240
Ind. Eng. Chem. Process Des. Dev. 1981, 20, 240-252
Principle of Corresponding States and Vapor-Liquid Equilibria of Molecular Fluids, and Their Mixtures with Light Gases Ray A. Mentrer, Robert A. Greenkorn, and Kwang-Chu Chao’ School of Chemical Engineering, Purdue Universe, West Lafayette, Indlana 47907
The shape factor method of corresponding states theory using methane as the reference fluid is examined to determine its usefulness for the prediction of phase equilibrium of pure fluids and their mixtures beyond the methane to pentane range. Vapor pressure and saturated fluid densities of pure components of various types are studied to give indications of the applicability of the method to their mixtures. Bubble points are calculated for binary mixtures of hydrogen, methane, carbon dioxide, and hydrogen sulfide with various hydrocarbons. Two binary interaction parameters are introduced and their values determined for each of the binary systems. Phase behaviors of three ternary systems are predicted using the binary parameters for comparison with experimental data. (Throughout this paper atm = 101.325 kPa.)
Introduction The principle of corresponding states (PCS) with molecular shape factors was originally developed by Leach et al. (1966, 1968) to calculate vapor-liquid equilibria for paraffin hydrocarbon systems. Methane was the reference fluid, and a one-fluid van der Waals model with no binary interaction parameters was adopted for mixtures. The calculation of enthalpies of hydrocarbon mixtures was also developed (Fisher and Leland, 1970);Fisher et al., 1968). Rowlinson and colleagues (Rowlinson and Watson, 1969; Watson and Rowlinson, 1969; Gunning and Rowlinson, 1973; Teja and Rowlinson, 1973) used the same formalism to calculate vapor-liquid equilibria, Joule-Thomson coefficients, enthalpies, critical states, and azeotropic states. One interaction parameter was introduced to characterize each binary pair. Mollerup used the same formalism (Mollerup and Rowlinson, 1974; Mollerup, 1975; Mollerup et al.,, 1976; Mollerup, 1977; Mollerup, 1978),but introduced two binary interaction parameters to describe the densities, enthalpies, and vapor-liquid equilibria of liquefied natural gas and liquefied petroleum gas mixtures. Several light inorganic gases and hydrocarbons up to pentane were the subject of these studies. Teja and Rice (1976) used the PCS to correlate the liquid densities of mixtures containing aromatics and paraffins up to hexadecane. The shape factor method of corresponding states theory has been widely used, and computer programs for its implementation are available from the Gas Processors Association. In this work we examine its usefulness for calculating vapor-liquid equilibria of pure fluids and their mixtures beyond the methane to pentane range. A number of polar nonassociating and associating fluids are included. Of particular interest are heavy hydrocarbons and their mixtures with light gases (hydrogen, methane, carbon dioxide, and hydrogen sulfide). Two interaction parameters are introduced to represent each unlike pair interaction, and the values are determined from experimental binary mixture bubble point data. Corresponding States Two pure fluids, cy and 0, are defined as being in corresponding states when the following two relations are met (Leach et al., 1968; and Rowlinson and Watson, 1969) Za[Ta,VaI = ZO[~O,VOI (1)
0196-4305/81/1120-0240$01.25/0
The equations map from the T-V space of fluid 0, the reference fluid, to the T-V space of fluid cy, the fluid of interest. Although the two configurationalproperties used in eq 1 and 2 are not the only properties which may be used to define a basis for fluids being in correspondong states, they are convenient when vapor-liquid equilibrium calculations are to be performed. Two conformal parameters are defined to relate the corresponding states of cy and 0
The first subscript is doubled for later generalization to mixtures. Equations 1and 2 may be written in terms of the comformal parameters
Other thermodynamic properties follow from eq 3 and 4.
To perform calculations using these equations one must know haa,o, and the thermodynamic properties of the reference substance. The utility of this approach lies in the ability to generalize the conformal parameters. For any pair of simple fluids (Ar, Kr, Xe) they are constants equal to the ratio of the respective critical properties. For normal fluids, they are found to be slowly varying functions of temperature and volume, and may be written as
faa,O
m
m r
la
la-
=To = T,c
(5)
In these expressions we choose the ratio of the critical temperatures or critical volumes as the reference for the ratio of temperatures or volumes. The functions e,,, and &a,O, called “shape factors”, correct for departure from the ratio of the critical values. The reduced temperature and volume of the reference fluid are therefore related to those of the fluid of interest by To = ____ T, = TaR TOR= (7) Toc T>erra,O e a a , ~ 0 1981 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 241
The function of the shape factors is to multiply the critical constants of the fluid of interest to form the reduced properties ToRand VoR,which will give the thermodynamic properties of substance a when substituted into an equation of state for fluid 0. Leach et al. (1966) developed generalized expressions for the shape factors from data for the normal paraffins ethane through pentadecane and isooctane. Methane was the reference substance. The shape factors were found to depend on temperature and, to a limited extent, density. The expressions are
LlJ
cc e
+
= 1 + (w, - wo)[0.0892 - 0.8493 In (TuR) (0.3063 - 0.4506/TUR)(VaR- 0.5)] (9)
daa,o = {I+ (w, - 00)[O.3903(VaR- 1.0177) Zuc
0.9462(VaR- 0.7663) In ( T a R ) ] } (10) y 20
In eq 9 and 10 the value of TaRshould not exceed 2.0, and VaRshould be between 0.5 and 2.0. If they are not, they should be adjusted for use in the equations as follows: when TuR> 2.0, set TaR= 2.0; when VaR> 2.0, set VuR= 2.0; when VaR < 0.5, set VuR = 0.5. In addition to the reduced variables, the shape factors depend on the acentric factors and critical compressibilitiesof the fluid of interest and the reference fluid. Equations 9 and 10 along with a description of the reference fluid are sufficient to make pure fluid calculations. Predicted vapor pressures and liquid densities at saturation for ethane, propane, butane, and pentane were found to be in good agreement with experimental data (Mollerup, 1975); calculated densities of compressed liquids have also been found to be quite accurate (Mollerup, 1977). In Table I the predicted behavior of several heavier hydrocarbons at saturation are compared with experimental data. Good agreement is found for compounds not used to develop the shape factor expressions, and for compounds very different in size and shape from methane, the reference. As one might expect, the largest deviations occur near the critical point. Table I will be discussed in detail later. The shape factor expressions have been found to be accurate to a reduced temperature of 0.3, although a different reference substance must be used since the triple point of methane occurs at a reduced temperature of 0.48. The PCS due to Pitzer et al. (1955) expresses the compressibility of a pure fluid as
Z [ TUR,peR] = .Bo)[ TaR,paR] + uUZ(l)[TaR,paR](11) The 2")function describes simple fluid behavior, while the function corrects for the departure of normal fluids from the reduced states behavior of simple fluids. Both of these functions are presented in tables and graphs with T R and p R as the independent variables. The Z(l)function in eq 11 and the shape factors of eq 7 and 8 serve similar purposes-to extend the PCS to normal fluid. However, their usefulness has turned out to be quite different. Equation 11expressed in tables and graphs is well suited for hand calculations. The shape factors, being complex functions of temperature and volume, are definitely computer oriented. A major advantage is offered by the shape factor method for mixture calculations in that only two conformal parameters need be combined. The extension of eq 11to mixtures, however, requires mixing rules for three parameters Tc,pc, and w. A sound mixing rule for the acentric factor, an empirical
1 10-2 1.700
BENZENE
0
A
,
2.5-OiME~WLHEXRNE,
2.100
2.500
1/T
2.900
DEGREES i!
3 300
3.7GO
X 10
Figure 1. Vapor pressure calculations at saturation for pentane, benzene, and 2,5-dimethylhexane. Data are from Timmermans (1950).
parameter, has remained elusive.
Equation of State for Reference The accuracy of the predictions using the PCS relies heavily on the accuracy with which the thermodynamic properties of the reference are known. The properties may be given in tabular form or expressed by an equation of state. Several equations of state for methane have been examined in this work Vennix and Kobayashi (1969), Bender (1971), METHERM4 by Goodwin (1971), and METHERM5 by Goodwin (1974). The first two equations are analytic, while the latter are nonanalytic. The METHERM4 equation of state was found to be most accurate and therefore was used in performing the calculations presented here. When calculating fugacities numerical integrations are performed which are time consuming. This increase in computations however, is the price that has to be paid for the high accuracy of METHERM4. Mollerup (1978) has extrapolated the METHERM4 equation of state for methane into the hypothetical liquid and vapor regions using thermodynamic data of propane. This extrapolation is used in the low-temperature calculations presented here. Pure Fluid Calculations The phase behavior of several pure fluids at saturation was calculated using the PCS. The calculations were performed by specifying the temperature and calculating the vapor pressure, liquid density, and vapor density, such that the pressures in each phase and fugacities in each phase are equal. Only the critical properties and acentric factor for a fluid need be known and there are no adjustable parameters. The values used in these calculations are summarized in Appendix I. (Appendix I has been deposited as supplementary material.) In Figures 1and 2 the vapor pressures and liquid molar volumes are shown as a function of temperature for pentane, benzene, and 2,bdimethylhexane. It is not surprising that the calculations for pentane are good, because data for pentane were used in developing the shape factor expressions. However, that these expressions permit the accurate determination of vapor-liquid equilibrium for
242
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
Table I. Pure Fluid Calculations at Saturation for Nonpolar Compounds no. data compound Trange, K pts. property AAPD propylene, C,H,
P V'
279-365 279-365 279-365 329-420 329-420 329-420 233-408 233-408 303-463 303-463 303-463 273-453 273-453 273-4 53 283-434 283-434 28 3-4 34 273-553 273-553 273-553 333-553
13 13 13 11 11 11 21 21 17 17 17 19 19 19 19 19 19 29 29 29 22
333-553 353-553 273-503 273-503 273-503 27 3-493 273-493 273-493 343-592 343-592 463-592 323-563
22 20 24 24 24 23 23 23 26 26 11 26
P
323-563
~~
BIAS
0.9 3.9 8.1 0.9 2.0 6.3 1.6 2.0 0.5 0.7 2.6 0.9 1.0 2.1 1.0 3.4 5.8 2.3 1.6 3.6 1.3
-0.9 -3.9 8.1 -0.9 -1.5 6.3 0.8 -2.0 0.3 0.1 2.4 0.9 -1.0 1.4 -0.9 -3.4 5.8 1.6 1.3 1.3 -0.9
P V' V' P
2.1 5.3 2.1 2.6 5.3 1.1 0.7 2.8 1.6 3.1 10.0 1.9
-2.1 4.5 -0.3 2.4 3.9 0.6 -0.7 0.5 1.0 1.0 10.0 0.1
26
V'
0.5
0.2
27 27 27 30 30 10 27 27 27 16 16 16 27 27 27 30 2 28 28 1 19
P
1-methylnaphthalene, C,,H,,
273-533 273-533 273-533 3 7 3-4 1 3 3 7 3-4 1 3 463-553 303-563 303-563 303-563 478-544 478-544 478-544 283-543 283-543 283-543 423-720 423-720 373-618 373-618 61 8 425-700
P
1.6 0.9 4.7 0.8 2.4 19.9 2.5 1.3 7.0 2.5 5.3 14.5 3.0 0.8 7.3 4.1 6.5 4.0 2.8 4.4 4.1
0.0 0.1 2.8 0.5 2.4 19.9 0.3 0.6 3.0 -2.5 -5.3 14.5 1.5 -0.6 5.4 2.9 6.5 -3.6 -2.5 4.4 3.0
440-550 491-700
4 26
V'
6.2
diphenylmethane, C,,H,,
P
1.1
6.2 -0.4
n-hexadecane, C,,H,
393-663
28
P
7.5
butene-1, C,H, isobutane, C,H,, n-pentane, C,H,, isopentane, C,H,, neopentane, C, HI, benzene, C,H, cyclohexane, C,H,,
n-hexane, C,H,, 2,3-dimethylbutane, C,H,, toluene, C,H, methylcyclohexane, C,H,,
n-heptane, C,H,, m-xylene, C,H,, n-octane, C,H,, isooctane, C,H,, 2,5dmethylhexane, C,H,, tetralin, C,,H,, n-decane, C,,H,,
VV
P V' V V
P V'
P V' VV
P V'
VV P V'
VV P V'
VV P
V' V' P V' V V
V' V'
V' V" P V' V' P V'
VV P V' V V
P V' VV
P V' P V'
VV
7.5
393-663 28 V' 3.2 -3.2 The reference to Reid e t al. (1977) signifies that the vapor pressures were obtained from equation.
AAPD = BIAS =
1 N
pred. - exptl exptl 1=1
x
1 N pred. - exptl L: ( exptl ),I N I=I -
x 100% x 100%
reference Sage and Lacey (1955) Sage and Lacey (1955) Sage and Lacey (1955) Sage and Lacey (1955) Sage and Lacey (1955) Sage and Lacey (1955) API 44 (1953) API 44 (1953) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Das et al. (1977) Das et al. (1977) Das et al. (1977) Timmermans (1950) Timmermans (1950) Timmermans (1950) M I 44 (1953) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Reid et al. (1977) Francis (1957) Landolt-Bornstein (1960) API 44 (1953) Reid et al. (1977)" API 44 (1953) Francis (1957) Timmermans (1950) Timmermans (1950) Timmermans (1950) Reid et al. (1977) Francis (1957) Landolt-Bornstein (1960) Timmermans (1950) Timmermans (1950) Timmermans (1950) Kay and Warzel (1951) Kay and Warzel(l951) Kay and Warzel (1951) Timmermans (1950) Timmermans (1950) Timmermans (1950) Kudchadker (1978) Timmermans (1950) M I 44 (1953) API 44 (1953) M I 44 (1953) API 44 (1953) Yao et al. (1978) API 44 (1953) Timmermans (1950) Simnick et al. (1978) API 44 (1953) Reid et al. (1977) Orwoll and Flory (1967) the Harlacher vapor pressure
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 243 360
I
1
I
I
I
0
PENTANE
0
BENZENE
A
2,s-DIMETHYLHEXRNE
I
I
/
I
4 ' 1
TEMPERRTURE DEGREES K
Figure 2. Liquid molar volume calculations at saturation for pentane, benzene, and 2,5-dimethylhexane. Data are from Timmermans (1950).
other fluids, such as benzene and 2,5-dimethylhexane, indicates the general nature of the shape factor expressions. In Table I the calculations for nonpolar fluids, with from 3 to 16 carbon atoms, are summarized. The calculations were carried out to a reduced temperature of 0.99. Both the average absolute percent deviation (AAPD) and bias are given in the table. The average absolute deviation of the calculated vapor pressures is 1-2% for the lighter hydrocarbons up to C7. The vapor pressure calculations are of approximately the same accuracy for all of the compounds with six carbon atoms (benzene, cyclohexane, 2,3-dimethylbutane, and n-hexane) although the molecular shapes are quite different. This same trend also holds for molecules with five and with seven carbon atoms. Larger deviations are observed for the heavier hydrocarbons; 4% for n-decane and 7.5% for n-hexadecane. The average absolute deviation for all of the hydrocarbons is 2.2% for vapor pressure, 2.5% for liquid density, and 6.9% for vapor density. Hydrogen is of great technological interest. It is a quantum gas. Leach et al. (1966) developed shape factors for quantum gases. However, since the hydrogen mixtures studied here are at relatively high temperatures we use the general shape factor equations for all calculations. To check the applicability of the latter to hydrogen we calculated the densities of pure hydrogen gas over a temperature range from 278 to 555 K up to a pressure of 422 atm. The average absolute deviation in density was 3.5% compared with the tabulation by McCarty (1975). Calculations for polar fluids are summarized in Table 11. For the ethers, ketones, mercaptans, sulfides, and amines, the calculated results generally agree well with the data, but not as well as for the lighter hydrocarbons. The exceptions are the poor results obtained for the saturated fluid densities of acetone, and for all properties of the higher molecular weight ketones. The good results for the amines are a surprise since all but tertiary amines are known to form hydrogen bonds. The results for alcohols are generally poor. The results for carbon dioxide are obtained with a constant value of the acentric factor. In this respect we
differ from the previous work of Mollerup (1975) in which the acentric factor was treated as a function of temperature. Several investigators introduced additional parameters to extend corresponding states correlations to polar fluids (Halm and Stiel, 1967; Eubank and Smith, 1962; O'Connell and Prausnitz, 1967). However, as Cook and Rowlinson (1953) showed, polar and nonpolar fluids are conformal when the angledependent potential function is free-energy averaged. No additional parameters are therefore employed in the shape factor method. The results of Table I1 confirm the validity of the method for moderately polar fluids that do not associate or hydrogen bond. PCS of Mixtures Both one-fluid and two-fluid mixture models have been used to determine the conformal parameters needed to describe mixture behavior (Rowlinson and Watson, 1969; Watson and Rowlinson, 1969; Gunning and Rowlinson, 1973). In the latter study the two-fluid model was found to be no more accurate than the one-fluid model, except possibly at low temperatures and high densities. A onefluid model was thus chosen for this work. According to the one-fluid model a mixture is described by two conformal parameters, fx,o and hx,o,which project the state of the mixture of interest onto the space of states of the reference fluid. To = T/fx,o (12)
vo = V/hx,o
(13) Leland et al. (1968)used the van der Waals mixing rules to relate the mixture conformal parameters fx,o and hx,O to those of the components as follows hx,~= CCXs&aa,O (14) a S
fx,ohx,o =
CCxJ~faa,&aa,o
(15)
a @
The unlike pair terms are represented in this work as faa,o
= ~adfaa,d~~,o)1/2
(16)
The two binary interaction parameters, lab and vag,are considered constants chosen to give the best agreement between vapor-liquid equilibrium data and the calculations. It is important to note that only binary Parameters appear in eq 14 and 15, and thus these are all that are needed for multicomponent mixture calculations. The conformal parameters faa,o and haa,oin eq 14 and 15 are obtained from eq 5 and 6, and the shape factors with the following reduced variables
For pure fluids the arguments of the shape factors reduce to TaR= T/T,C and VaR= V / V,C. However, for mixtures the shape factors have a slight composition dependence, which results in the need for an iterative calculation procedure. The composition dependence accounts for the different environment which a molecule is subjected to in a mixture as compared to a pure fluid. The composition dependence is introduced into eq 18 and 19 in order that
244
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
Table 11. Pure Fluid Calculations at Saturation for Polar Compounds -
compound
T,K
no. data pts. property
AAPD
BIAS 2.8 -2.4 3.0 -2.4 -0.9 -0.7 1.0 9.2 -4.5 -4.0 0.4
reference
Ethers dimethyl ether, C,H,O methyl ethyl ether, C,H,O diethyl ether, C,H,,O ethyl propyl ether, C,H,,O diisopropyl ether, C,H,,O
diphenyl ether, C,,H,,O
acetone, C,H,O 2-butanone, (methyl ethyl ketone), C4H8O 2-pentanone, C,H,,O methyl isobutyl ketone, C,H,,O 2-heptanone, C,H,,O methyl phenyl ketone, C,H,O 2-nonanone, C,H,,O 2-undecanone, C,, H,,O 2-tridecanone, C,,H,,O
hydrogen sulfide, H,S methyl mercaptan, CH,S ethyl mercaptan, C,H,S dimethyl sulfide, C,H,S diethyl sulfide, C4H,,S
ethylamine, C,H,N diethylamine, C,H,,N triethylamine, C,H,,N
quinoline, C,H,N
ethanol, C,H,O propanol, C,H,O
P
250-400 250-400 250-400 280-438 280-438 308-467 30 8-4 6 7 308-467 335-500 335-500 297-340
19 19 19 18 18 19 19 19 18 18 19
V' VV P V' P V' VV P V'
P
2.8 2.5 7.3 3.4 1.9 1.0 1.9 9.2 4.5 4.0 0.4
293-298
2
V'
5.1
-5.1
47 7 -544 303-767 553-767
17 26 13
P V' VV
0.9 6.1 14.7
0.9 1.8 12.3
329-508 3 29- 50 8 329-508 316-362 288-323
Ketones 20 P 20 V' 20 VV 17 P 5 V'
2.0 18.2 15.6 0.5 8.5
-2.0 18.2 1.5 -0.5 8.5
283-373 283-373 295-389 293-373 313-423 313-423 353-388 329-388 343-433 343-433 343-423 343-423 343-423 343-423
10 10 9 5 12 12 19 5 10 10 9 9 9 9
0.9 0.4 7.6 0.7 0.6 0.5 4.0 2.7 3.8 3.1 28.8 6.8 139.7 10.6
0.9 0.4 -7.6 -0.7 -0.2 0.1 -4.0 2.7 -3.8 -3.1 28.8 -6.8 139.7 -10.6
Sulfur-Containing Compounds 13 P 284-373 1.o 284-373 13 V' 3.9 13 VV 284-373 7.0 21 P 279-470 1.5 27 9-470 21 V' 3.1 308-499 21 P 1.3 308-49 9 21 V' 2.9 P 21 309-503 1.2 309-503 21 V' 4.5 P 21 363-557 6.0 363- 5 5 7 21 V' 3.3
-1.0 -3.8 7.0 -1.3 1.0 -0.9 0.5 -0.9 2.5 -6.0 -3.3
Sage and Lacy (1955) Sage and Lacy (1955) Sage and Lacy (1955) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928)
P V' P V' P V' P V' P V' P V' P V'
Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Cidlinsk? and Polak (1969) Riddick and Bunger (1970) Collerson et al. (1965) Landolt-Bornstein (1960) Landolt-Bornstein (1960) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Collerson et al. (1965) Timmermans (1950) Owen et al. (1942) Meyer and Wagner (1966) Meyer and Wagner (1966) Timmermans (1965) Timmermans (1965) Meyer and Wagner (1966) Meyer and Wagner (1966) Timmermans (1950) Timmermans (1950) Meyer and Wagner (1966) Meyer and Wagner (1966) Meyer and Wagner (1966) Meyer and Wagner (1966) Meyer and Wagner (1966) Meyer and Wagner (1966)
289-456 411-420 302-4 5 7 329-497 329-497 3 29-49 7 323-368 333-533
11
Amines P 2 V' 11 VV P 19 19 V' 19 VV P 16 21 V'
2.8 0.1 9.3 2.3 3.6 11.6 1.9 6.1
-1.2 0.0 6.7 -1.6 -0.7 -7.5 -1.7 -6.1
363-533 431-724 431-511
19 20 3
20.1 2.3 1.1
19.3 -2.2 -1.1
Timmermans (1950) Timmermans (1950) Timmermans (1950) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Boublik e t al. (1973) Int. Crit. Tables (1928) Timmermans (1965) Int. Crit. Tables (1928) Sebastian et al. (1978) Lumdsen (1907)
351-516 351-516 351-516 370-537 370-537 370-537
Alcohols 19 P 19 V' 19 VV 19 P 19 V' 19 VV
5.4 12.8 20.7 6.4 13.4 24.1
-5.4 2.2 20.7 -6.4 0.9 24.1
Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928)
VV
P V'
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 245
Table I1 (Continued) no. data pts. property
T,K
compound 2-propanol, C,H,O
carbon tetrachloride, CCl,
chlorobenzene, C, H, C1 bromobenzene, C,H,Br m-cresol, C,H,O carbon dioxide, CO,
24
P
17.7
-17.7
407-507
16
V'
13.0
-13.0
40 7-50 7
16
V V
51.9
51.9
2.6 0.9 3.1 2.5 5.0 14.5 3.5 2.9 1.2 2.2 3.7 2.2 2.9 2.3 1.9 3.3 7.7
1.6 0.3 3.1 -2.5 1.1 14.5 3.0 2.2 1.0 2.2 3.7 2.2 -0.4 -2.3 -1.9 -3.3 -7.7
Other Compounds P 31 23 V' 21 VV P 20 V' 20 20 VV P 30 V' 30 11 VV 4 P V' 27 VV 13 P 19 V' 19 P 19 V' 19 V V 19
the calculated properties of a mixture be independent of the particular reference fluid chosen for the calculations. The fugacity of component CY in solution is determined by the PCS as (Joffe, 1948; Leach et al., 1968)
The internal energy deviation, Avo, is obtained from the
P-V-T properties of the reference fluid by
It is convenient to express the derivatives of the conformal parameters in eq 20 in terms of mole fractions rather than mole numbers, since the mixing rules, eq 14 and 15, are given in terms of mole fractions. Whereas the mole numbers of the components are independent quantities, the mole fractions are not. Let a l d x , denote a differentiation in which all the mole fractions are treated as if they are independent (Chao and Greenkorn, 1975). Using this operator eq 20 can be expressed as
The working equation used to calculate the equilibrium ratio, K , = ya/x,, is obtained by applying eq 22 to both the liquid and vapor phases. In K , = In
(L) -In (") x& Yap liquid
BIAS
395-508
253-556 323-553 343-553 375-549 375-549 3 7 5-54 9 273-632 273-632 44 3-54 3 393-423 283-543 423-543 388-662 388-662 218-304 218-304 218-304
propyl acetate, C,H,,O,
AAPD
(23) vapor
reference Ambrose and Townsend (1963) Ambrose and Townsend (1963) Ambrose and Townsend (1963) Timmermans (1960) Timmermans (1950) Timmermans (1950) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Int. Crit. Tables (1928) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Timmermans (1950) Simnick et al. (1979a) TRC (1977) Din (1956) Din (1956) Din (1956)
The derivatives (df,$dx,) and (dlZ,,o/dx,)p,~in eq 22 are determined from eq 14 and'15, and the f o l l o w equations written by analogy with eq 18 and 19.
These unlike pair shape factor expressions are only used in the evaluation of the derivatives of the conformal paand l ~ , , for ~ use in eq 14 and rameters. The quantities 15 are determined from eq 16 and 17. For more details about the solution of these equations, see Leach et al. (1968). K-Value Calculations The equilibrium ratios and vapor pressures are calculated by specifying the temperature and liquid phase composition and equating the pressure in each phase and the fugacity of each component in each phase. As previously mentioned, the van der Waals one-fluid model, with two interaction parameters per binary pair, was chosen to describe a mixture. The interaction parameters, which reflect unlike pair interactions, are determined so as to obtain the best relative agreement between calculated and experimental equilibrium ratios. A Marquardt optimization procedure (Himmelblau, 1972) was used to find the optimum values of fa@ and vag. Often all of the experimental data could not be included in the optimization due to computation time considerations. In those cases four values of pressure on each isotherm were chosen, such that the logarithms of the pressures are equally spaced. In Figures 3 and 4 the calculated equilibrium ratios for methane and propane mixtures are compared with experimental data. The calculations exhibit the correct trend even through the critical region. Similar plots are given in Figures 5 and 6 for binary mixtures of butane and decane. Again the calculations are excellent as the critical region is approached. Only at the lowest temperature do
246
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 50.0
I
, ,, I
I
I
I
'
l
l
,
0
277.59 r
1
0
29u.26 K
1
A
31G.93 K
0
327.59
K
0
~
'
W
377.56 K
A 910.89
K I
0
W'r.22 K
V
1177.56 K
1 ~
W
2
3 J
C
5.0
U
>
7 Y
x
2.0
I .o 1.0
2.0
PRESSUSE R T M
5.0
10.0
a1.0
50.0
IO'
PRESSURE HTM
Figure 3. K value of methane vs. pressure for the mixture methane-propane. Data are from Reamer et al. (1950).
Figure 5. K value of butane vs. pressure for the mixture butane decane. Data are from Reamer and Sage (1964).
cI
w 3 -1 U
>
.5
c
x 0 277.59 K
299.26 K A 310.93 K
o 327.53 0
n
3VY.2E K
0 360.91 K
L-d-&,d
,2 5 .o
10.0
20 .o
so .a
102
PRESSURE FITbl
5.0 1.0
2.0
5.0
10.0
2u.o
50.0
102
PRESSURE A T M
Figure 4. K value of propane vs. pressure for the mixture methane-propane. Data are from Reamer et al. (1950).
Figure 6. K value of decane vs. pressure for the mixture butanedecane. Data are from Reamer and Sage (1964).
the K values of decane begin to deviate from the data. The equilibrium ratios for carbon dioxide and quinoline mixtures are shown in Figures 7 and 8. The K values of carbon dioxide are seen to undergo an inversion with respect to temperature. The calculations represent this phenomenon well, but not the data at the highest temperature. The calculations for quinoline are excellent at all temperatures. In Figures 9 and 10 the K values for mixtures of hydrogen and butane are plotted. The calculated equilibrium ratios of hydrogen have the correct shape, but are in error at the temperature extremes. The theory does not represent the K values of butane at high pressures well, although the agreement is satisfactory at lower pressures. The calculated equilibrium ratios for mixtures of hydrogen and benzene are excellent, as shown in Figures 11and 12. In Figures 13 and 14 the equilibrium
ratios for mixtures of hydrogen sulfide and toluene are shown. The K values of hydrogen sulfide are represented well; those of toluene not quite as well at the lower temperature. The calculations for sixty-three binary mixtures are summarized in Table 111. Optimum values of the interaction parameters are reported. Although the calculations for the methane and carbon dioxide mixtures with hydrocarbons up to pentane have been reported previously (Mollerup, 1975,19781,we also report these results because a different objective function was used to find the optimal values of f and tl to obtain the best agreement between the theory and data. Mollerup (1978) included liquid densities in the objective function, while we chose not to include them since they are not known for many of the mixtures examined in this study. Furthermore, in the calculations
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 247
50T-- - l
t
461.75 K
0
0 6Li2.60 K
20.0-
W 3 -I
10.0
-
5.0
-
I
a
> I
x
'
10.0
FI
1
I
.\I
0 3L)Li.E K A 360.95 K
I
0
i
0
377.55 K
0
39'1.25 K
I .o
5 .o
10.0
50.0
20.0
I
lo2
50 .o
P .O
PRESSURE R T M
Figure 7. K value of carbon dioxide vs. pressure for the mixture carbon dioxide-quinoline. Data are from Chao (1979). I
I
I
102
2 .o
PRESSURE RTM
I
l
l
1
Figure 9. K value of hydrogen vs. pressure for the mixture hydrogen-butane. Data are from Klink et al. (1975).
1
-5
c
W
3
-I
P
> I
x
.2
-
0 '161.75 K 0
327.65 K
0
3Li4.25 K
A
360.95 K
0 5Y2.60 K
t 10-2
I
10.0
,
1
20 .0
1
623.62 K
A
I
l
50 .0
l
l
I
l
1
102
PRESSURE STV
0
5.0
t 20.0
-
0 377.55 K V
39'1.25 K I
I
I
50.0
I
I
I
I
102
2 .o
PRESSURE A T M
Figure 8. K value of quinoline vs. pressure for the mixture carbon dioxide-quinoline. Data are from Chao (1979).
Figure 10. K value of butane vs. pressure for the mixture hydrogen-butane. Data are from Klink et al. (1975).
presented here, the acentric factors of ethane and carbon dioxide are treated as constants, whereas in previous studies they were not. The calculations are most accurate for mixtures containing methane or carbon dioxide with paraffins up to about n-hexane. Good results are also obtained with heavier substances if they have a cyclic molecular structure. In general the more dissimilar the components of the mixture are, the poorer the results. This limitation of the procedure is due to the fact that the pure fluid calculations tend to be less accurate for the paraffins beyong C,, and the one-fluid model gives a poor representation of mixtures of highly dissimilar components. The calculations for hydrogen mixtures are the least accurate. Whereas for a few systems (hydrogen + butane, octane, benzene, and toluene) the calculations are in good agreement with data, for others the agreement is quite poor.
The interaction parameters listed in Table I11 are close to unity except for mixtures containing hydrogen. The geometric mean combining rule for the conformal paramin eq 16 eter fa ,o should be the maximum, and thus s h o u d b e less than unity (Patterson, 1976). This interaction parameter was found to be less than or close to unity for all mixtures except for those containing hydrogen. On the other hand, the values of vaSare generally slightly greater than unity, with the exception of hydrogen mixtures. Although the binary interaction parameters are determined from bubble point pressures and equilibrium ratios they can be used to calculate other thermodynamic properties. These parameters were used to predict densities for several of the mixtures in Table 111. The calculations are summarized in Table IV. The temperature range and maximum pressure are the same as those listed previously.
raB
248
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
ommmooooot-
t-mwr-mmr-mo9~ rl
++++++
rl
rlrl
+++
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 249
'l33.15
K
'163.15 K L193.15 K
""\ 0
523.15 K 2 .o
10.0
50.0
20.0
IO2
2.0
PRESSURE A T M
Figure 11. K value of hydrogen vs. pressure for the mixture hydrogen-benzene. Data are from Connolly (1962).
I
\
\
I
\
o L(63.15 K A '193.15 K
o 523.15 n
5.0
10.0
20.0
50.0
IO2
2 .o
PRESSURE A T M
Figure 12. K value of benzene vs. pressure for the mixture hydrogen-benzene. Data are from Connolly (1962).
aJ
5
aJ
B
CI
0 c
+
0"
u
The average absolute deviation for all of the binary mixtures listed in Table IV is 1.9% for liquid density and 10.2% for vapor density. Henry's constants were also calculated for a few of the systems listed in Table 111. The working equation for calculating the Henry's constant of solute CY in solvent 0 at the pressure p is
where the quantity in parenthesis is obtained from eq 20. The predictions are compared with experimental data in Figure 15 for the systems: methane + l-methylnaphthalene, carbon dioxide + 1-methylnaphthalene, and carbon dioxide + n-hexadecane. The results are quite good for the first system, but not as good for the others. Once
250
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
Table IV. Comparison of Calculated Saturated Molar Volumes of Binary Mixtures with Experimental Data no. of AV' % AV" % system data pts. AAPD (BIAS) AAPD (BIAS) reference methane + isobutane methane + pentane methane + octane methane + cyclohexane CO, + propane CO, + butane CO, + butane
38 33 33 54 38 34 40
2.0 (0.6) 2.0 (-0.6) 1.2 (-1.0) 1.8 (-1.5) 6.1 (6.0) 3.7 (2.5) 2.7 (0.1)
CO, + isobutane CO, + pentane CO, t isopentane CO, + heptane CO, t decane CO, + cyclohexane hydrogen + hexane hydrogen + cyclohexane H,S t pentane H,S + decane
29 48 41 28 33 31 64 53 37 30
4.8 (4.6) 1.1(-0.3) 0.7 (-0.4) 2.7 (2.4) 1.4 (-1.3) 6.0 (5.9) 7.6 (-7.3) 3.1 (-3.1) 1.4 (0.7) 0.9 (0.5)
5.8 (1.9) 7.6 (1.8)
Olds et al. (1942) Sage et al:( 1942) Kohn and Bradish (1964) Reamer et al. (1958) Reamer et al. (1951a) Olds et al. (1949) Kalra et al. (1976) Besserer and Robinson (1971) Besserer and Robinson (1973b) Besserer and Robinson (1973a) Besserer and Robinson (1975) Kalra et al. (1978) Reamer and Sage (1963) Krichevskii and Sorina (1960) Nichols et ai. (1957) Berty et al. (1966) Reamer et al. (1953a) Reamer et al. (1953b)
___ ___ ___
6.8 (6.4) 12.5 (4.5) 7.4 (5.0) 3.8 (2.4) 24.3 (23.6) 11.7 (8.1)
-__
14.5 (12.9)
___ ___
5.1 (0.3) 12.7 (0.9)
Table V. Comparison of Vapor-Liquid Equilibrium Calculations for the System Methane-Butane-Decane with the Experimental Data of Reamer et al. (l949,1951b, 1952) liquid mole fractions experimental values predicted values
P, atm
K,
K2
0.331
0.267
0.401
68.0
0.104 0.153 0.197 0.239
0.358 0.339 0.482 0.457
0.538 0.508 0.321 0.304
27.2 40.8 54.4 68.0
8.59 5.95 4.43 3.68
0.006 0.013 0.037 0.060 0.084 0.108 0.155 0.198
0.199 0.395 0.386 0.377 0.366 0.356 0.336 0.320
0.795 0.592 0.577 0.563 0.550 0.536 0.509 0.482
6.8 13.6 20.4 27.2 34.0 40.8 54.4 68.0
so c 1
I
I
I
c i
20 0-
A \
1
I I / / /
I
I
I
K,
P,atm
K3
Values at 277.6 K 2.98 0.050 0.0015
K,
K3
56.9
2.96
0.076
0.0001
Values at 344.3 K 0.293 0.0032 0.263 0.0033 0.263 0.0053 0.260 0.0066
25.4 37.5 52.1 63.9
8.19 5.81 4.38 3.67
0.409 0.323 0.281 0.267
0.0026 0.0024 0.0032 0.0038
6.2 12.7 18.9 25.1 31.8 38.7 52.7 66.4
35.6 17.8 12.4 9.62 7.75 6.48 4.94 4.04
3.63 1.89 1.36 1.09 0.911 0.794 0.658 0.587
0.075 0.050 0.038 0.032 0.028 0.027 0.025 0.026
Values at 410.9 K 37.4 3.61 0.067 17.4 1.91 0.047 11.7 1.42 0.037 8.94 1.19 0.033 7.25 1.02 0.030 6.12 0.899 0.029 4.71 0.759 0.029 3.86 0.688 0.031
/lllll
0
310.93
0
352.59
h
A
339.26
r
0 477.59
K
Y
I
W 3 -I
a >
x
0
0
L O
PRESSURE Q T Y
Li77.59 H , / / , I
5.0
2.0
5.0
10.0
20.0
5C.G
ID5
q
1
2.C
PRESSURE G T K
Figure 13. K value of hydrogen sulfide vs. pressure for the mixture hydrogen suffide-toluene. D a b are from Robinson and Ng (1978).
Figure 14* value of toluene w*pressurefor the mixing hydrogen sulfide-toluene. Data are from Robinson and Ng (1978).
the binary interaction parameters have been determined multicomponent vapor-liquid equilibrium calculations can
also be performed, since the mixing rules, eq 14 and 15,
only contain pair interactions. Bubble point predictions
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 251 Table VI. Comparison of Vapor-Liquid Equilibrium Calculations with Experimental Data for Ternary Systems
system methane + propane + decane methane + butane + decane
AT,K 278-511
ethane + butane t heptane
sw
AP
AAPD (BIAS)
0 303
AK,
AAPD (BIAS)
68
30
8.6 (-4.4) 3.9 (3.1)
278-411
68
41
7.0 (-6.8) 3.5 (1.5)
339-450
82
100
5.0(1.8)
c
”-S W I t
-
no. of Pmax, data atm pts.
0 METHANE +I-METHYLNAPHTHALENE 0 CARSON DIOXIDE HEXAOECANE
+
350
400
450
500
TEMPERATURE, K
Figure 15. Henry’sconstants as a function of temperature for three binary systems. Data are: 0,from Chappelow and Prausnitz (1974); 0 and A, from Tremper and Prausnitz (1976).
were made on three ternary systems: methane-propanedecane, methane-butane-decane, and ethane-butaneheptane. In Table V predicted bubble point pressures and K values for the system methane-butane-decane are compared with experimental data. The calculations for all three ternary systems are summarized in Table VI. The agreement between the theory and experimental data is about comparable to that of the binary systems. Conclusions The shape factor method of the PCS with methane as the reference predicts the phase behavior at saturation of pure hydrocarbons up to about C, and polar nonassociating fluids. Only the critical properties and acentric factor of a fluid need be known. The van der Waals one-fluid mixture model, with two binary interaction parameters, is capable of describing mixtures of light gases, other than hydrogen, with hydrocarbons. Multicomponent vaporliquid equilibrium predictions can be made in terms of the binary interaction parameters. The interaction parameters have a strong effect on the calculations, particularly for mixtures of dissimilar molecules and for mixtures near the critical region. The accuracy of predictions is directly related to how well the interaction parameters are known. Once known, however, they have been shown to successfully predict a variety of thermodynamic properties-not just those properties used to evaluate the parameters. The interaction parameters listed in Table I11 should thus prove useful to the user of this method. Although the shape factor method of the PCS has been found to be the most accurate method currently available for predicting the densities of liquified natural gas mixtures (Mollerup, 1977), a comparison with other methods has not been carried out for the types of mixtures considered here. The detailed results presented in Tables I-VI should prove useful if a comparison with other methods is desired.
AK,
AAPD (BIAS)
6.9 (2.6)
AK,
AAPD (BIAS)
reference
41.3 (-41.3) Wiese et al. (1970)
16.5 (10.3) 25.3 (-23.6) Reamer et al. (1949) Reamer et al. (1951b) Reamer et al. (1952) 3.9 (-3.6) 6.1 (5.8) 12.1 (6.6) Mehra and Thodos (1966) Mehra and Thodos (1968)
Acknowledgment We would like to thank Dr.J. Mollerup of the Instituttet for Kemiteknik, Danmarks Tekniske Hajskole, Lyngby, Denmark, for supplying us with computer program LNG Property, and Dr. J. J. Simnick of Purdue University for his help in compiling the data bank used for making comparisons. This work was supported by National Science Foundation Grant EN76-09190 and Electric Power Research Institute Grant RP-367. Nomenclature d = density f = corresponding-statesparameter or fugacity depending on subscripts h = corresponding-statesparameter H = Henry’s constant K = equilibrium ratio n = number of moles p = pressure R = gas constant T = temperature U = internal energy V = molar volume x = mole fraction y = vapor phase mole fraction Z = compressibility, p V / R T Greek Symbols A = difference O,q5 = shape factors {,v = binary interaction parameters w = Pitzer’s acentric factor Subscripts 0 = reference substance cr,p = general components x = pseudo fluid Superscripts c = critical point 1 = liquid R = reduced property v = vapor Literature Cited Ambrose, D.; Townsend, R. J. Chem. Soc.1963, 3614. American Petroleum Instltute Project 44, “Selected Values of Properties of Hydrocarbonsand Related Compounds”,Carnegie Press, Pittsburgh, Pa., extant tables, 1953-1977. u n g 23, 258. Bender, E. K a ~ e f e c h n ~ - K i i ~ f i s ~ r1971. Berty, T. E.; Reamer, H. H.; Sage, B. H. J . Chem. Eng. Data 1966, 7 7 , 25. Besserer, 0.J.; Robinson, D. B. Can. J. Chem. Eng. 1971, 49, 851. Besserer, G. J.; Robinson, D. B. J. Chem. €ng. Data 1973~1,78. 416. Besserer, G. J.; Robinson, D. B. J. Chem. Eng. Data 1973b, 18. 298. Besserer. G. J.; Robinson, D. B. J. Chem. Eng. Date 1975, 20, 93. Bierlein, J. A.; Kay, W. B. Ind. Eng. Chem. 1953, 45, 618. Boubllk, T.; Fried, V.; Hale, E. “The Vapor Pressures of Pure Substances”, Elsevler Scientific Publishing Co.: New York, 1973. Burlss. W. L.; Hsu, N. T.; Reamer, H. H.; Sage, B. H. Ind. Eng. Chem. 1953, 45, 210.
252
Id.Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
Chao, K. C., and co-workers, unpublished data (1979) purdue Unhrersky, School of Chemical Englnwrhg. Chao, K. C.; Greenkorn, R. A. “Thermodynamics of Fluids”, Marcel Dekker. Inc.: New York, 1975; p 69 ff. ChappebW, C. C., 111; Prausnk, J. M. AIChf J. 1974. 20, 1097. Chu, T. C., Chen, R. J. J.; Chappelear, P. S.; Kobayashi. R. J. Chem. fng. Date 21. -.- 1978. .- .-, . , 4.1.. CMUnSW, J.; Polak, J. CoNect. Czech. Chem. Commun. 1989, 34. 1317. wlerson, R. R.; Counsell, J.; Handley, R.; Martin, J.; Sprake, C. J. Chem. Soc. 1985. 3697. Connolly, J. F: J. Chem. phys. 1982, 36. 2897. Connolly, J. F.; Kandalic, G. A. Paper No. 14-83 presented at the API 28th Midyear Meeting, Philadelphia, 1963. Cook, D.; Rowlinson, J. S. Roc. R . Soc. A 1953, 279. 405. Das, T. R.; Reed, C. 0.; Eubank. P. T. J. Chem. fng. Data 1977, 22, 16. Davalos, J.; Anderson, W. R.; Phdps, R. E.; KMnay, A. J. J. Chem. fng. Data 1978, 27, 81. Dean, M. R.; Tooke, J. W. Ind. fng. Chem. 1948, 38, 389. Din, F., Ed. “Thermodynamic Functions of Gases”, Butterworths: London, 1956; Vol. I. Donnely, H. G.; Katz, D. L. Ind. Eng. Chem. 1954, 46, 51 1. Elliot, D. G.; Chen, R. J.; Chappelear, P. S.; Kobayashl, R. J. Chem. f n g . Data 1974. 79, 71. Eubank, P. T.; Smith, J. M. AIChf J. 1982, 8 , 117. Fisher, G. D.; Chappelear, P. S.; Leland, T. W. Proceedings of the 47th Annual Conventkn of the Natural (3es Process Association, 1968, p 26. Fisher, G. D.; Leland, T. W. Ind. f n g . Chem. Fundam. 1970, 9 , 537. Francis, A. W. Ind. fng. Chem. 1957, 49, 1779. Fredenslund, A.; Molierup, J. J. Chem. Soc., Faraday Trans. 11974, 70,
1653. Goodwin, R. D. NBS Report 10 715 (1971). Goodwin, R. D. NBS Tech. Note 653 (1974). Gunn, R. D.; McKetta, J. J.; Ata, N. AIChE J. 1974, 20, 347. Gunning, A. J.; Rowlinson, J. S. Chem. Eng. Sci. 1973, 28, 521. Halm, R. L.; SUel, L. 1. AIChf J. 1987, 13, 351. Hamam, S. E. M.; Lu, 0. C. Y. J. Chem. Eng. Data 1978, 27, 200. Himmelblau, D. M. “Applied Nonlinear Proqamming”, McGraw-Hill: New York. 1972. ”International Critical Tables”, Vol. 111, 1st ed.; McGraw-Hill: New York, 1928; p 87. Joffe, J. Ind. f n g . Chem. 1948, 40, 1738. Kaka, H.; Krishnan, T. R.; Robinson, D. 0. J. Chem. Eng. Data 1978, 27, 222. Kaka, H.; Kubota, H.; Robinson, D. B.; Ng, H. J. J. Chem. Eng. Data 1978, 23. 317. Kay, W. B. Ind. Eng. Chem. 1941, 33, 590. Kay, W. B.; Warzei, F. M. Ind. Eng. Chem. 1951, 43, 1150. Klink, A. E.; Cheh, H. Y.; Amick, E. H., Jr.. AIChE J. 1975, 27, 1142. Kobayashi. R.; Chappelear, P. S.; Leland, T. W. GPA Publication TP-4, 1974. Kohn, J. P.; Bradlsh, W. F. J. Chem. fng. Data 1984, 9. 5 . Krichevskii, I. R.; Sorlna, G. A. Russ. J. Phys. Chem. 1980, 34, 679. Kudchadker, A. P., private communication, Department of Chemical Engineering, Indian Institute of Technology, Bombay, India, 1978. LandoIt-Bknstein, Band 11, Teil 2, Springer-Verlag: Berlin, 1960. Leach, J. W.; Chappelear, P. S.; Leland, T. W. Proc. Am. Pet. Inst. (Div. Refining) 1988, 46, 223. Leach, J. W.; Chappelear, P. S.; Leland, T. W. A I C M J. 1988. 74, 568. Leland, T. W.; Rowlinson, J. S.; Sather, G. A. Trans. Faraday Soc. 1988, 64, 1447. Lin, H. M.; Sebastlan, H. M.; Simnick, J. J.; Chao, K. C. J. Chem. Eng. Data 1979. 24, 146. Lumdsen, J. S. J. Chem. Soc.1907, 97, 26. McCarty, R. D. “Hydrogen Technological Survey-Thermophysical Properties”, National Aeronautics and Space Adminlstratlon, 1975. Mehra, V. S.; Thodos, G. J. Chem. Eng. Data 1965a, 70, 307. Mehra, V. S.; Thodos, G. J. Chem. Eng. Data 1985b. 70, 211. Mehra, V. S.; Thodos, G. J. Chem. fng. Data 1988, 17, 365. Mehra, V. S.; Thodos, G. J. Chem. fng. Data 1988, 73, 155. Meyer, E. F.; Wagner, R. E. J. Phys. Chem. 1988, 70, 3162. Mollerup, J.; Rowlinson, J. S. Chem. Eng. Sci. 1974, 29, 1373. Molierup, J. Adv. Cryog. Eng. 1975, 20, 172. Mollerup, J.; Fredensiund, A.; Graus0, L. “Prediction of SNG, LPG, and LNG Thermodynamic Properties”, presented at the Centennlai ACS Meeting of the American Chemical Society, New York, April 1976. Mollerup, J. Ber. Bunsenges. Phys. Chem. 1977, 87, 1015. Mollerup, J. Adv. Cfyog. Eng. 1978, 23, 550. Mraw, S.; Hwang, S. C.; Kobayashl, R. J. Chem. fng. Data 1978, 23, 135. Ng, H. J.; Robinson, D. 8. J. Chem. Eng. Data 1978, 23, 325. Nichols, W. B.; Reamer, H. H.; Sage, 0. H. AIChf J. 1957, 3 , 262. O’Connell, J. P.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1987. 6, 245. Ohgaki, K.; Katayama, T. J. Chem. Eng. Data 1978, 27, 53.
olds. R. H.; sage, B. H.: ~acey,w. N. rnd. EW. chem.1942. 34, 1008. Olds, R. H.; Reamer, H. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1949, 47, 475. Orrvoll, R. A.; Flory, P. J. J. Am. Chem. Soc. 1987, 89, 6814. Owen, K.; Quayle, 0. R.; Clegg, W. J. J. Am. Chem. Soc. 1942, 64, 1294. Patterson, D. Pure App~.chem. 1978, 47,305. Peter, S.; Relnhartz, K. Z. phys. Chem. 1980, 24, 103. Pker, K. S.; Uppmann, D. Z.; Curl, R. F., Jr.; Hugglns. C. M.; Petersen, D. E. J. Am. Chem. Soc. 1955, 77, 3433. Prodany, N. W.; WlUlams, B. J. Chem. fng. Data 1971, 76, 1. Reamer, H. H.; Olds, R. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1942, 34, 1526. Reamer, H. H.; Fiskin. J. M.; Sage, B. H. Ind. fng. Chem. 1949, 47, 2871. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1950, 42, 534. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1951a, 43, 2515. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Ind. fng. Chem. 195lb, 43, 1436. Reamer, H. H.; Sage,B. H.; Lacey, W. N. Ind. fng. Chem. 1952, 44, 1671. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1953a, 45, 1805. Rei&,- H. H.; Selleck, F. T.; Sage,B. H.; Lacey, W. N. Ind. Eng. Chem. 1953b. 45. 1810. Reamer, H. H:; Sage, B. H.; Lacey, W. N. Chem. Eng. Data Ser. 1958, 7 , 29. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Chem. Eng. Data Ser. 1958, 3 , 240. Reamer, H. H.; Sage,B. H. J. Chem. fng. Data 1983, 8 , 508. Reamer, H. H.; Sage, 8. H. J. Chem. fng. Data 1984, 9 , 24. Reamer, H. H.; Sage, B. H. J. Chem. Eng. Data 1968, 7 7 , 17. Reid, R. C.; Prausnb, J. M.; Sherwood, T. K. “The Properties of Gases and Liquids”, 3rd ed.; McGraw-HlIl: New York, 1977; Appendix A. Rlddlck, J. A.; Bunger. W. B. ”Techniques of Chemistry. Volume 11. Organlc Solvents”, 3rd Ed., Why-Interscience: New York, 1970. Robinson, D. B.; Ng, H. J. GPA Report RR-29, 1978. RowHnson. J. S.; Watson, I.D. Chem. fng. Sci. 1989, 24, 1565. Sage, B. H.; Hicks, B. L.; Lacey, W. N. Ind. fng. Chem. 1940, 32, 1085. Sage, B. H.; Reamer, H. H.; Olds, R. H.; Lacey. W. N. Ind. fng. Chem. 1972, 34, 1108. Sage, B. H.; Lacey. W. N. “Monograph on API Research Project 37: Some Propertles of the m e r Hydrocarbons, Hydrogen Sultlde, and Carbon DC oxlde”, American Petroleum Institute, 1955. Sebastian, H. M.; Sbnnlck, J. J.; Lin, H. M.; Chao, K. C. J. Chem. Eng. Data 1978, 23, 305. Sebastlan, H. M.; Simnick, J. J.; Lin, H. M.; Chao. K. C. J. Chem. fng. Data 1979, 24, 149. Simnick, J. J.; Lawson, C. C.; Lln, H. M.; Chao, K. C. A I C M J. 1977, 23, 469. Slmnlck, J. J.; Sebastlan, H. M.; Lin, H. M.; Chao, K. C. J. Chem. Eng, Data 1978, 23, 339. Simnlck, J. J.; Sebastlan, H. M.; Un, H. M.; Chao, K. C. J. Chem. Thermodyn. l979a, 7 7 , 531. Slmnick, J. J.; Sebastian, H. M.; Lin. H. M.; Chao, K. C. F/uM phese EquiUbrla 1979b, 3, 145. Simnkk, J. J.; Sebastlan, H. M.; Lln, H. M.; Chao, K. C. J. Chem. Eng. Data 1979c, 24, 239. TeJa, A. S.; Rowlinson, J. S. Chem. Eng. Sci. 1973, 28, 529. TeJa. A. S.; Rice, P. Chem. fng. Sc/. 1978, 27, 173. Thermodynamic Research Center, Texas Experimental Stath, Texas ABM Unhrerslty, College Station, Texas, “Thermodynamic Properties of ChemC cal Compounds of Importance to Processing Lignite”, July 15, 1977. Thompson, R. E.; Edmister. W. C. AIChE J. 1965, 7 7 , 457. T i m m n s , J. “PhyslcoChemicel Constants of Pure Organic Compounds”, Elsevier Publishing Co. Inc.: New York, 1950. Timmermans, J. “PhysWhemicel Constants of Pure Organlc Compounds”, Vd. 2, Elsevier Publishlng Co. Inc.; New York, 1965. Tremper, K. K.; Prausnb, J. M. J. Chem. fng. Data 1978, 27, 295. Vennix, A. J.; Kobayashi. R. A I C M J. 1989, 75, 926. Watson, I.D.; Rowlinson, J. S. Chem. fng. Sci. 1989, 2 4 , 1575. Wiese. H. C.; Reamer, H. H.; Sage,8. H. J. Chem. Eng. Data 1970, 75. 75. Yao, J.; Sebastian, H. M.; Lin, H. M.; Chao. K. C. F/ukfPhasefqu//br/a 1978, 7, 293.
Received for review December 7, 1979 Accepted October 20, 1980
Supplementary Material Available: Appendix including critical properties and acentric factors (1 page). Ordering information is given on any current masthead page.
