PREDICTION AND CORRELATION OF PHASE EQUILIBRIA AND
THERMAL PROPERTIES WITH THE BWR EQUATION OF STATE R .
V .
O R Y E '
Shell Development Co , Emer\Lzile, Calif
94608
Parameters for the Benedict-Webb-Rubin equation of state extend its range of validity to the low temperatures now encountered in natural gas processing. The components covered are methane, ethylene, ethane, propylene, propane, 2-methylpropane, 2-methylpropene, n-butane, 2-methylbutane, n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, benzene, hydroge.n, nitrogen, carbon dioxide, and hydrogen sulfide. Although the pure component properties of all these compounds are accurately accounted for by a modified form of the BWR equation, special binary mixture parameters had to be determined to correlate known thermodyncrmic properties.
ASearly
as 1951, Benedict et al. suggested that one of the parameters in their equation of state be made a function of temperature, in order ,to treat hydrocarbon systems a t very low temperatures. The original coefficients for the equations were based on vapor pressures from 1 to 2 atm. to the critical pressure and PVT for superheated or supercritical vapors of each pure component. Using the original Benedict coefficients, for temperatures below the normal boiling point, the vapor pressure of pure compoiients is greatly underestimated and the enthalpy is overestimated by the equation. Adler et al. (1968), Barner and Adler (1968), Barner and Schreiner (1966), Motard and Organick (1960), and Stotler and Benedict (1953) have reported determination of BWR coefficients suitable for accurate calculation of vapor pressures and enthalpies of pure components a t temperatures well below their normal boiling points, but numerical values have rarely been given. The eight-parameter Benedict equation of state gives the relation among pressure, P, temperature, T, and density, p , as
P = RTp
+
C, B,RT - A , -7 p L) + T-
(bRT - a)p'
-
(P-,-)
1:
du-ln-+-RT
PU RT
1 (2)
where 11 is the molar volume, u = l / p . Equation 2 assumes that a t unit pressure the gas is ideal, so that the reference fugacity f " = 1.0. Thus for the Benedict equation
' Present address, Shell Oil Co., Wilmington, Calif.
i
B,RT
-
2
- + - 6anpj 5
A,] -
T'
t
For a given pressure and temperature in the two-phase region, Equation 1 has two equilibrium solutions for the density, p ' and p ' , the saturated vapor and liquid densities. respectively. A third solution exists, p ' < p < p L , which corresponds to an unstable equilibrium. The two equilibrium densities may be used with Equation 3 to determine the vapor and liquid fugacities, f ' and f L , for the selected P and T. If f L > f ' , the pressure chosen is lower than the vapor pressure predicted by the equation of state, and conversely if f ' > f L , the pressure is too high. A new pressure can be selected in accordance with the magnitudes of f ' and f L until
Pb', TI
(4)
f b ' , T ) = f h L ,T )
(5)
=
and
CI, +mpb+ 7 (1 T
RT
+ 2p
3p'(bRT - a )
Phi,
If a pure component can exist a t equilibrium in two phases a t a given P and T , the thermodynamic variable defining equilibrium is the fugacity, which must be the same for both phases. The thermodynamic relation between the PVT properties of a substance and its fugacity is
1 lnf=-J RT
I"
R T In f = RT 1x1 pRT
90744
This pressure will be the saturation vapor pressure a t the given temperature. The calculated pressure will, or will not, agree with sufficient accuracy with experimentally known vapor pressures, depending on the accuracy of the parameters in the equation of state. The coefficients originally given by Benedict et a1 (1951) reproduce vapor pressures of the common light hydrocarbons, C1to n-C-, to about 1 to 3% between the normal boiling point and the critical temperature. For temperatures below the boiling point, Benedict recommended that parameter C, be determined to fit the vapor pressure curve while the other seven coefficients are kept constant. Some values of C, a t low temperatures were given a t discrete temperatures, but they do not extend low enough in temperature to be useful for many of the new hydrocarbon processing schemes. Also it is desirable to obtain VOL. 8 NO. 4 OCTOBER 1969
579
C, as a smoothly varying function of temperature, so that the equation may be more easily used in flash and distillation computer programs. Barner and Schreiner (1966) discussed the general technique of determining C, and presented results graphically for the lightest hydrocarbons: C,, CT, C2, C,;., and C1. However, it is necessary to have values for C, accurat,e t o six or seven significant figures, if the equation is to be used in computing phase equilibria and thermal properties. Further, for natural gas processing calculations, one must make adjustments to the BWR coefficients for heavier hydrocarbons also and include in the component list the more common nonhydrocarbons. Table I gives the eight RWR coefficients which apply a t high temperature for 20 components that are the most common in natural gas systems. The units are English: p.s.i.a., cu. feet, lb. mole, OR. With the except,ion of those listed for n-octane, n-nonane, and n-decane, the nonaromatic hydrocarbon values are from Benedict et ul. (1951). For the three heaviest hydrocarbons, coefficients were estimated by the method of Canjar et al. (1955), which is sufficiently imprecise that C , had to be determined over the entire saturation curve to obtain the required fugacity equality of Equation 5. The values of C, listed for Cq, C9, and Clo are thus not those that would be obtained from Canjar's equations. Similarly, C, had to be adjusted over the entire two-phase region from the normal boiling point to the critical for hydrogen sulfide, and the C , given is not that of Kate et al. (1968). Of the nonhydrocarbons, hydrogen is a special case. Both b and y have been made temperature-dependent by Motard and Organick (19601, in order to correlate phase equilibria data for hydrogen-hydrocarbon systems. For this compound, C, remains constant and
b = 0.08682 +
The temperature dependence of the C, coefficients listed in Table I1 have been correlated using the variable IC: ' ( T ) ,where
l C i ' ( T ) = Cb'(T,)
ACA ' ( T )= Q102 + Q?O'
T
C3
I-c,
580
-
T,j
0 = _____ ,
TO
+ Qie4+ QIOi
IC: ' ( T )=
TOR.
(8)
Qi
+ Q?T+ QiTL+ Q.tTJ,T O R .
(9)
Kaufmann (1968) has given coefficients for C,(T) for czs2-butene, 1-pentene, methylacetylene, and 1,3-butadiene. For the lightest hydrocarbons, methane through propane, the method of Barner and Schreiner (1966) was employed to determine C, down to -300°F. However, in obtaining C, as a function of temperature from vapor pressure data for heavier hydrocarbons, it was found that the lowest pressure for which data were available was about 0.1 p.s.i.a. --for example, for n-heptane the lowest pressure data available correspond to a temperature of 0 ° F . As a result C,>(T) for that compound was determined directly from vapor pressures over the range 210' to 0°F. The higher temperature is the To for heptane given in Table 11. Also listed is TI, the lowest temperature for which Equation 'iapplies. T ofor heptane corresponds to -150" F. Between 0' and -150"F., an extrapolation was made, taking into account curvature, to obtain C, down to T I , For completeness, Table I1 also gives DCDT for the heavier hydrocarbons, CO?, and H S . D C D T is dACA '/ dT, which can be used for a linear extrapolation of IC:' below TI. This variable is set a t zero for CI to C1, because TI is already so low that practical process calculations would not be made a t temperatures below -300" F. For the hydrocarbons iC4 to nC-, D C D T is given, but again TI is low enough that the correlation breaks
197.194
RT
I. BWR Parameters
B"
A0
CO
B
A
C
Alpha
Gamma
0.6824010 0.8919800 1.0055400 1.3626300 1.5588400 2.2032900 1.8585800 1.9921100 2.5638600 2.5109600 2.8483500 3.1878200 2.4316500 2.6158700 2.7671700 0.8057382 0.3339370 0.7336413 0.7994960 0.5582140
6995.2500 12593.6000 15670.7000 23049.2000 25915.3999 38587.3999 33762.8999 38029.5996 48253.5996 45928.7998 54443.3999 66070.5996 55471.7996 6035 1.5000 64360.5000 24548.4800 585.1270 4'496.9410 10322.7999 11701.10QO
0.2757630 + 09 0.1602280 + 10 0.2194270 + 10 0.5365970 + 10 0.6209930 + 10 0.1038470 + 11 0.1132960 + 11 0.1213050 + 11 0.2133670 + 11 0.2591720 + 11 0.4055620 + 11 0.5798400 + 11 0.8810000 + 11 0.1219000 + 12 0.1608000 + 12 0.4190775 + 11 0.4110000 + 07 0.7195331 + 08 0.1698000 + 10 0.2360000 + 10
0.8673250 2.2067800 2.8539300 4.7999700 5.7735500 10.8889999 8.9337499 10.2636000 17.1441000 17.1441000 28.0031998 38.9916997 73.0545998 100.3569994 130.2536983 19.6634109 0.0868200 0.5084650 1.0582000 1.1354300
2984.120 15645.500 20850.200 46758.600 57248.000 117047.000 102251.000 113705.000 226902.000 246148.000 42990 1.000 626106.000 1259500.000 1825500.000 2497800.000 336468.000 98.599 900.070 8264.460 8758.270
0.4981060 + 09 0.4133600 + 10 0.6413140 + 10 0.2008300 + 11 0.2524870 + 11 0.5597770 11 0.5380720 + 11 0.6192560 + 11 0.1362050 + 12 0.1613060 + 12 0.2960770 + 12 0.4834270 + 12 0.8823030 + 12 0.1398020 + 13 0.2040170 + 13 0.2302473 + 12 0.1423170 + 07 0.1072668 + 09 0.2919710 + 10 0.3660180 + 10
0.511172 0.731661 1.000440 1.873120 2.495770 4.414960 3.744170 4.526930 6.987770 7.439920 11.553900 17.905600 17.942 100 23.910500 30.294000 2.877295 0.479116 1.198386 0.348000 0.289043
1.539610 2.368440 3.027900 4.693250 5.645240 8.724470 7.594010 8.724470 11.880700 12.188600 17.111500 23.094200 24.568000 29.996700 35.421700 7.5 18409 0.828100 1.924507 1.384000 1.168890
I & E C PROCESS D E S I G N A N D DEVELOPMENT
(7)
or, for octane, nonane, decane, and hydrogen sulfide
T > 459.69OR. 0.8281 - 0.00051(459.69 - T ) (51 0.6751 T < 160.69"R.
C; C,
(6)
where
y = 0.8281
C1
CiL(T)
C,' '( Tc2)is the high temperature value of Ci ' given in Table I. For temperatures above T o , C, is a constant. For temperatures below T o , the following equations are used for ACb '( T ):
___
Table
-
+
Table II. C, Temperature Dependence
T,,
1 x 4
I-C, n-C I I-c n-C n-Cr n-Cn-C, n-C n-Cli, Cb"
H? S
CO
H3
TI
DCDT
159.69 159.69 159.69 159.69 159.69 269.69 269.69 269.69 309.69 309.69 309.69 309.69 459.69 459.69 484.69 492.00 0.00 0.00 333.34 383.29
289.69 369.69 424.69 459.69 509.69 484.69 529.69 529.69 514.69 629.69 629.69 669.69 1009.69 1059.69 1059.69 671.69 0.00 0.00 449.69 649.69
0.1165490 + 05 0.3404110 + 05 0.1599320 + 05 0.4823550 + 05 0.8239730 + 04 0.1078770 + 06 0.1061340 + 06 0.9480760 + 05 0.1040800 + 06 0.4517410 + 05 0.9696390 + 05 0.3805060 + 05 0.4763729 + 05 0.5239423 + 05 0.7181043 + 05 0.2507454 + 05 0.0000000 0.0000000 0.5051527 + 04 0.2543442 + 05
0.00000 0.00000 0.00000 0.00000 0.00000 -22.12256 -32.83256 -34.32522 -29.57480 -32.49820 -40.00000 -62.00000 -33.88000 -40.76000 -41.04000 -20.44400 0.00000 0.00000 -l7.10000 -25.00000
down before D C D T would be required. However, the term is important for calculations involving Cs to Clc, and benzene, as the Ti for these components is just below ambient. The enthalpy which can be derived from Equation 1 is :
0.3367750 + 05 0.1493090 + 06 0.1018240 + 05 0.1412580 + 06 -0.4473340 + 05 0.7314030 + 06 0.5923800 + 06 0.5009210 + 06 0.4990670 + 06 0.1520220 + 06 0.1985850 + 06 -0.2426230 + 06 -0.1977239 + 03 -0.2271831 + 03 -0.3177407 + 03 0.2649263 + 06 0.0000000 0.0000000 0.2958724 + 05 -0.1153709 + 03
0.5279740 + 05 0.2039330 + 06 0.1962190 + 05 0.1202830 + 06 -0.2319690 + 0x5 0.2231160 + 07 0.1416790 + 07 0.1266080 + 07 0.1479550 + 07 0.4837050 + 06 0.9049590 + 05 -0.3495650 + 06 -0.8194300 - 04 -0.8627400 - 04 -0.1355970 - 03 0.1843210 + 07 0.0000000 0.0000000 0.1204273 + 07 -0.7045528 - 04
PR.
H"=H+ET+FT' 0.18504( (B,RT - 2A0- 4C0/ TL)p
p dC, + -~ +
p TdA, p dT
C
i [ 1 - exp(-?p') (-,PI
7 T
-
-2000 t o 0" F. 0" t o 200" F. 200" to 400" F .
RTp' db 2 dT
H20, E20, F20 H02, E02, F02 H24, E24, F24
Base enthalpy is 0 B.t.u. per lb. mole a t O'R. and zero pressure. For H?S, the temperature ranges are -200" to 200°F. and 200" to 600°F. For benzene. the coefficients cover 0" to 600°F.
~~
2 2P 4 + 1 + -)
(11)
Three temperature ranges have been fitted:
+ (2bRT - 3 a ) p 2 / 2+ 6acup5/5
+
0.6926850 + 05 0.3106840 + 06 0.2180010 + 05 0.2164240 + 06 -0.6114080 + 05 0.2187170 + 07 0.1565130 + 07 0.1358720 + 07 0.1385770 + 07 0.4747210 + 06 0.2112580 + 06 -0.5757700 + 06 0.2315804 + 00 0.2585502 + 00 0.3794226 + 00 0.1263452 + 07 0.0000000 0.0000000 0.5381413 + 06 0.1630762 + 00
The last four terms are t o account for the temperature dependence of parameters in Equation 1. A , can vary with temperature for mixtures. The variation of b and y with temperature is solely for hydrogen. Coefficients for the zero pressure enthalpy are given in Table I11 for the equation
H ( P , T )- H ( 0 , T ) =
T dT
44
Q3
622
QI
d-Y
J -1dT
Table I l l . Zero Pressure Enthalpy H20
CI C C C C,
I-c, I-C n-C I I-C n-C n-Ch n-C n-C, n-C n-C I C H,
*
H 1. CO
HS
E20
-i .D----/a i i
53.79870 5.91303 281.60090 6.00104 218.70210 5.5890S 242.49020 5.48101 208.21010 4.76323 201.06840 133.07950 5.38280 4.65502 280.73720 3.93494 224.40240 3.82904 353.25960 3.00306 425.78210 2.17708 498.30460 1.42584 557.08179 0.60910 627.70390 698.32619 -0.20764 1022.70000 -0.29233 4.99027 388.82700 6.95997 -1.73620 174.88500 5.49357 10.60000 7.86700
0.635000 - 03 0.368500 - 02 0.586500 - 02 0.898000 - 02 0.109500 - 01 0.170700 - 01 0.155350 - 01 0.176000 - 01 0.224850 - 01 0.242450 - 01 0.308800 - 01 0.375350 - 01 0.440718 - 01 0.507063 - 01 0.573409 - 01 0.184900 - 01 0.205000 - 02 0.392000 - 07 0.317000 - 02 0.161600 - 03
EO2
HO2
F2O
5.73525 3.62628 4.08475 4.45322 3.32171 4.40449 5,52312 4.73843 3.72134 6.13987 7.64823 8.99370 10.36414 11.66136 13.04109 -0.29233 6.44515 6.92022 5.66096 7.86700
477.23690 775.98910 688.51600 514.20900 714.79089 292.01520 203.79110 268.80720 294.05910 -173.32400 -643.47160 -1070.43889 -1507.44800 -1921.35199 -2357.97998 1022.70000 67.64600 8.08931 134.92700 10.60000 ~~~~~
FO2
H24
E24
F24
0.263500 - 02 0.632000 - 02 0.790500 - 02 0.101650 - 01 0.132550 - 01 0.174200 - 01 0.148950 - 01 0.174750 - 01 0.226200 - 01 0.217100 - 01 0.258450 - 01 0.301300 - 01 0.343909 - 01 0.387181 - 01 0.429730 - 01 0.184900 - 01 0.40.5000 - 03 0.400000 - 04 0.299500 - 02 0.161600 - 03
941.71999 994.16060 1100.43079 906.98080 523.92480 180.40050 -113.42670 -37 1.39950 -394.43740 -1256.92780 -2 175.10368 -3060.63199 -4905,25897 -5829.24597 -6753.23395 1022.70000 -64.09240 69.67570 -170.10100 66.97000
4.24943 2.85028 2.69118 3.22783 3.70341 4.55391 6.52843 6.51703 S.53687 9.30636 12.17665 14.96598 20.31667 23.20830 26.10003 -0.29233 6,86255 6.73451 6.59172 7.21430
0.382000 - 02 0.699500 - 02 0.902500 - 02 0.111200 - 01 0.131150 - 01 0.174500 - 01 0.141000 - 01 0.162500 - 01 0.214500 - 01 0.194000 - 01 0.225000 - 01 0.256500 - 01 0,271022 - 01 0.301840 - 01 0.332659 - 01 0.184900 - 01 0.550000 - 04 0.180000 - 03 0.228500 - 02 0.107500 - 02
~
VOL. 8
N O . 4 OCTOBER 1 9 6 9
581
The enthalpy prediction is excellent for pure components a t low temperature, for the following reason. Since C, was determined so as to reproduce the vapor pressure curve very accurately by equating fugacities for both liquid and vapor phases, the Clausius-Clapeyron equation must be accurately followed: ~
dP dT
__
AHvap 1 1 - 7)
'(a
Table IV. Modified BWR Equation for Heats of Vaporization
Temp,. F.
Components Methane
-189.69 -207.69 -225.69 -243.69 -252.69 -261.69 -279.69
1596.4 1695.6 1782.3 1872.8 1916.9 1960.0 2021.9
1581.9 1706.5 1807.5 1894.0 1933.4 1970.3 2033.0
,Ethane
-99.69 -117.69 -135.69 -153.69 -171.69
3318.8 3435.4 3645.6 3643.6 3729.1
3349 3458 3557
22.8 7.104 -13.182 -43.71 -69.918 -118.59 -122.52 -147.802 -160.64
4000.6 4113.7 4259.5 4468.9 4631.8 4886.4 4944.8 5021.1 5091.5
(12)
For low temperatures, this will be even more accurate, since p L >> p L and the gas is nearly ideal. Table I V compares heats of vaporization from the modified BWR with experimental data. Modified Benedict Equation for Mixtures
Propane
Since the pure component properties of the compounds have now been accurately correlated in the two-phase region, the ability of the modified Benedict equation t o predict multicomponent phase equilibria will be set by the rules used to determine the composition dependence of the parameters. The usual mixing rules for this equation of state are:
Bo = &Bot
Cal G Mole 1Ht exptl 1 H Lcalcd ( A P I , 1966)
... 3731 4032 4149 4289 4487 4643 4902
... ...
...
Equation 16 is the same as Equation 13 if M,, = 2, but, as described below, M , has now been determined from data on hydrocarbon equilibria. Special consideration has also been found necessary when COz and HzS are present. Even the nitrogen-methane binary requires adjustment a t very low temperature, as was shown by Stotler and Benedict (1953). The equation for the fugacity of a component in a multicomponent mixture is, where N,is moles of component i,
RT In f, =
where x, is t..e mole fraction of i -ar either phase. Occasionally, the Lorentz rule or a quadratic form for Bo of the mixture is used:
using Equation 16 to replace A, in Equations 13 and
1,
[
RT In fi /x,= R T In p RT + ( B o+ B,,)RT Z(C,C,,)' '/T' - 2x1A,, -
B, =
x,Bti'l (Quadratic) i
2
The Lorentz rule gives some improvement in calculated values for hydrocarbons, but historically the linear form has been more popular and gives satisfactory results in practical applications. Experience with the A, equation in the above form has shown that when it is applied t o mixtures, inaccuracies may still be encountered even though the pure components have been well described. This failure is ascribed to failure of the mixing rules t o account fully for solution nonideality. Again following the suggestion of Stotler and Benedict (1953), the rule for determining A, has been modified. I t is replaced by
, # I l > i
582
M,,x,(A,,A,)'' ] p
1 # I
I & E C PROCESS D E S I G N A N D DEVELOPMENT
+ 32 [(b'b,)' 3RT - (a2a,)'' ] p 2 -
where x, may be either liquid or vapor mole fraction and the density of liquid or vapor would be used accordingly. The equilibrium vaporization ratio, or K value, is obtained simply as
Table V. K Values from the Modified BWR Equation for Methane-Propane
Pressure, PSIA
Eiptl
Kc M, = 2 0
-150
100 200 300
4.17 2.01 1.30
3.32 1.82 1.22
-200
50
2.50
2.12
Temp , F
Exptl
Kc M, = 2 0
M ,= 1 9
4.28 2.12 1.28
0.0080 0.0091 0.0160
0.0057 0.0045 0.0064
0.0057 0.0046 0.0075
2.56
0.0026
0.0005
0.0003
M,
19
=
I
-
+I\
Yc For hydrocarbon systems, inaccuracies in predicted K values resulting from use of Equations 16 and 18 with M , , = 2.0 become more severe the lower the temperature and the greater the carbon number difference between i and J . Improvements that can be made in calculated equilibria are shown in Table V for the system methanepropane. Contrasted with the data of Price and Kobayashi (1959) are modified BWR results for M , of 2.0 and 1.9. The latter value of M,, effects a considerable improvement in correlation of methane's K value, but the very low K of propane is virtually unaffected. Although there is some doubt about the accuracy of the experimental values given for propane, as discussed by Adler et al. t1968) and Price and Kobayashi (1959), from examination of many other systems, it appears generally true that for components with K values of 0.1 to 0.01 or less, the effect of altering M, is slight. Shown in Figures 1 through 3 are comparisons for the methane-n-heptane system. The first figure gives data
I
I
1
1
1
l
1
1
1 D
Figure 2. Vaporization equilibrium ratio, K = y / x , for methane-n-heptane
00
Kohn (1961)
... BWR equation 0.1
Modified BWR equation, M . = 2.0
I
0
4
-e
a
7 0.01
=.
Kc,
10
-
9 Y
0.11 I00
I
I
I
1
1 I l l 1
1
I000 P, p i a
1
I
-\ i T, OF -
9
0
-20
1 85
0
-80
1.75
I
-
0.001
Figure 1 . Equilibrium vaporization ratio, K = y / x , for methane-n-heptane
1
100" F. 0 Reamer et a/. (1956) ... BWR equation
Temperature.
Modified BWR, M
=
20
Modified BWR and data curve same for methone
VOL. 8 N O . 4 OCTOBER 1 9 6 9
583
1400
yu-l T, OF
0
0
I
h
C
7
Y
/
t
1
\
Mii
40
1.60
0 -20
I . 35
ZGO
400
600
800
I000
I200
P, p i a 0
Figure 4. Methane-n-deca ne
00
M o l e F r a c t i o n Ethane
Koonce and Koboyoshi (1964)
Figure 6. Ethane-benzene
- Modified BWR eauation
A00 -
a t 100"F., the lowest temperature for which M,, = 2.0 is accurate. The use of more accurate parameters in the modified BWR equation slightly improves calculated K values, but any attempt to improve the heavy component equilibrium value further by alteration of the mixing rule will cause serious errors for the light component. Fortunately, for most process calculations it is the light component K value which is of most importance. Therefore, as the criterion for determination of M,, from binary data, we have used the best fit of the light component K value. Figure 2 shows that the modified BWR equation with the usual quadratic mixing rule, A , = x:A, + ~ X ~ X ~ ( )AI 2 , ,+A xiAu9, ~ is inadequate a t low temperature. Figure 3 shows the fit of the methane-heptane system a t low temperature with the new mixing rule for A,, A , = x:A, + M 1 2 ~ l ~ 2A(oA) '0* + d A o . M G is function of temperature in Figure 3. This will affect the enthalpy calculation in Equation 10, where the term dA,/ dT appears.
Kay and Nevens (1955) BWR equotion
The binary interaction parameter, M,,, is also dependent on carbon number difference. Figure 4 shows the parameters required to correlate the Koonce and Kobayashi (1964) data on methane-n-decane. At -20" F., this system requires M , = 1.35, whereas a t the same temperature, the solubility of methane in n-heptane is fitted by M , = 1.85. Coefficients for pure benzene were given over 20 years ago by Organick and Studhalter (1948), but to our knowledge their accuracy for prediction of phase equilibria has never been evaluated. The BWR equation has been applied to systems of benzene with light hydrocarbons with the usual mixing rules (M,, = 2.0), which appears
P, mia
I
0
P. a t m
Figure 5 . Ethylene-benzene
00 584
Hiraoka (1958) Modified BWR equation
l & E C PROCESS D E S I G N A N D DEVELOPMENT
0
I
1
0.2
I 0.4
I
!
I
0.6
Mole Fraction Propane
Figure 7. Propane-benzene
00 -
Sage and Lacy (19551 BWR equotion
! 0.8
1
1.0
I200 Liquid
1
Liquid
760
Solid
~
1000
"p BOO L
MI0
4oc
Liquid
0.2
I
Vapor
m
I
I
141
0.4
0.2
0
0.4
Ij
/
1
I
"
0.8
0.6
~
L
I
I
I
'
.o
Mole Fraction Methane
Mole Fraction Methane
Figure 10. Methane-carbon dioxide
Figure 8. Methane-carbon dioxide
Temperature. -100" F. Liquid plus solid
Temperature. 8" F. 0 Donnelly and Katz (1954) 0 Modified BWR equation, M,, = 1.8
ODonnelly and Katz (1954) OModified BWR equation, M , = 1.8
to be adequate for temperatures above 212°F. Largely because of lack of data, no attempt was made to determine a t what lower temperatures this correction would be required. Figures 5 , 6, and 7 show the prediction for ethylene, ethane, and propane binaries. Of the nonhydrocarbons, hydrogen and nitrogen equilibria with hydrocarbons have been discussed by Motard and Organick (1960) and Stotler and Benedict (1953). The coefficients are included here for completeness. For hydrogen, equilibria with light hydrocarbons were employed to determine "pure component" parameters for
0
0.2
0.4
0.6
0.8
1.0 0
H1, and the mixing rule for A , was left unaltered from the quadratic form. At very low temperatures, the mixing rule for A, has been altered for nitrogen-methane and more recently Barner and Adler (1968) have stated that variation of nitrogen's y parameter with temperature is useful for phase equilibria correlation. Although the pure, component properties of Con are well correlated with the parameters given by Cullen and Kobe (1955), their use with the Equation 13 mixing rules predicts very poor liquid-vapor phase equilibria. Again, as was the case with hydrocarbons of large carbon number
0
I
I
i
I
I
I
I
I
I
Mole Fraction Methane
Figure 9. Methane-carbon dioxide Temperature, -65"
F.
0Donnelly
and Kotz (1954) OModified BWR equation, M . = 1.8 AModified BWR equotion, original mixing rule, M , = 2.0
VOL. 8 N O . 4 OCTOBER 1 9 6 9
585
difference, the original mixing rules do not properly account for solution nonideality. Unlike the situation found for hydrocarbon systems, however, the M , values required by Equation 16 do not appear t o be strongly temperature-dependent. Apparently, M , 2.0 as T increases, but no data were available to determine the trend. In any event, the correlation parameters determined for C02-hydrocarbon systems cover a broad range of temperature, for which they are very accurate. Particular emphasis has been given to the low temperature regions, because knowledge of the precise phase distribution is tantamount to setting the solidification points for CO? in light hydrocarbon systems.
-
Figures 8, 9, and 10 show correlated phase equilibria in the methane-C0, system between 8"and -1OO'F. Figure 9 also gives for comparison the modified BWR prediction based on the original mixing rules. A slight carbon number dependence exists for CO? systems. The M , , given for propane-C0, in Figure 11 is close to that for the methane binary and it correlates the data of Akers et al. (1954) very well between 32" and -40°F. The weak trend of 1
18001
'"E I
0
0
1400
0
I
0
I
I
I 0.4
0.2
I
I
I
I
0.6
0.8
I
1 1 .o
M o l e Fractlon n-Butane
Figure 12. Carbon dioxide-n-butane 0 Olds ef 01. (1949)
0 Modified BWR
equation, M , = 1 . i 2
Figure 14. Methane-H?S
180C
0 -
160C
Kohn and Kurata (1958) Modified BWR, M
=
1.75
800 k
140C a
d 120C
I CQC
80C
01 0
I
I I 1 0 4 0 6 Mole F r a c t i o n H,S
0.2
M o l e Fraction Methane
Figure 13. Methane-HlS
0
Kohn and Kurata (1958) - Modified BWR, M , = 1.75
586
1 8 E C PROCESS D E S I G N A N D D E V E L O P M E N T
I
Figure 15. HZS-n-pentane 0 Reamer et a/.( 1 9530)
-
Modified BWR, M , = 1.95
I 08
I
1 0
decreasing M , with increasing carbon number is continued in the n-butane-C02 system (Figure 12). The phase behavior of hydrogen sulfide-hydrocarbon and hydrogen sulfide-carbon dioxide-hydrocarbon systems can also be correlated now within the modified BWR framework. Modification of the mixing rules is required and a somewhat stronger trend with temperature and carbon number has been found than for COZ-hydrocarbon systems. Results for methane-HpS are given in Figures
13 and 14. For pentane-HzS a t 160°F., Figure 15 shows that the greater the carbon number the nearer M,, is to the usual value of 2.0. I n the decane-H2Ssystem (Figure 16) a t the same temperature the value of M , actually exceeds 2.0. Figure 17 establishes a temperature trend for pentane-HzS. As shown in Figures 18 and 19, a very satisfactory fit of the H2S-C02 binary can be obtained a t 68" F., but the shape of the phase boundary a t -60" F. is not well reproduced. The primary purpose of this paper is to present pure component coefficients for the BWR equation to extend its range of validity to low temperatures, which are now becoming more common in natural gas processing. However, considerable attention must be given to the mixing rules used in the equation of state before accurate process calculations can be made of phase equilibria in binary and multicomponent systems.
I 0
I
0
i
0.2
i
I
0.4
0.8
0.6 Mole F r a c t i o n HIS
1.0
Figure 16. HjS-n-decane
0 -
Reamer et 01. (1953b) Modified BWR, M,, = 2.10
I
I
20
I
0
-
0.2
I
0.4
I
Figure 17. HnS-n-pentane
0 -
I
I
0 6 Mole Fraction H,S
Reamer et 01. (1953a) Modified BWR, M , , = 1.85
8
1
I
1
Mole F r a c t i o n H,S
0
Figure 19. H?S-CO?
0
Sobocinski and Kurata (1959) - Modified BWR, M , = 1.70
...
Modified BWR, M
= 1.60
VOL. 8 N O . 4 OCTOBER 1 9 6 9
587
Acknowledgment
The author acknowledges the interest of C. Black, who first introduced him to the use of equations of state for calculation of vapor-liquid equilibria, and the continuing advice of C. H. Deal throughout the development of this work. B. J. Duplantis and W. N. Kuhn, Shell Oil Co., Houston, assisted in determining pure component parameters for the heavier hydrocarbons. Literature Cited
S.B., Ozkardesh, H., Schreiner, W. C., Hydrocarbon Process. Petrol. Refiner 47, No. 4, 145 (1968). Akers, L., Kelley, R. E., Lipscomb, T. G., Ind. Eng. Chem. 46, 2535 (1954). American Petroleum Institute, Xew Y ork, “Technical Adler,
Data Book, Petroleum Refining,” 1966. Barner, H. E., Adler, S. B., Hydrocarbon Process. Petrol. Refiner, 47, KO. 10, 150 (1968). Barner, H. E., Schreiner, W. C., Hydrocarbon Process. Petrol. Refiner 45, No. 6, 1969 (1966). Renedict, Manson, Webb, G. B., Rubin, L. C., Chem. Eng. Progr. 47, 419 (1951). Bierlein, J. A., Kay, W. B., Ind. Eng. Chem. 45, 618 (1953). Canjar, L. N.,Smith, R. F., Volianitis, Elias, Galluzzo, J. F., Cabarcos, Manuel, Ind. Eng. Chem. 47, 1028 (1955). Cullen, E. J., Kobe, K. A., A.I.Ch.E. J . 1, 452 (1955). Donnelly, H. G., Katz, D. L., Znd. Eng. Chem. 46, 511 (1954). Hiraoka, H., Rev. Phys.-Chem. Japan 8, 64 (1958).
Kate, F. H., Robinson, R. L., Chao, K. C., Chem. E%. Progr. Symp. Ser. 64, No. 88, 91 (1968). Kaufmann, T. G., Znd. Eng. Chem. Fundamentals 7, 115 (1968). Kay, W. B., Nevens, T. D., Chem. Eng. Progr. S y m p . Ser. 48, No. 3, 108 (1955). Kohn, J. P., A.I.Ch.E. J . 7, 514 (1961). Kohn, J. P., Kurata, Fred, A.Z.Ch.E. J . 4, 211 (1958). Koonce, K . T., Kobayashi, Riki, J . Chem. Eng. Data 9, 490 (1964). Motard, R. L., Organick, E . I., A.I.Ch.E. J . 6, 39 (1960). Olds, R. H., Reamer, H. H., Sage, B. H., Lacey, W. K.,Znd. Eng. Chem. 41, 475 (1949). Organick, E. I . , Studhalter. W . R., Chem. Eng. Progr. 44, 847 (1948). Price, A. R., Kobayashi, Riki, J . Chem. Eng. Data 4, 40 (1959). Reamer, H. H., Sage, B. H., Lacey, W. X., Znd. Eng. Chem. 45, 1805 (1953a). Reamer, H. H., Sage, B. H., Lacey, W. X., J . Chem. Eng. Data 1, 29 (1956). Reamer, H. H., Sage, B. H., Lacey, W. N.,Selleck, F. T., Znd. Eng. Chem. 45, 1810 (1953b). Sage, B. H., Lacey, W. X., “Some Properties of Hydrocarbons,” API Research Project 37 (1955). Sobocinski, D. P., Kurata, Fred, A.Z.Ch.E. J . 5, 545 (1959). Stotler, H. H., Benedict, Manson, Chem. Eng. Progr. Symp. Ser. 49, No. 6, 25 (1953). RECEIVED for review January 13, 1969 ACCEPTED May 9, 1969
SOLVENT EFFECTS ON PHASE EQUILIBRIUM OF Cq HYDROCARBON-SOLVENT SYSTEMS G E O R G E
D .
D A V I S
A N D
E .
C .
M A K I N ,
J R .
Hydrocarbons and Polymers Division, Monsanto Co., St. Louis, Mo. 63166 Phase equilibrium studies of Cd hydrocarbons in various selective solvents reveal significant differences in the relative volatilities of the C4 components. Hydrocarbon composition, solvent composition-e.g., water content-temperature and pressure alter the two-phase boundary in multicomponent systems and influence solvent selectivity. Definition of these variables is necessary before relative solvent selectivities may be determined. Several solvents were selected for preliminary studies and one was chosen for more detailed investigation. Multicomponent equilibria data were determined and phase boundaries for the system were established for a wide range of pressure in a select temperature region.
BUTADIENE cannot be
distilled as a pure material from close boiling C4 hydrocarbons. Aside from small differences in relative volatilities of the key components, the n-butane-butadiene azeotrope limits butadiene purity at practical recovery levels. Altering the relative volatilities by extractive distillation with a selective solvent is the most practical means of obtaining pure butadiene commercially (Table I). The boiling point of butadiene lies in the middle of the C4 mixture, which means two sharp fractionations in a normal distillation system. The light key component, 1-butene, boils only about 2” C. lower than butadiene and its volatility relative to butadiene 588
l & E C PROCESS D E S I G N A N D DEVELOPMENT
is 1.046. The heavy key, n-butane, boils about 4‘C. higher than butadiene, with a relative volatility of 0.870. This would be an easy separation if it were not for the abovementioned azeotrope. A selective solvent can change the relative volatilities and make the almost impossible separation easy. I n the presence of the solvent shown in Table I , the relative volatility of n-butane is more than doubled and that of 1-butene is increased by 50% with respect to butadiene. The new key or closest boiling component in the extractive distillation system becomes cis-2-butene. Since cis-2-butene is easily separated by conventional dis-
