462
Ind. Eng. Chem. Process Des. Dev. 1963, 22, 462-468
Sasse, R. A. Anal. Chem. 1965. 3 7 , 604. Show, S. K.: Walker, R. D., Jr.; Qubblns. K. E. J . phvs. Chem. 1969, 73, 312. SkJoMJorgensen, S.; Rasmussen, P.; Fredenslund, AA. Chem. Eng. Sci. 1980. 3 5 , 2389. Tasslos, D. Paper presented at Annual AIChE Meetlng. Washlngton, DC, 1969. Tassbs, D. AIChE J . 1971, 17, 1367. Tokunaga, J. J. Chem. Eng. Data 1975, 20, 41.
Tokunaga, J.: Kawal, M. J . Chem. Eng. Jpn. 1971, 8, 326. Tremper, K. K.;Rausnk, J. M. J . chsm.Eng. Data 1976, 2 1 , 295. Yen, L. C.; McKetta, J. A I C M J . 1962, 8 . 501. Wong, K. F.; Eckert, C . Ind. fng.Chem. Fundem. 1971, TO, 20.
Received for review January 21, 1981 Revised manuscript received September 16, 1982 Accepted November 1, 1982
Use of the Soave Modification of the Redlich-Kwong Equation of State for Phase Eq~#MrCumCakulations. Systems Containing Methanol Te Chang, Ronald W. Roumeau,' and James K. Ferrell Department of Chemlcal E ~ i n w h g North , Carollna State Unlverslty, Rahsbh, North Carollna 27650
The Soave modification of the Redlich-Kwong equation of state is used to predict phase equilibrium in mixtures found in acid gas removal processes used to clean gases produced from coal. B h r y equilibrium calculations compare favorably with data obtained from the literature, provided a temperatur-ndent interaction parameter
is used in some cases. Predictions of equiilbrium behavior in systems containing methanol were satisfactory if
the solute composition in the liquid was Umited to approximately 5 mol % nitrogen or 30 mol % for the other components. Parameters evaluated, and their correlations with temperature, were used to Illustrate predictions of multicomponent system behavior. The results should be applicable in many systems of industrial interest where the concentration is maintained at levels consistent with those found as upper limits on the accuracy of the Soave
equation.
Introduction Gasification of coal produces a product that contains a variety of species, such as carbon dioxide, hydrogen d i d e , carbonyl sulfide, carbon disulfide, aromatic hydrocarbons, and mercaptans, in addition to the desired gases: carbon monoxide and hydrogen. Separation of these components is accomplished in a multistep process involving quenching and water scrubbing, followed by treatment in an acid gas removal system. The acid gas removal system typically involves absorption-stripping operations which utilize either a physical or chemical solvent. The physical solvent that has shown the most promise is methanol; it has been used in all of the commercial coal gasification operations to date. Despite this fact, models describing the equilibrium behavior of the species mentioned above in refrigerated methanol have not been adequately developed. In an earlier work (Rousseau et al., 1981),a thermodynamic model was developed for the description of systems containing methyl alcohol, carbon dioxide, nitrogen, and hydrogen sulfide. This model used the Soave modification of the Rediich-Kwong (SRK) equation of state (1972) to describe deviations of gas mixtures from ideal behavior and third-order Margules equations to express activity coefficients describing liquid nonidealities. Binary interaction parameters in the Soave equation were estimated from available equilibrium data. Unfortunately, there was considerable uncertainty in the evaluation of these parameters, especially for the methyl alcohol-nitrogen mixtures. In addition, the resulting model covered the modest temperature range from 0 to -15 O C . The SRK equation of state was originally developed to describe phase equilibrium behavior of hydrocarbon mixtures, and subsequent inclusion of a parameter to account 0196-4305/83/1122-0462$01.50/0
for interactions between unlike molecules extended its capability to the description of phase-equilibrium behavior for nonhydrocarbons. Graboski and Daubert (1978b) studied interactions in mixtures of carbon dioxide, hydrogen sulfide, nitrogen, and carbon monoxide. Evelein and Moore (1979) modified the SRK equation to include an interaction constant in the mixing rules for both SRK parameters; they successfully applied their resulting expression to the prediction of phase equilibrium in a variety of mixtures formed from components found in natural gases. Evelein and Moore (1976) obtained reasonable correlations of H20-C02 and H20-H2S data by adding a correction factor accounting for the temperature dependence of the Soave parameter. The purpose of this study was to test the validity of using the SRK equation of state to describe both liquid and gas phases in mixtures found in the separation of gases produced from coal. Data used in evaluating this approach were taken from the literature.
The SRK Equation The Soave modification of the Redlich-Kwong equation of state has the following form P = R T / ( u - b ) - aa/u(u + b ) (1) where the quantity a is a function of temperature. ai = (1
+ mi(l - Tr,0.6))2
(2)
G r a b k i and Daubert (1978a) used a regression program to evaluate mi based on API vapor pressure data for hydrocarbons and gases. They correlated mi with the Pitzer acentric factor
mi = 0.48508 + 1.551710, - 0.156130,~ 0
1983 American Chemical Society
(3)
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
Table I. Check List of Binary Data Set Including Major Components from Coal Gasificationa MeOH CO, H2S N, COS CH, H, CO MeOH
X
X X
X X
X
+
X X X
X
+
X X X
+
0,
CZH,
+
X
C,H,
0
0
X
X
X
X X
X X
X
X
X
X
X X
X
463
X X X X X
X
Symbols: available.
X =
[I
P-x-T or -P-x-Y-T data available; 0 = not enough isothermal data available; + = only solubility data -
Soave suggested th,e addition of a second system-dependent parameter in correlating oi;this parameter was included to assist with the description of polar compounds. Although a later paper (Soave, 1980) discussed evaluation of both parameters, there has been no test of this revised approach against mixture data. Furthermore, both parameters must be evaluated from individual vapor pressures and the above generalized form (eq 3) no longer holds. For any pure component, the constants a and b can be found from the critical properties. ai = 0.42747R2T2/P,
bi = 0.08664RTci/Pci
(4) (5)
The Soave modification of the Redlich-Kwong equation can be extended to mixtures using the mixing rules N N
01
= CCxixjffi]aij i=lj=1
N
b=
Cxibi i=l
(7)
where the cross parameter is given by Letting z = Pv/RT
(9)
A = auP/RzF
(10)
B = bP/RT
(11)
the SRK equation (eq 1) can be written as z3 - z2 - z(A
- B - B2) - AB = 0
(12) A generalized treatment of the system allows evaluation of the fugacity coefficient of any component in a mixture from the equation 1 In & = [ ( a P / a n i ) ~ , v-, ~RT/VJ ~ dV - In z (13) RT v
-1
Using the SRK equation in eq 13 gives In di = bi(z - l ) / b - In (z - B ) N
A(2Cxjaijuij/aa - b i / b ) (In [ l + B/z])/B (14) ]=1
Equation 14 can be used to calculate fugacity coefficients of a component in both liquid and gas phases a t equilibrium. In these calculations, the compressibility factor z is obtained by solving eq 12. The largest root of eq 12 is used to evaluate gas-phase fugacity coefficients; the
smallest root of eq 12 is used to evaluate liquid-phase fugacity coefficients. The advantage of solving eq 12 rather than using eq 1is that the compressibility factor is, in most cases, between 0 and 1, while volume u is unbounded. Equation 12 can be solved by a Newton-Raphson calculational technique with initial estimates of the compressibility factor being set at 1for the gas phase and 0 for the liquid phase. It is interesting to note that Evelein and Moore (1979) included a second interaction constant in the mixing rules for bi.. Their results on two systems (N2-H2S and C02-&H8) were not significantly better than results overlapping those of this study. Introduction of a factor to correct for polar compounds was suggested by Evelein and Moore (1976). This approach was tested for methanol but resulted in no significant improvement. Accordingly, the single interaction constant approach was maintained.
Binary Data Sets Binary vapor-liquid equilibrium data for mixtures involving methyl alcohol, carbon dioxide, nitrogen, hydrogen sulfide, carbonyl sulfide, methane, hydrogen, carbon monoxide, oxygen, ethane, and propane were obtained from the literature. Most of the methyl alcohol-gas binary mixtures provide P-x-T data or solubility data. Unfortunately, there is no way to check the consistency of these data. Although some of the sources reported vapor phase compositions, the methyl alcohol concentrations were usually very low and often inaccurate. All available data points were used in the initial evaluation of the SRK constants. Later, data points which appeared to be obviously inaccurate or close to the critical conditions, were rejected. A list of binary mixtures formed from species preaent in most acid gas removal systems that process gases from coal is given in Table I. Evaluation of SRK Binary Interaction Constants For nonhydrocarbons, a binary interaction constant must be evaluated for inclusion in the Soave modification of the Redlich-Kwong equation of state. Evaluation of these constants is from binary mixture data, and preferably from phase-equilibrium data. According to Graboski and Daubert (1978b), the best criterion for selecting the optimum interaction parameter is a minimization of bubble point pressure variance, as defined by the equation N
2=
c [(Pe- Pc3/P,12k
k-1
(15)
This criterion was used in two search procedures to evaluate SRK interaction parameters. In the f i i t , a search procedure bracketed the desired value and in the second a Fibonacci search technique was used to determine the optimum interaction parameter. Two ranges of this parameter are recommended to begin the search procedure.
484
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
mwton-Rmphmo
Road Tc.. Ps.. W
I
I
I
P-X-T data
CmIcuImlm b y
SRK mqumtlon
I
11
Road Inltlml Kl, Inimrvml
Call BRACK
Inltlal eatlmatlon
Calsulmta
Call FOBN
0: 0: 11
Calculato
Call FUNB
Cmkulmtm Zv by 8RK mqumtlon
9
Obtaln optlmum KII In amallor Intorval
objoctivo function
1 Call FIB0
1,;
Call VLFQCP
-
I
,
on. datum polnt
OBF=#(-J
-
- -
=
c*~cu~ai~on
8olv. by mwton-M.phmo method Inltlmlly I m t ZI I O . 0
Call VLFQCP Call VLFQC2
Calculato +:(P.YI,T)
a Call NEWRAP
2.0 atm
i
Bubbb POlnt pramaura
1, XI
P
Cmloulmlm 21 b y
P, Y l
for each datum
Normalho Y I
polni
(Intorval ollminatlon)
Yl
3
YI
YVYSUM
= XI
YSUM
+:/+;
= ZYl
P = P x YSUM Calculate Pcml, YI,
+:, +:,zv,
21;
from optimum KII
L7-O Prlnt roaultr
Output P, YI, FB
Figure 1. Logic flow diagram for evaluating interaction parameter Kij.
Figure 2. Logic flow diagram for bubble point pressure calculation.
Table 11. Physical Properties of Pure Components components
T,,K
P,, atm
methanol
512.6 304.2 126.2 373.2 318.8 369.8
79.9 72.8 33.5 88.2 62.66 41.9
co
2
N2
H2S
cos C,H, a
Reid et al. (1977).
W
ref
0.559 0.225 0.040
a a
0.100
a a, b
0.099 0.152
a
u
Robinson and Senturk (1979).
One is from 0 to 0.25 and the other is from -0.3 to 0. A schematic diagram outlining the calculational technique is given in Figure 1. Binary P-x-T data were used in this study. The calculated pressures for each data point were evaluated through a bubble point calculational routine from the given values of temperature and composition. The criteria for equilibrium is fiV
= ft
(16)
which can also be written as (17) where Cbiv and 9p are obtained from eq 14. Iterations proceed until mole fractions in the vapor phase s u m to one. A schematic diagram for the bubble point pressure calculational technique is given in Figure 2. The complete computer programs are available from the authors. Utilization of the Soave modification of the RedlichKwong equation of state requires critical temperatures, critical pressures, and acentric factors for each of the individual components of a mixture. Table I1 lists values of these quantities used in this work. Interaction parameters for the binary mixtures formed by methanol, carbon dioxide, hydrogen sulfide, nitrogen, y&V
= Xi&
-5.0
I
I 220
240
260
280
300
320
Temperature 1,OK Figure 3. Interaction parameter for methanol-nitrogen mixtures.
carbonyl sulfide, and propane were evaluated from binary equilibrium data covering the most important ranges of operation for acid gas removal systems that use refrigerated methanol as a solvent. Most of the interaction parameters were found to be independent of system temperature, pressure, and composition. However, certain of the methanol-gas systems were found to exhibit interaction parameters that were dependent on temperature. Methanol-Nitrogen. A significant improvement in the accuracy of bubble point pressure calculations was found when a temperature-dependent interaction parameter was introduced to the calculations. Interaction parameters for the methanol-nitrogen system evaluated at four different temperatures are given in Table 111. Root mean percentages of bubble point pressure deviations were all less than 473, which is a significant improvement from the 16% deviations noted when a single value of the parameter was
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 465 Table 111. The Comparison of Interaction Constante in Soave Equation from Optimization of Bubble Point Pressure Calculations Based on Isothermal p-x-T Data for the Methanol-N, Methanol-CO,, and Methanol-COS Systems ranges optimum % bubble no. of point dev, aa T, K P,atm data points ref binary system Kij MeOH-N, -0.2890 3.92 225.0 20.71 167.1 5 b 250.0 24.21177.0 6 1.24 -0.2626 275.0 25.21172.7 5 2.06 -0.2332 300.0 20.91 175.4 5 3.85 -0.2058 16.64 225.01300.0 20.71 177.0 21 -0.2704 MeOH-CO, 0.0100 7.39 228.15 1.018.2 8 c-h 10.28 233.15 1.015.0 2 0.0106 7.70 237.15 1.0111.5 11 0.0130 243.15 1.0113.7 11 7.95 0.0209 7.77 247.15 1.0116.0 16 0.0181 253.15 1.0110.0 3 7.43 0.0282 258.15 4.0120.0 5 8.26 0.0264 273.15 1.0132.9 16 8.63 0.0361 298.15 2.16160.48 21 5.70 0.0356 313.15 5.70179.53 9 4.85 0.0547 11.64 223.151313.15 1.0179.53 104 0.4210 MeOH-COS 0.0209 11.29 233.15 0.4411.59 15 i 253.15 0.3813.38 14 8.82 0.0319 11.73 273.15 0.0501 2.1616.55 11 293.15 1.57111.11 11 9.48 0.0617 16.33 233,151293.15 0.0333 0.44111.11 51 Bezdel and Note: a = {zln[(P- Pc,l)/Pe]2/n)"ZX loo%, where n = no. of data points. Weber and Knapp (1978). Teodorovich (1958). a Katayama et al. (1975). e Krichevskii and Lebedeva (1947). f Ohgaki and Katayama (1976). Yorizane et al. (1969). I Oscarson (1981). g Shenderer et al. (1959).
used to describe the behavior over the range of temperatures from 225 to 300 K. Figure 3 shows the interaction parameters evaluated from data at four temperatures. Clearly the interaction parameter for this binary mixture depends upon temperature; it was correlated by the equation
Kij(T)= -0.5406
+ 0.1116 X 10-%"(K)
(18)
MethanolXarbon Dioxide. MethanolXOS. Including a dependence of the interaction parameter on temperature for these systems also improved the fit of the calculated equilibrium conditions to those measured. Figure 4 shows plots of interaction parameters as a functions of temperature. These results were correlated by the expressions methanol-COz:
Ki, = -0.0972
+ 0.4741 X10-3T(K) (19)
methanol-COS:
Kij = -0.1436
+ 0.7020 X 103T(K)
(20) Table I11 shows how allowing the SRK interaction parameter to depend on temperature improves the fit of the model to experimental data from the literature. Methanol-H2S, Methanol-Propane. Binary interaction parameters for these two systems were assumed to be independent of temperature. Weber (1979) indicated that mixtures involving methanol should include a dependence of the interaction parameter on temperature, but insufficient data were found to develop such a correlation. Even so, the root percentages of bubble point pressure deviations were between 10 and 15%. Interaction parameters for these are given in Table IV. The relatively high deviations of calculated bubble point pressures from experimental measurements indicates that the SRK equation may be unacceptable for binary phase equilibrium calculations involving these mixtures. This is undoubtedly due to the polarity of the components in the system. Gas-Gas Systems. Interaction constants for the four gas-gas pairs were calculated from available equilibrium
220
240
260
280
Temperature T,
300
320
O K
Figure 4. Interaction parameters for methanol-C02 and Methanol-COS mixtures.
data. The values obtained are given in Table IV. These values are slightly different from those determined by Graboski and Daubert (1978a), apparently because different data were used in the evaluation of the parameters. Root mean percentages of bubble point pressure deviations were less than 4% for carbon dioxide-hydrogen sulfide mixtures and the carbon dioxide-propane mixtures. For carbon dioxidenitrogen and the nitrogen-hydrogen sulfide mixtures, deviations were between 6 and 7 % . Graboski and Daubert (1978a) observed that the interaction constant in the Soave modification of the RedlichKwong equation of state did not play a strong role in equilibrium calculations for these components. In this work, the interaction parameter also showed little effect on bubble point pressure variances. Phase Equilibrium Calculations Introduction of a binary interaction parameter in the Soave equation makes it possible to calculate phase
466
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 aoo
12
10
160
E * p^
zoo
f
E
c
0
6
a
t n
d
f
-
160
(D
c
0 0
8
t
4
n 2
0
.Z
1
1
0 0
.o 1
.o 2
.OS
.04
.4
.O
*a
1.o
Molo Fraction COS In.Llquld, X, Figure 7. Methanol-carbonyl sulfide equilibria: data from Oscarson (1981).
.os
Mole Fraction Nz in Liquld, Xnz
Figure 5. Methanol-nitrogen equilibria: data from Weber and Knapp (1978).
E
CI
d ! a 0
-!!
n 4 e
0
I-
a
2
-a
n
~~ ~
~~
0
30
c
~
~~
.2
.4
.a
.8
1.o
Mole Fractlon CO2, Xcoz or Ycor
0
I-
Figure 8. Carbon dioxide-hydrogen sulfide equilibria: (0) Sobocinski and Kurata (1959); (0)and (A) Bierlein and Kay (1953).
20
*O
0 0
.4
.O
.s
1.0
Molo Fractlon COSin Llquld, Xco,
Figure 6. Methanol-carbondioxide equilibria: (A)Krichevskii and Lebedeva (1947); (0) Bezdel and Teodorovich (1958); (VI Ohgaki and Katayama (1976); ( 0 ) Katayama et al. (1975); ( 0 )Yorizane et al. (1969); ( 0 )Shenderer et al. (1959).
equilibrium behavior for nonhydrocarbon mixtures. An equation of state for all fluid phases has many advantages in such calculations. For example, it eliminates the troublesome necessity of defining a reference state for a
multicomponent mixture that includes one or more supercritical components. Ita primary drawback is that it is difficult to apply to systems containing polar compounds, large molecules, or electrolytes (Prausnitz, 1977). In this work a multicomponent bubble point pressure calculation program has been developed. This program was used to describe phase equilibrium behavior of several binary and ternary mixtures. Figures 5-9 illustrate the agreement between predicted and experimental equilibrium behavior for selected binary mixtures. Figure 5 shows excellent agreement of bubble point pressure calculations for methanol-nitrogen mixtures. Methanol-carbon dioxide and methanol-hydrogen sulfide mixtures were well described for liquids containing less than 0.3 to 0.4 mole fraction of H2S or COz in the liquid phase, Figure 6 illustrates this behavior for methanol-
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 467
Table IV. Interaction Constantrs in Soave Equation from Optimization Bubble Pressure Based on Binary p-x-T Data for the Methanol Gas and the Gas-Gas Systems binary system MeOH-H,S
optimum Kij Graboski this work
ranges
% bubble
point dev, u a
P, atm
T,K
no. of data points
ref
248.151273.15 2. 01 10.0 22 b MeOH-C ,H, 293.05 2.671 7.94 11 C C0,-H,S 0.102 224.821313.15 6.8160.0 76 d, e CO ,-N , -0.022 218.151273.15 12.61137.1 34 f-h CO ,-C,H, 0.1018 244.261310.95 3.30137.43 66 I-m N,-H,S 0.140 227.981300.04 3.301204.14 40 0,P " loo%, where n = no. of data oints. Yorizane et al. (1969). Nagahama et al. a Note: u .= {:,"[(P, - P ~ ) / P e ] * / n ) * X Bierlein and Kay (1953). e Sobqcinski and Kurata (1959). PAral et.al. (1971). g Krichevskii and Lebedeva (1979). (1962). Kaminishi and Toriumi (1966). Muirbrook and Prausnitz (1965). 1 Yorizane et al. (1970). Zenner and Dana (1963). Hamam and Lu (1976). Nagahama et al. (1974). " Reamer et al. (1951). O Besserer and Robinson (1975). Kalra et al. (1976). 160
0.0545 0.0043 0.1036 -0.0295 0.1358 0.1727
10.09 13.79 2.00 6.32 3.62 7.00
i
i
\
/ '
lZO 100
I O
eo
-
40
-
*66' 1 t 01 0
I
.I
-1
.a
.4
.I
.I
.I
.I
Mol. Fraction MI, XN, or YN, Figure 9. Carbon dioxidenitrogen equilibria: (0) Muirbrook and Prausnitz (1965);(0)Zenner ad Dana (1963).
carbon dioxide mixtures. For the methanol-propane and methanol-carbonyl sulfide systems, predictions were acceptable only for liquids comprised of less than 15 mol % propane or COS in the liquid. This behavior is shown for mixtures of methanol and COS in Figure 7. Predictions of behavior at low temperatures were better than those at high temperature for all methanol-gas systems. Predicted bubble point pressures were generally low, except for the methanol-nitrogen system, at high dissolved gas concentrations. This may be due to inadequacies in the SRK equation, most likely because of the simple mixing rules (Vidal, 1978; Huron and Vidal, 1979). In addition, equations of state are generally poor in calculating properties of weak polar compounds such as methanol. Figure 8 gives isothermal pressure composition diagrams for carbon dioxide-hydrogen sulfide mixtures. Excellent agreement is noted over the range of compositions and temperatures studied. Similar agreement was noted for carbon dioxide-propane mixtures. Figure 9 shows good agreement between experimental and model predictions of bubble point pressures and vapor compositions, except close to the critical regions, for carbon dioxide-nitrogen mixtures. Similar results were obtained for mixtures of hydrogen sulfide and nitrogen. Vapor-liquid equilibria were calculated for ternary mixtures of methane-ethane-propane, methanol-carbon dioxide-nitrogen, and methanol-carbon dioxide-propane.
2o
0
.?
.4
.I
.e
1.o
Mole Fraction COz in Liquld, Xco,
Figure 10. Bubble pressure calculations on methanol-carbon dioxide-nitrogen mixtures: conditions corresponding to 2 mol % Nz in the liquid.
Bubble point pressure calculations in which binary interaction parameters were set to 0 showed excellent agreement for the hydrocarbon data of Price and Kobayashi (1972). Results for methanol-carbon dioxide-nitrogen are given in Figure 10 for fixed nitrogen mole fractions in the liquid phase. The inversion observed at a COz mole fraction of approximately 0.1 represents unusual behavior. More typical are the results obtained for methanol-carbon dioxide-propane mixtures, shown graphically in Figure 11 for conditions corresponding to 2% propane in the liquid phase. Unfortunately, no experimental data were found for these two ternary systems which would allow model predictions to be checked. Conclusions The Fibonacci search technique was useful in determining optimum interaction parameters for the Soave modification of the Redlich-Kwong equation of state. The bubble point pressure variance provided a useful objective function in this search procedure. The interaction parameter in the methanol-nitrogen system is a strong function of temperature. The interaction parameters for methanol-carbon dioxide and methanol carbonyl sulfide mixtures are weak functions of temperature. Interaction parameters for the other methanol-gas and gas-gas mixtures considered in this study were
468
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
40
5a
= temperature critical temperature LTT, T , = reduced temperature, TIT, =
v = specific volume V = volume x, = mole fraction i xi = mole fraction i in liquid phase of two-phase mixture y i = mole fraction i in vapor phase of two-phase mixture z = compressibility factor = h / R T
50
p'
/
Greek Letters temperature-dependent parameter in SRK equation 9,= fugacity coefficient of i wi = Pitzer acentric factor Registry No. Methanol, 67-56-1. ai =
I
0 0
.2
.4
.O
.a
1.o
Moh Fractkn COS In Llquld, XcoI Figure 11. Bubble pressure calculations on methanol-carbon dioxide-propane mixtures: conditions correspondingt~ 2 mol % C3Hs
in the liquid.
Literature Cited Arai, Y., Kamlnlshi, G.4.; Saito, S. J . Chem. Eng. Jpn. 1971, 4 , 113. Besserer, G. J.; Robinson, D. B. J . Chem. €ng. Data 1975, 20, 157. Bezdel, L. S.; Tecdorovich, V. P. r3azov. Prom. 1958, 8 , 38. Bierleln, J. A.; Kay, W. 8. Ind. Eng. Chem. 1959, 45, 618. Evelein, K. A.; Moore, R. G. Ind. Eng. Chem. Process Des. Dev. 1978, 75, 423.
Evelein, K. A,; Moore, R. G. Ind. Eng. Chem. Process Des. D e v . 1979, 18,
assumed to be independent of temperature. Calculated binary interaction parameters in this study should be useful in multicomponent phase-equilibrium calculations in which the thermodynamic model is used to describe deviations of the vapor phase from ideal gas behavior. It is not expected that these parameters would be universally acceptable in describing liquid phase behavior for mixtures containing methanol. Phase equilibrium calculations using the Soave modification of the Redlich-Kwong equation of state were satisfactory for mixtures of methanol-nitrogen and methanol-gas systems at low gas concentrations in the liquid phase and all gas-gas systems. It did not provide satisfactory predictions for methanol-gas systems containing high gas concentrations in the liquid phase. However, many of the systems of interest, such as absorbers, flash tanks,and strippers, operate at liquid circulation rates that maintain the levels of C02 and other dissolved gases below those a t which the SRK equation loses its accuracy. Acknowledgment The authors gratefully acknowledge support of this research effort by the Environmental Protection Agency under Grant No. R804811. Nomenclature a = constant in SRK equation b = constant in SRK equation f, = fugacity of i K,,= interaction parameter in SRK equation m, = parameter in SRK equation n, = moles of i in mixture P = pressure P, = critical pressure R = gas constant
618.
Graboski. M. S.; Daub&, T. E. Ind. Eng. Chem. Process Des. Dev. 1978a, 17, 443.
(Laboski, M. S.; Daub&, T. E. Ind. €ne. Chem. Process D e s . Dev. 1978b, 77, 448.
Hamam, S. E. M.; Lu, C.-Y. J . Chem. Eng. Dara 1978, 27, 200. Huron, M.J.; Vldal, J. Fluld phese E q d b . 1979. 3 , 255. Kaka, H.; Krlshan, T. R.; Robinson, D. B. J . Chem. Eng. Data 1978, 27, 222.
Kamlnlshl, 0.; Torlami, T. J . Chem. Soc.Jpn. Ind. Chem. Sec. (Kogyo Kagaku Zasshl) 1988. 69, 175.
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Received for review March 25, 1982 Accepted October 12, 1982
