overall
0.037
6.23
0.0079
data ref Stryjek et al.,
dev.
T, K 261 278 311 278 344 311 411 311 348 373
max
P, bar 17
24 45 31 55
62 48 16
60 60
IAuVu'sLv, %
l
