5454
Ind. Eng. Chem. Res. 1997, 36, 5454-5460
Prediction of Vapor-Liquid Equilibria with the LCVM Model: Systems Containing Light Gases with Medium and High Molecular Weight Compounds Christos J. Boukouvalas, Kostis G. Magoulas,* Sofia K. Stamataki,† and Dimitrios P. Tassios Laboratory of Thermodynamics and Transport Phenomena, Department of Chemical Engineering, National Technical University of Athens, Zographou Campus, 9, Heroon Polytechniou Str., 15780 Athens, Greece
The LCVM model (Boukouvalas et al., 1994) is applied to the prediction of vapor-liquid equilibria (VLE) for a variety of binary, ternary, and multicomponent mixtures involving gaseous components (CH4, H2S, C2H6, C3H8, and CO2) with medium and high molecular weight hydrocarbons and/or polar compounds. New interaction parameters (CH4/-CH2O-, CH4/OCCOH, and CH4/gases) are evaluated, and some existing ones (H2S/-CH2-, CH4/ACH, CH4/ ACCH2, and C2H6/ACCH2) are reevaluated by using additional data. Very satisfactory results are obtained in all cases, even for asymmetric systems, where the MHV2 model (Dahl et al., 1991) fails. Of special interest are the successful results for the multicomponent systems that involve up to 24 components, including a H2S-rich sour gas mixture. LCVM is, thus, a powerful model for the prediction of VLE for a broad range of binary and multicomponent systems. 1. Introduction Several equation of state/excess Gibbs energy (EoS/ GE) models have been proposed for the prediction of vapor-liquid equilibria: MHV2 (Dahl et al., 1991); PSRK (Holderbaum and Gmehling, 1991; Fischer, 1993); LCVM (Boukouvalas et al., 1994). The main characteristic of these EoS/GE models is that the mixing rule for the attractive parameter R of the EoS is derived by setting the expression for GE obtained from the EoS equal to that from an existing GE model. This method can be applied at infinite pressure (Vidal, 1978), or at zero pressure (Michelsen, 1990a,b). Boukouvalas et al. (1994) have developed a mixing rule that is a linear combination of the Vidal and Michelsen mixing rules. Of course, there is no need for specified reference pressure. The use of this mixing rule with the t-mPR EoS (Magoulas and Tassios, 1990) and the original UNIFAC (Hansen et al., 1991) leads to the LCVM model studied here. As demonstrated in previous publications (Boukouvalas et al., 1994; Spiliotis et al., 1994; Apostolou et al., 1995; Voutsas et al., 1996; Yakoumis et al., 1996) all models mentioned before present a comparable and very satisfactory behavior in the prediction of vapor-liquid equilibria (VLE) in systems with components of similar size. The main application of EoS/GE models, however, is in the prediction of high-pressure VLE, where the presence of gases with medium to high molecular weight compounds (i.e., significant size difference) represents the typical case. In this case, LCVM yields very good results, while the other models perform poorly. LCVM is, therefore, applied in this study to such systems giving emphasis to multicomponent mixtures whose practical importancesespecially in the petroleum industrysis apparent. We begin our presentation by extending the available table of interaction parameters (Voutsas et al., 1996) * Author to whom correspondence should be addressed. E-mail:
[email protected]. Tel.: (301) 772 3152, (301) 772 3230. Fax: (301) 772 3155. † Department of Mining and Metallurgy. S0888-5885(97)00058-4 CCC: $14.00
Table 1. New UNIFAC Interaction Parameters for the LCVM Model i
j
Aij [K]
Bij
Aji [K]
Bji
H2S H2S H2S H2S H2S CH4 CH4 CH4 CH4 C2H6
-CH2N2 CH4 C2H6 CO2 -CH2O-OCCOH ACH ACCH2 ACCH2
192.54 402.18 218.94 117.97 131.96 64.75 262.57 -146.92 5.29 140.44
0.5567 -0.0641 -0.4903 -0.3531 -0.2171 -1.5710 -0.2592 -0.2919 -0.2547 -0.6003
113.44 333.66 147.29 154.01 112.46 248.76 473.34 343.82 70.73 -65.93
-0.5465 -3.3077 0.0258 -0.9625 -0.1514 2.6235 -0.1803 0.1720 0.1387 -0.3377
and proceed with the prediction of binary and ternary VLE. We consider then several multicomponent mixtures of interest, mainly, to the petroleum and petrochemical industry and close with our conclusions. Representative predictions with MHV2 are also included for comparison purposes. For the n-alkanes involved in these mixtures, Tc, Pc, and ω values suggested by Magoulas and Tassios (1990) were used. For other compounds involved, Tc, Pc, and ω values and vapor pressure data were obtained from Daubert and Danner (1985). 2. Interaction Parameters LCVM utilizes group interaction parameters in the form
{
Ψij ) exp -
}
Aij + Bij(T - 298.15) T
(1)
where T is in K. Values for parameters Aij and Bij evaluated in this study are presented in Table 1 and were obtained by regressing the available data. New interaction parameters (CH4/-CH2O-, CH4/-OCCOH, and CH4/gases) are evaluated, while the parameters for H2S/-CH2-, CH4/ACH, CH4/ACCH2, and C2H6/ACCH2 are now based on a larger database than that used when they were originally determined (Spiliotis et al., 1994). © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5455 Table 2. Results for H2S/Alkanes Systems MHV2
LCVM
H2S with
T range [K]
P range [bar]
NDP
ref
∆P%
∆y × 1000
∆P%
∆y × 1000
C3 nC4 nC5 nC6 nC7 nC9 nC10 nC12 nC15 nC16 nC20 iC4 iC5
217.0-344.3 366.5-418.2 277.6-444.3 323.0-422.7 310.9-477.6 310.9-477.6 277.6-444.3 313.3-434.3 422.6 323.3-423.3 323.0-423.3 277.7-377.6 323.2-413.2
1.4-27.6 14.8-78.9 1.3-89.6 4.3-75.5 1.6-95.5 1.4-27.7 1.4-124.1 5.7-56.8 11.3-112.1 5.3-74.1 4.0-76.7 2.1-61.7 3.1-82.8
49 51 53 25 49 15 44 33 8 25 28 34 33
3 33 44 30 39 7 45 11 31 13 12 48 34
8.3 6.6 6.5 4.4 6.9 6.8 7.2 17.4 31.6 22.9 31.3 3.5 6.3
36 23 42 6 19 8 7 11 36 40
3.3 1.6 2.6 2.4 5.4 2.8 3.8 10.4 13.4 5.5 5.4 3.0 4.0
17 25 35 7 19 6 3 1 23 28
Table 3. Prediction Results for CO2/Higher Alcohol Systems MHV2
LCVM
CO2 with
T range [K]
P range [bar]
NDP
ref
∆P%
∆y × 1000
∆P%
∆y × 1000
nC14OH nC16OH nC18OH
373.2-473.2 373.2-573.2 373.2-573.2
10.1-50.7 10.1-50.7 10.1-50.7
15 15 15
21 21 21
47.7 39.8 47.9
4 5 3
8.7 8.1 6.8
5 8 9
ref
∆P%
∆y × 1000
∆P%
∆y × 1000
16 20 20 5 5
44.3a
-
5.3 2.5 6.6 8.9 13.6
-
Table 4. Prediction Results for CH4/n-Alkane Systems MHV2 CH4 with nC16 nC24 nC32 nC36 nC44 a
T range [K] 287.7-363.2 373.2-473.2 373.2-473.2 373.2-423.2 373.2-423.2
P range [bar] 26.6-705.8 10.1-50.7 10.1-50.7 8.4-79.3 6.8-55.7
NDP 185 15 10 14 15
38.9 54.7 79.7 92.6
LCVM
Fails to perform BP pressure calculations for 97 points.
Interaction parameters for other pairs are given by Voutsas et al. (1996). The obtained results are very satisfactory, including very asymmetric systems. Typical results are presented in Table 2 for H2S with large n-alkanes. The MHV2 model, which is also presented in Table 2, provides results that become progressively poorer as the asymmetry increases. This failure of MHV2 is typical with large asymmetries and this is also the case with the PSRK model as well (Boukouvalas et al., 1994; Spiliotis et al., 1994; Apostolou et al., 1995; Voutsas et al., 1996; Yakoumis et al., 1996). The results for the other systems obtained during the parameter estimation procedure are presented in Tables S-1-S-6 in the Supporting Information. 3. Prediction Results: Binary Systems Prediction results for several gas/solute systems are presented in Tables 3 and 4. Prediction results are also presented in Tables S-7 (propane/n-alkane systems) and S-8 (ethane/n-hexadecane, benzene/TEG, toluene/TEG systems) in the Supporting Information. The following comments summarize our observations on the obtained results. Satisfactory results are obtained in all cases with the LCVM model. The MHV2 model provides again poor results for asymmetric systems as Tables 3, 4, and S-7 indicate. Very satisfactory results are obtained with LCVM for the C3H8/n-alkane systems. The results of Table S-7 are also shown graphically in Figure 1 for the propane/ n-alkane systems, where the average absolute percentage deviation in bubble point pressure prediction is plotted versus the number of carbon atoms in the alkane
Figure 1. Average absolute percentage deviation in BP pressure prediction with the LCVM and MHV2 models for C3H8/n-alkane systems. Zero interaction parameters are used with LCVM while values for them with MHV2 are obtained by Dahl et al. (1991).
with the LCVM and MHV2 models. Notice that for LCVM zero group interaction parameters have been used, while MHV2 utilizes the interaction parameters proposed by Dahl et al. (1991). The MHV2 model fails also at high pressures. Thus, as Figure 2 indicates with the results of the C1/nC16 system, MHV2 provides results that become progressively poorer with increasing pressure failing to provide any results at the x1 ) 0.887 isopleth.
5456 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
sizes of the mixture components. The results with MHV2 are not included as they are consistently poorer than those with LCVM. Actually, for the very asymmetric systems, such as methane/ethane/n-tetradecylbenzene, methane/ethane/nC22, and ethane/propane/ nC32, MHV2 fails to predict a significant number of data points. 5. Prediction Results: Multicomponent Mixtures 5.1. H2S-Rich Sour Natural Gas Mixture. The successful prediction of the VLE behavior of natural gas mixtures is very important in the petroleum industry. The performance of the LCVM model and the PR/kij approach (the PR EoS with conventional mixing rule) are compared in the prediction of the bubble point (BP)/ dew point (DP) pressures for H2S-rich sour natural gas mixtures. The experimental data and the results with the PR/kij approach are obtained from Li et al. (1994). Three mixtures are studied and their compositions are reported in Table 6a. The corresponding results are shown in Table 6b. The results for mixture 3 are also presented graphically in Figure 3. It is shown that both models successfully predict the BP/DP pressures without significant differences. 5.2. Aromatic Hydrocarbons in Triethylene Glycol (TEG). Recently, the prevention of air/water contamination by hazardous pollutants has become a matter of high priority. One such source of pollution is a glycol dehydration unit, used for the dehydration of gases. Recent public awareness and governmental regulation on hydrocarbon emissions into the atmosphere from these units has created an impact on the
Figure 2. Prediction results with the LCVM and MHV2 models for three isopleths of the CH4(1)/nC16(2) system. The results for x1 ) 0.887 with MHV2 are not included because the model fails to predict BP pressures. Experimental data from Glaser et al. (1985).
4. Prediction Results: Ternary Systems Prediction results for ternary systems are presented in Table 5. These systems consist of components with considerable molecular size differences (e.g., gases with high molecular weight hydrocarbons). LCVM performs very satisfactorily, independently of the difference in Table 5. Prediction Results for Ternary Systems
LCVM systems H2S/nC6/nC15 CO2/nC16/n-dodecan-1-ol CO2/C2/n-tetradecylbenzene 1-hexene/H2O/n-methylpyrrolidone CH4/C2/n-tetradecylbenzene CH4/C2/nC22 C2/C3/nC32 CO2/n-butylbenzene/nC20 CO2/n-butan-1-ol/nC8
T range [K]
P range [bar]
NDP
ref
∆P%
∆y1 × 1000
∆y2 × 1000
425 363-414 393 288-298 363-413 278-298 298-303 323-343 303 383
12-75 250 100-250 41-67 0.2-6.7 40-62 47-55 43-49 68-72 40-141
21 18 15 39 37 64 36 18 12 13
31 54 54 38 14 22 22 10 37 40
7.0 7.6 3.5 2.1 4.3 2.5 4.3 6.2 5.4 15.8
14 11 3 20 22 14 9 21 24
14 1 1 20 13 8 21 23
Table 6. Composition and Bubble and Dew Point Pressure Prediction Results for Three H2S-Rich Sour Natural Gas Mixtures H2S mix. 1 mix. 2 mix. 3
CO2
91.67 70.83 50.64
N2
CH4
0.31 0.62
mix. 1 T [K} 298.2 323.2 343.2 348.2 avg. ∆P%
Pexp [bar] 23.8 56.0 41.3 70.2 62.0 84.8 68.3 88.8
D/B pt D B D B D B D B
C2H6
C3H8
(a) Composition (mol %) (Li et al., 1994) 8.33 0.30 25.70 1.79 0.83 0.59 42.53 3.53 1.64
iC4H10
nC4H10
C5H12
0.12 0.24
0.10 0.20
0.02 0.01
mix. 2 ∆P% PR/kij
LCVM
T [K]
Pexp [bar]
D/B pt
mix. 3 ∆P% PR/kij
LCVM
T [K}
(b) Bubble (B) and Dew (D) Point (Pt) Pressure Prediction Results 6.7 5.5 293.2 28.2 D 6.7 4.6 283.2 1.3 4.6 102.1 B 4.0 8.9 3.6 2.9 313.2 46.9 D 5.5 4.1 293.2 1.1 1.9 111.2 B 2.7 6.2 2.3 1.9 323.2 60.0 D 5.0 3.5 303.2 0.7 2.0 116.2 B 0.7 5.5 1.9 1.6 333.2 77.2 D 4.0 2.3 313.2 0.6 0.8 119.0 B 1.0 3.3 2.3
2.7
3.7
4.8
∆P%
Pexp [bar]
D/B pt
PR/kij
LCVM
32.0 117.2 43.8 122.0 59.6 125.7 81.5 117.4
D B D B D B D B
9.1 1.1 9.4 0.4 9.4 3.8 6.0 2.5
5.3 1.5 6.2 0.4 5.9 1.0 1.0 2.3
5.2
2.9
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5457 Table 7. BP Pressure Prediction Results for a Six- and Seven-Component Mixture Involving CH4 and Aromatic Hydrocarbons with Dry and Wet TEG (Ng et al., 1993) H2O in TEG (in mol %) 0 T [°C] 25 25 50 50 75 125 177 204 avg. ∆P%
1
2
P [bar]
T ∆P% [°C]
P [bar]
T ∆P% [°C]
P [bar]
∆P%
20.7 69.0 20.7 69.0 6.89 6.89 1.45 1.38
2.1 0.7 4.7 1.5 8.2 6.0 12.7 8.2
20.7 69.0 20.7 69.0 6.89 6.89
8.1 4.7 7.9 6.0 17.7 16.7
20.7 69.0 20.7 69.0 1.50 1.62
21.7 22.3 19.4 23.6 0.2 10.7
25 25 50 50 75 125
5.5
overall avg. ∆P%
25 25 50 50 177 204
10.2
16.3 10.2
Figure 3. Prediction of the phase envelope of mixture 3 (Table 6a) with the LCVM model and PR/kij approach. Experimental data from Li et al. (1994).
Figure 4. Prediction of BP pressures of mixture 4 (Table 8a) with the LCVM and MHV2 models. Data from Daridon et al. (1996).
oil and gas industry. Hazardous compounds such as benzene, toluene, and the xylenes together with water may be removed from gas streams by the glycols. However, when the glycol is reconcentrated, poor process design may result in losses, creating an environmental hazard. The development of reliable predictive models, thus, is very important to optimize the design of TEG dehydration units. Experimental equilibrium data for a multicomponent mixture containing CH4, benzene, toluene, ethylbenzene, o-xylene, H2O, and TEG, presented by Ng et al. (1993) are used here. TEG concentration (which is the dominant component) varies from 50-99 mol %. Prediction results with the LCVM model for three such systems are presented in Table 7 and can be considered quite satisfactory considering the highly nonideal character of these mixtures. 5.3. Methane-n-Decane-Multiparaffin Systems. Petroleum reservoir fluids contain a considerable amount
Figure 5. (a) Vapor and liquid phase compositions for CO2 and CH4 in system 2 (Table 9a). Symbols are experimental points (Angelos et al., 1992); smooth curves represent prediction results with LCVM. (b) Vapor and liquid phase compositions for nC6 and n-butylcyclohexane in system 2 (Table 9a). Symbols are experimental points (Angelos et al., 1992); smooth curves represent prediction results with LCVM.
of heavy hydrocarbons. However, in some deep reservoirs, where fluids are under high-pressure and -temperature conditions, the light components being in supercritical state are able to dissolve a significant amount of high molecular weight compounds. A decrease of temperature or pressure or modification of the
5458 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 8. Composition and BP Pressure Prediction Results for the CH4/n-Decane/Multiparaffin Mixtures NComp mix. 1 mix. 2 mix. 3 mix. 4
CH4
(a) Composition (mol %) (Daridon et al., 1996) 43.70 46.10 43.80 45.90 43.60 46.15 44.00 45.80
13 15 12 4 mix. 1
T [K] 291.1 304.2 314.2 322.1 333.2 342.7 352.1 362.0 374.0 382.7 393.3 401.7 413.1 422.7 a
P [bar]
multiparaffin mixture
nC10
mix. 2 ∆P%
LCVM
MHV2
T [K]
122.0 127.5 132.0 136.0 140.0 143.5 145.5 148.0 150.5 152.0 153.0 153.5 154.5 155.0
8.6 6.2 5.2 5.1 4.4 4.2 3.4 3.2 3.0 3.0 2.7 2.5 2.8 3.0
12.9 1.0 10.4 16.7 25.7 32.2 38.9 44.4 50.0 53.3 57.1 59.5 61.4 62.5
296.7 303.7 313.3 322.1 333.2 343.2 353.2 362.2 373.3 382.7 393.0 402.7 412.7 422.9
avg. ∆P%
4.1
37.6
P [bar]
mix. 3 ∆P%
LCVM
MHV2
T [K]
35.4
mix. 4 ∆P%
P [bar]
(b) BP Pressure Prediction Results 126.0 8.5 7.7 294.2 125.0 130.0 8.0 1.2 304.5 129.0 134.8 7.4 7.6 313.5 134.0 138.8 6.9 15.0 323.8 138.5 143.0 6.2 23.9 333.2 141.5 146.2 5.7 31.1 341.3 144.5 149.7 5.7 36.9 353.3 147.5 152.0 5.5 41.8 362.5 149.5 153.9 5.1 47.4 372.7 151.0 155.0 4.7 51.6 382.8 152.5 156.5 4.7 54.8 394.3 154.0 157.5 4.8 57.2 403.2 155.0 158.3 4.9 58.9 413.4 156.0 158.8 5.1 60.1 423.8 156.5 6.0
nC20 up to nC30a nC18 up to nC30a nC18 up to nC27a nC18, nC30b
10.20 10.30 10.25 10.20
LCVM
MHV2
9.6 7.6 7.3 6.7 5.8 5.6 4.9 4.5 3.9 3.7 3.7 3.8 4.1 4.3
11.3 0.4 7.2 15.9 23.8 29.3 37.4 42.7 48.1 52.3 55.9 57.9 59.4 60.5
5.4
35.9
∆P%
T [K]
P [bar]
LCVM
MHV2
312.0 323.4 332.6 342.6 352.7 362.1 371.0 383.0 393.3 402.5 412.3 422.3
125.0 129.0 134.0 138.5 141.5 144.5 147.5 149.5 151.0 152.5 154.0 155.0
0.2 1.1 0.3 0.2 0.0 0.3 0.9 0.8 0.9 1.4 2.0 2.6
16.0 27.5 33.8 40.2 46.9 51.7 55.0 60.1 63.4 65.1 66.1 66.8
0.9
49.4
b
Contains all n-alkanes in the given range. Contains nC18 and nC30 only.
composition of the light components throughout the oil processing or transportation through pipelines constitutes potential risk of wax precipitation. To prevent paraffin deposition, which may cause serious plugging of process equipment, thermodynamic tools which can reliably predict temperature and pressure limits are necessary. Daridon et al. (1996) present solid-liquid and vaporliquid equilibrium data that can be used to test such models. We concentrate here on the prediction of the VLE of four such mixtures (that is the objective of this paper) using the LCVM and MHV2 models. These mixtures contain up to 15 components and their composition is summarized in Table 8a. Very satisfactory results are obtained with LCVM, but not MHV2, as Table 8b and Figure 4 demonstrate. 5.4. Synthetic Polydisperse Mixtures. Two synthetic polydisperse (continuous) systems containing CO2, CH4, and complex hydrocarbon mixtures are considered here. Experimental T-P-x-y data have been obtained by Angelos et al. (1992). The systems contain distributions of paraffins, naphthenes, and aromatics, and thus mimic actual light oils. The composition of these systems is presented briefly in Table 9a, and these systems contain 24 and 19 components, respectively. BP pressure prediction results obtained with the LCVM model are presented for both systems in Table 9b. The experimental and predicted BP pressures and vapor phase compositions of CO2 and CH4 in system 2, at 323.2 K, are compared in Figure 5a. Figure 5b is a similar plot for two heavy hydrocarbon components of system 2, n-hexane and n-butylcyclohexane. For light gases, the agreement between experimental and calculated values for both the liquid and vapor phase is very satisfactory. For heavy components, there is good agreement in the liquid phase, but the deviation in the vapor phase is not satisfactory. Note, however, that for such low mole fractions the experimental uncertainty is comparable to the observed deviations of the predicted values (Angelos et al., 1992).
Table 9. Components and BP Prediction Results for Two Synthetic Multicomponent Mixtures (a) Components (Angelos et al., 1992) system 1 (24 components) CO2 n-paraffins nC4 up to nC13 n-alkylcyclohexanes cyclohexane, methylcyclohexane up to heptylcyclohexane n-alkylbenzene toluene, ethylbenzene up to pentylbenzene system 2 (19 components) CO2 CH4 n-paraffins n-alkylcyclohexanes
nC5 up to nC13 cyclohexane, methylcyclohexane up to heptylcyclohexane
(b) BP Pressure Prediction Results temperature: 323.2 K system 1 P [bar] 71.2 74.7 78.0 81.8 85.1
avg. ∆P%
system 2
xCO2
∆P%
0.5550 0.5938 0.6463 0.6863 0.7313
10.55 8.92 5.77 5.52 4.84
7.1
P [bar]
xCO2
∆P%
48.3 55.2 62.1 68.9 75.8 82.7 89.6 96.5
0.3810 0.4088 0.4597 0.5117 0.5450 0.5821 0.6132 0.6451
4.51 0.41 1.30 3.94 1.94 1.21 0.15 0.06 1.7
The comparison of Figures 5a and 5b with the respective ones of Angelos et al. (1992) showed that the results obtained with the LCVM model is at least as successful as the results obtained using a PR/kij-based model presented in that work. However, the results with LCVM represent straight predictions. 5.5. Gas Condensate of a Synthetic Multicomponent Mixture. The performance of the two EoS/GE models, LCVM and MHV2, along with the t-mPR/kij approach (the t-mPR EoS with conventional mixing rule) in the prediction of the K values for a gas
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5459
Figure 6. Prediction of the K values of the eight-component mixure (Table 10a) with the LCVM and MHV2 models. Data from Yarborough (1972). Table 10. Feed Composition and Average Absolute Percentage Error in the Prediction of K Values for a Synthetic Multicomponent Mixture T [K]
P [bar]
N2
310.9
16.2-209.6
0.48
component N2 CO2 CH4 C2H6 C3H8 C5H12 C7H16 C10H22 avg.
CO2
CH4
C2H6
C3H8
(a) Feed Composition (mol %) (Yarborough, 1972) 0.19 80.32 6.02 3.07 t-mPR/kij
C5H12
C7H16
C10H22
4.38
3.11
2.43
MHV2
(b) Average Absolute Percentage Error in the Prediction of K Values 14.9 22.0 7.9 13.9 19.0 20.2 2.4 9.1 4.5 11.1 9.9 23.0 13.2 35.2 37.5 66.2 13.7
condensate of a synthetic eight-component system (Yarborough, 1972) is studied here. The feed composition of the eight-component mixture is presented in Table 10a. The prediction results with LCVM and MHV2 and the prediction results of t-mPR/kij (kij values for N2/HC, CO2/HC, and CH4/HC are obtained by Avlonitis et al. (1994) and Kordas et al. (1994, 1995) respectively; kij values for HC/HC were set zero) are presented in Table 10b. Both LCVM and t-mPR with conventional mixing rules perform very well with a small advantage of LCVM. On the other hand, MHV2 performs worse than the other two models. These results are also presented graphically in Figure 6. The results with t-mPR/kij are not included in the
25.1
LCVM 14.4 14.6 6.2 3.0 4.0 9.2 12.6 37.7 12.7
figure because they almost coincide with the results of LCVM. Conclusions The performance of the LCVM model in the prediction of vapor-liquid equilibria of mixtures containing gaseous components is evaluated. Very satisfactory results are obtained for both binary and multicomponent mixtures. Of special interest are the successful results for the H2S-rich sour natural gas mixtures (Table 6b), the CH4/nC10/multiparaffin mixtures (Table 8b), the gas condensate of a synthetic multicomponent mixture (Table 10b), and the CO2/CH4/complex hydrocarbon mixtures (Table 9b) that involve up to 24 compounds
5460 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
and are also very asymmetric with respect to the size of the mixture components. LCVM is, thus, a powerful model for the prediction of VLE for a broad range of binary and multicomponent systems. The MHV2 model, by contrast, fails for asymmetric systems and this failure becomes more pronounced when high pressures are involved. Supporting Information Available: As Supporting Information, the following items are available: (1) VLE results with the LCVM model (Tables S-1-S-8) and (2) the data references for all the systems in Tables 2-5 (presented in this paper) and S-1-S-8 (presented as Supporting Information), listed in the Table Data References section (5 pages). Nomenclature R ) EoS attractive term (cohesion) parameter Aij, Bij ) coefficients defined in eq 1 BP ) bubble point DP ) dew point GE ) excess Gibbs free energy HC ) hydrocarbons SC ) supercritical T ) temperature [K] TEG ) triethylene glycol xi ) mole fraction of liquid phase (of component i) Ψij ) interaction energy parameter in UNIFAC Table Symbols - ) vapor phase composition not available D/B ) dew (D) or bubble (B) point ∆P% ) average absolute error percentage in bubble- or dew-point pressure ∆yi ) average absolute error in vapor phase composition (of component i) NDP ) total number of data points per system ref ) reference number from Table Data References section in Supporting Information NComp ) number of components in the mixture
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Received for review January 22, 1997 Revised manuscript received September 5, 1997 Accepted September 8, 1997X IE970058V X Abstract published in Advance ACS Abstracts, November 1, 1997.
