Application of sPC-SAFT-JC and sPC-SAFT-GV to Phase Equilibria

This paper reports on the ability of sPC-SAFT extended with the polar terms of Gross and Vrabec (GV) and Jog and Chapman (JC) to predict the phase equ...
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Application of sPC-SAFT-JC and sPC-SAFT-GV to Phase Equilibria Predictions of Alkane/Alcohol, Alcohol/Alcohol, and Water/Alcohol Binary Systems Adriaan J. de Villiers,† Cara E. Schwarz, Krasimir G. Chobanov, and Andries J. Burger* Department of Process Engineering, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa S Supporting Information *

ABSTRACT: This paper reports on the ability of sPC-SAFT extended with the polar terms of Gross and Vrabec (GV) and Jog and Chapman (JC) to predict the phase equilibria of alkane/alcohol, alcohol/alcohol, and water/alcohol binary systems. These non-hydrogen-bonding/hydrogen-bonding and hydrogen-bonding/hydrogen-bonding systems are investigated using the 2B, 3B, and the newly developed 2C association schemes for alcohols and the 4C scheme for water. For these selected binary systems, the GV and JC polar terms deliver similar results when incorporated into sPC-SAFT. Notably, the 2C association scheme offers improved predictions compared to the 2B and 3B association schemes, especially when water/alcohol systems are modeled.

1. INTRODUCTION One of the most successful theories that evolved from SAFT (statistical associating fluid theory)1−4 is PC-SAFT (perturbedchain SAFT).5 The PC-SAFT equation of state (EOS) considers molecules as chains composed of hard spherical segments and the influence of chain length is accounted for in both repulsive and dispersive contributions. In addition, association is explicitly accounted for, and thus, the PC-SAFT family of EOSs is particularly suitable to model systems containing associating components, such as alcohols and water. As PC-SAFT is numerically intensive, a simplified PC-SAFT (sPC-SAFT) EOS6 was proposed in order to reduce the computational times without compromising model performance.6−8 The simplification assumes that all segments in the mixture have the same segment diameter, with the constraint that the volume fraction calculated with this new diameter gives the same volume fraction as the actual mixture.6 The implementation of this new segment diameter significantly reduces the mathematical complexity of the radial distribution function, which in turn simplifies the hard chain and association terms.7 sPC-SAFT and PC-SAFT are the same for pure components; the simplification only affects the calculation of mixture properties.8 Polar interactions can be accounted for by including a polar term in the state function. Three polar terms, namely, that of Jog and Chapman9 (PC-SAFT-JC), Gross and Vrabec10 (PCSAFT-GV), and Karakatsani et al.11 (PC-SAFT-KSE), have previously been incorporated into the PC-SAFT EOS to predict the vapor−liquid equilibrium (VLE) of alcohol/alkane, alcohol/alcohol, and alcohol/water binary systems.12 Al-Saifi et al.12 found that improved prediction of the phase behavior was obtained using the polar versions compared to the original PC-SAFT model. However, noticeable errors in binary VLE predictions were still present for a few alcohol/alkane binary systems. PC-SAFT-JC provided reasonable alcohol/water representations, but only short-chained alcohols were considered. Furthermore, Al-Saifi et al.8 modeled both water and alcohols using the 2B association scheme and did not consider © 2014 American Chemical Society

any other association scheme configurations. They did, however, mention that improved results may be obtained if other configurations could be investigated. They also set the np parameter in PC-SAFT-GV (by default) equal to 1 for water and alcohols and did not consider it as an adjustable parameter in their regression procedure. Elsewhere, Kleiner and Sadowski13 investigated mixtures of water and cross-associating dipolar components that do not self-associate, using PC-SAFTGV. They found that, when dipolar interactions were explicitly accounted for within the model, worse VLE results were obtained compared to when water was modeled without explicitly accounting for dipolar interactions. Consequently, they modeled water only as an associating component without a contribution from the GV polar term. Alcohols have traditionally been modeled using the 2B or 3B association scheme, as originally proposed by Huang and Radosz.3,4 Recently a new association scheme, the 2C scheme, with association properties between those of the 2B and 3B schemes, has been proposed.14 In general, the 2B association scheme, where molecules are modeled to contain one electron donor site and one electron acceptor site, tends to underestimate association in alcohols when incorporated within PCSAFT-based EOSs. Conversely, the 3B association scheme, where molecules are modeled to contain two electron donor sites and one electron acceptor site, while being theoretically more accurate, tends to overestimate association within the PCSAFT framework. The 2C association scheme combines one of the electron donor sites with the electron acceptor site into a single bipolar site. Therefore, when using this association scheme, molecules are modeled with two association sites, a bipolar and an electron donor site. In short, the 2C scheme provides self-association behavior that is similar to that of the 2B scheme and cross-association behavior that is similar to that Received: Revised: Accepted: Published: 6065

November 19, 2013 February 25, 2014 March 12, 2014 March 12, 2014 dx.doi.org/10.1021/ie403918s | Ind. Eng. Chem. Res. 2014, 53, 6065−6075

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Table 1. sPC-SAFT-GV Model Parameters for Associating Compounds methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol methanol ethanol propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol water

scheme

Mw (g/mol)

σ (Å)

m

ε/k (K)

np

μ (D)

εAB/k (K)

κAB

VLE data and ref

2B 2B 2B 2B 2B 2B 2B 2B 2C 2C 2C 2C 2C 2C 2C 2C 3B 3B 3B 3B 3B 3B 3B 3B 4C

32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 18.015

2.7164 3.0954 3.3093 3.4799 3.6846 3.7951 3.9324 4.0346 3.1616 3.2558 3.3108 3.5584 3.7464 3.8609 3.9627 4.0233 2.7169 2.9519 3.2899 3.4585 3.6411 3.8058 3.9387 4.0188 2.6204

2.5541 2.5766 2.8182 3.0286 3.0395 3.2100 3.3700 3.4766 1.7023 2.2361 2.8017 2.8439 2.9049 3.0600 3.3250 3.4971 2.6253 3.0099 2.9001 3.0982 3.1551 3.2001 3.3990 3.5284 1.50518

177.84 194.85 225.43 244.82 258.33 269.07 273.10 280.68 197.42 202.27 223.67 249.85 261.98 274.08 274.25 279.31 184.07 198.77 230.11 244.97 256.69 271.54 275.19 280.45 149.96

0.4534 0.9684 1.6270 2.1267 2.8120 3.2378 3.5211 3.8898 0.8712 1.1933 1.7900 2.4012 3.0290 3.4930 3.9540 4.4152 0.0994 1.5453 1.1578 1.4524 2.0850 2.1001 2.1001 2.1141 0.3161

1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.85

2296.3 2474.3 2342.9 2413.7 2443.4 2750.9 2899.9 2985.2 2627.8 2695.1 2466.7 2609.8 2622.1 2945.8 3159.9 3112.8 2073.1 2002.0 2039.7 2132.9 2134.1 2460.4 2685.2 2639.6 1816.0

0.23514 0.07586 0.03578 0.01595 0.01390 0.00551 0.00474 0.00451 0.05194 0.03035 0.02063 0.00702 0.00661 0.00244 0.00164 0.00230 0.11135 0.06557 0.02419 0.01346 0.01268 0.00507 0.00322 0.00465 0.20245

n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 −

Table 2. sPC-SAFT-JC Model Parameters for Associating Compounds methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol water

scheme

Mw (g/mol)

σ (Å)

m

ε/k (K)

xp

μ (D)

εAB/k (K)

κAB

VLE data and ref

2B 2B 2B 2B 2B 2B 2B 2B 2C 2C 2C 2C 2C 2C 2C 2C 3B 3B 3B 3B 3B 3B 3B 3B 4C

32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 32.042 46.068 60.095 74.122 88.148 102.17 116.20 130.23 18.015

2.7721 3.1053 3.2424 3.4648 3.7011 3.8144 3.9465 4.0510 3.1718 3.2876 3.2777 3.4803 3.7261 3.8261 3.9788 4.0488 2.6231 2.9784 3.1338 3.4512 3.6366 3.8065 3.9500 4.028 2.6179

2.5391 2.5570 2.9841 3.0771 3.0186 3.1800 3.3101 3.4483 1.6887 2.1752 2.8852 3.0345 2.9606 3.1511 3.2864 3.4503 2.7184 2.9434 3.3026 3.1233 3.1754 3.2068 3.3826 3.5081 1.500

176.67 192.25 219.17 243.92 260.36 271.36 275.01 283.14 192.36 198.25 218.69 244.09 262.16 272.08 277.01 282.74 183.94 199.29 218.64 244.23 256.37 271.58 275.04 281.64 144.82

0.06951 0.16095 0.17079 0.21892 0.300023 0.31273 0.31001 0.29186 0.2960 0.2525 0.2030 0.2507 0.3343 0.3470 0.3814 0.3347 0.0238 0.0483 0.0713 0.1513 0.2145 0.2161 0.2501 0.1659 0.1250

1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.70 1.70 1.68 1.67 1.70 1.65 1.74 1.65 1.85

2318.3 2483.8 2263.7 2340.6 2381.3 2701.8 2857.7 2964.7 2621.3 2734.2 2416.1 2452.0 2508.9 2828.6 3054.3 3089.0 2072.6 2023.4 1891.3 2099.5 2085.3 2430.9 2647.6 2641.7 1838.9

0.23930 0.08310 0.05209 0.01971 0.01619 0.00614 0.00574 0.00472 0.06390 0.03440 0.02910 0.01090 0.00828 0.00310 0.00198 0.00224 0.11125 0.06206 0.04085 0.01497 0.01432 0.00538 0.00345 0.00457 0.20936

n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 n-hexane25 n-heptane23 n-heptane26 n-nonane27 n-heptane28 n-hexane29 n-decane30 n-decane31 −

of the 3B scheme, thus combining the two schemes and changing how hydrogen bonding of the molecules is represented. In this work, sPC-SAFT-GV and sPC-SAFT-JC are combined with the 2B, 2C, and 3B association schemes for alcohols for the first time. The performance of all three

association schemes were previously tested within the framework of sPC-SAFT, with particular focus on applications to systems containing alcohols.14 However, these association schemes have previously only been applied to sPC-SAFT without inclusion of a polar term, and sPC-SAFT-GV and sPC6066

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larger than those in the gas phase, the conventional approach was followed, i.e., the gas-phase dipole moment was used for all components at all conditions. The model parameters for water were determined by following a similar strategy as proposed by Grenner et al.16 for sPC-SAFT and were based on the same physical arguments: (a) the segment number (m) should be small; (b) the dispersion energy parameter (ε/k) should be in the range between 47 and 160 K, as determined by Errington17 (this range is not absolute, but an indication of where the parameter can be expected); and (c) the association energy value (εAB/k) should be close to 1813 K.18 While physical arguments may suggest that the np and xp parameters for the sPC-SAFT-GV and sPC-SAFT-JC models respectively should be close to unity, poor model performance was achieved in such a case. Similar results were obtained by Kleiner and Sadowski13 and Al-Saifi et al.12 The smaller numerical values for np and xp were thus regarded as acceptable, highlighting the fact that application of polar theories to water is challenging. Additionally, while the segment number of 1 for water is theoretically more correct, the values of the segment number and that of other parameters obtained in this work correspond well to those of Grenner et al.16 The average absolute deviation (%AAD) values of the 1alcohol pure component properties showed that simultaneous accurate correlations of the saturated vapor pressure, liquid density, and heat of vaporization are obtained with both sPCSAFT-GV and sPC-SAFT-JC and for all three association schemes (see Table S1, Supporting Information). The smallest %AAD is usually observed when the 2C association scheme is used. For all the considered association schemes of the homologous series of 1-alcohols, the values of the segment number, segment diameter (σ), and the dispersion energy increase with increasing molecular mass. The association energy parameter is of the same magnitude for the short-chain alcohols (1-propanol, 1-butanol, and 1-pentanol) but is approximately 20% larger for the longer-chain alcohols. This observation is the most evident for the parameters based on the 3B association scheme. Such trends are in good agreement with the association parameter values determined by Al-Saifi et al.12 Nath and Bender20 measured the enthalpy of association for methanol and reported a value of 2630 K. Using the 2C scheme, the association energy parameter of methanol for sPCSAFT-GV is 2627.8 K and for sPC-SAFT-JC is 2621.3 K. These are both remarkably close to the measured value. For the polar theories, the methanol association energy parameter values are approximately 2300 and 2070 K for the 2B and 3B schemes, respectively. Thus, the values based on the 2C scheme correspond significantly better to measured literature data than the values generated with the 2B and 3B schemes. Furthermore, Kontogeorgis et al.21 reported the enthalpy of association data, as originally measured by Pimentel and McClellan22 for C2−C6 alcohols, to be between 2526 and 3007 K. Comparing the alcohol association energy parameters of both polar theories and based on the various schemes, it seems that the parameters based on the 2B and 2C schemes correspond well with the measured values.

SAFT-JC have not been extensively tested for associating compounds. Results are presented on the performance of sPC-SAFT-GV and sPC-SAFT-JC in predicting the VLE of non-hydrogenbonding/hydrogen-bonding and hydrogen-bonding/hydrogenbonding systems. Alkane/alcohol systems are considered representative of the former systems and alcohol/alcohol and water/alcohol systems representative of the latter. The previous study,14 which introduced the 2C association scheme, showed that for sPC-SAFT without the inclusion of polar terms, the main advantage of the 2C scheme is that improved VLE predictions of water/alcohol systems are obtained compared to the 2B and 3B association schemes, especially for short-chained alcohols. However, slightly worse VLE predictions of alcohol/ alkane systems are obtained using the 2C scheme. This paper therefore aims to provide an outcome as to whether sPCSAFT-GV and sPC-SAFT-JC suffer from the same shortcomings as sPC-SAFT when alcohols are modeled with the 2B and 3B schemes in VLE predictions of alkane/alcohol, alcohol/ alcohol, and water/alcohol systems and if the advantages gained by modeling alcohols with the 2C scheme with sPC-SAFT are also applicable to sPC-SAFT-GV and sPC-SAFT-JC. New component parameters have been regressed, and the models are applied to alkane/alcohol and alcohol/water binary VLE systems. From the results presented, an outcome as to the most appropriate association scheme for alcohols within the framework of the sPC-SAFT-JC and sPC-SAFT-GV EOSs is proposed. For comparative purposes, graphical results with the 2B parameters determined by Al-Saifi et al.12 are included in this work (Annotated sPC-SAFT-GV-2B-Lit and sPC-SAFTJC-2B-Lit).

2. MODEL PARAMETERS Pure component model parameter values for sPC-SAFT-GV and sPC-SAFT-JC are presented in Tables 1 and 2, respectively. The new model parameters for alcohols based on the three association schemes (2B, 2C, and 3B) were determined using a previously defined regression function,15 where saturated vapor pressure, saturated liquid density, heat of vaporization, and binary VLE data were included in the objective function. Large regression weights were assigned to the pure component data and small regression weights to the binary VLE data. These regression weights not only ensured that the parameters were dominated by the pure component data but also provided the correct dispersion and polar term contributions. Refitting the parameters therefore ensures a fair and unbiased evaluation of the models as well as comparison between the different association schemes. It is well-known that a single set of parameters are often not able to predict all phase behavior satisfactorily. For example, the ethanol parameters of Al-Saifi et al.12 (determined without the inclusion of binary VLE), used in conjunction with the 2B association scheme, are able to predict the ethanol/n-heptane VLE very well yet are at the same time unable to describe the VLE of the water/ethanol binary system accurately. This dilemma is encountered for most alcohol/alkane and alcohol/ water systems. It is thus believed that incorporation of the VLE, albeit with only a small regression weight, will provide a more globally correct pure component parameter set, hence the inclusion of the VLE in the regression function. The dipole moments (μ) were not treated as adjustable parameters, and values obtained from the literature19 were used. While dipole moments in the liquid phase are generally

3. PHASE BEHAVIOR OF ALKANE/ALCOHOL SYSTEMS Modeling of alkane/alcohol systems is quite challenging, because of the large difference between the so-called like and unlike interactions. Here, the performance of sPC-SAFT-GV 6067

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Table 3. Summary of Phase Equilibria Predictions of Systems Studied Using Various sPC-SAFT Models alkane/alcohol

alcohol/alcohol

water/alcohol

mixture

Δy (×102)

ΔP (%) or ΔT (K)

Δy (×102)

ΔP (%) or ΔT (K)

Δy (×102)

ΔP (%) or ΔT (K)

sPC-SAFT-2C sPC-SAFT-2B sPC-SAFT-3B sPC-SAFT-GV-2C sPC-SAFT-GV-2B sPC-SAFT-GV-3B sPC-SAFT-JC-2C sPC-SAFT-JC-2B sPC-SAFT-JC-3B

2.90 1.74 1.66 1.12 1.12 1.18 1.17 1.14 1.20

7.95 4.45 4.21 2.18 2.16 2.27 2.33 2.35 2.36

1.04 2.48 0.76 1.06 0.92 0.62 1.02 0.91 0.79

1.31 6.53 1.91 1.58 2.03 1.53 1.53 2.00 1.82

1.34 4.29 3.92 1.11 3.61 1.96 1.24 3.55 2.37

1.39 8.56 5.59 1.06 7.25 2.73 1.02 7.85 3.34

ref 14 14 14 this this this this this this

work work work work work work

Figure 1. VLE predictions for the methanol/n-hexane system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Oracz.29

interaction parameters (BIPs) reported in Tables S4 and S5 in the Supporting Information). Al-Saifi et al.12 reported that PC-SAFT-JC and PC-SAFT-GV are also prone to predicting false phase splits at lower temperatures for some binary systems. This may possibly be an indication that the temperature dependencies of these models are not completely correct and should be improved in future studies. Representative phase equilibria results for some binary alcohol/alkane systems are discussed below. Figure 1 (VLE of methanol/n-hexane) indicates that the performance of the respective GV- and JC-based models are very similar, implying that the two polar theories are more or less equivalent. When methanol is modeled according to the 3B association mechanism, a false liquid−liquid phase split is obtained, which can easily be corrected with a small BIP. Additionally, it is noted that all the models only provide an approximate prediction of the azeotrope. The predictions using the 2B regression parameters published in the literature (AlSaifi et al.8) are slightly inferior to those using the 2B regression parameters determined in this work. This improved prediction can be attributed to the inclusion of binary VLE data in the regression function, as Al-Saifi et al.12 only included pure component properties in their parameter estimation routine (in PC-SAFT-GV, np was set equal to 1, and in PC-SAFT-JC, xp was constrained so that xp multiplied by m equals 0.5) . Considering the liquid−liquid equilibrium (LLE) of methanol/n-hexane (Figure 2), it is noted that the correlations

and sPC-SAFT-JC are compared, while applying either the 2C, the 2B, or the 3B association schemes for the alcohols. The predictions with the different association schemes are indicated as sPC-SAFT-GV-XX and sPC-SAFT-JC-XX, where the XX refers to the association scheme used to model the alcohol. A summary of results for %AAD in pressure or temperature and vapor phase mole fraction are presented in Table 3 for sPCSAFT, sPC-SAFT-GV, and sPC-SAFT-JC, with detailed results in Tables S2 and S3 in the Supporting Information for the sPCSAFT-GV and sPC-SAFT-JV models, respectively. From Table 3, it follows that similar alcohol/alkane VLE representations are obtained with the three association schemes. A previous study14 showed that when alcohols are modeled with the 2C scheme in normal sPC-SAFT, slightly worse predictions were obtained compared to the 2B scheme for these types of systems. However, by now including the polar term in the state function, this is no longer the case, and predictions with all three association schemes are similar. Therefore, the inclusion of the polar theories improves the prediction for all three association schemes. Unfortunately, for some systems containing short carbon chain alcohols, false liquid−liquid demixing is predicted at lower temperatures by both models and with all three association schemes. For both models, the problem is most severely encountered when alcohols are modeled as 3B components, least severe with the 2B scheme, and in between with the 2C scheme (see the magnitude of the binary 6068

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Figure 2. Liquid−liquid equilibrium predictions for methanol/n-hexane system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Hradetzky and Lempe.32

Figure 3. VLE predictions for the n-hexane/1-hexanol system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Oracz.29

based on the 2B parameters from Al Saifi et al.12 provide the least accurate representation of the LLE (sPC-SAFT-GV-2B-Lit and sPC SAFT JC-2B-Lit). The best correlation of the LLE is achieved with sPC-SAFT-JC-2C. Attempts were made to redetermine methanol model parameters for sPC-SAFT-GV2C, but no parameter sets could be regressed to provide improved LLE correlations without sacrificing accuracy in the VLE representations. In general, the 2B and 2C schemes provide better predictions than the 3B scheme. As is the case for the methanol/n-hexane system, the VLE predictions for the ethanol/n-heptane system are similar for all models and are in very good agreement with the experimental data.23 Once again, the only model that provides a slightly less accurate prediction compared to the other models is sPCSAFT-JC-2B-Lit. VLE predictions for the n-hexane/1-hexanol system (Figure 3) show that good phase behavior results are obtained by both

polar sPC-SAFT models for binary systems with components that have a relatively large difference in vapor pressure. Moderate errors in the VLE predictions of some systems are observed (%AAD < 6.5%, see Table S4, Supporting Information). The 1-butanol/n-octane system (Figure 4) is a typical example. However, the deviations can easily be reduced by using a small BIP (Figure 5). It could be that the deviations between the model predictions and the experimental data24 may lie in the temperature dependency of the models (probably from either the polar or dispersion terms), or alternatively, the VLE data may contain inaccuracies. At this point, and within the boundaries of this study, there is no major difference between the performance of sPC-SAFTGV or sPC-SAFT-JC in predicting phase equilibria of alcohol/ alkane mixtures. While inclusion of the polar theory significantly improves the phase behavior prediction, the influence of the association scheme is negligible in both sPCSAFT-GV and sPC-SAFT-JC. The main exception seems to be 6069

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Figure 4. VLE predictions for the 1-butanol/n-octane system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Hiaki et al.24

Figure 5. VLE correlations for the 1-butanol/n-octane system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Hiaki et al.24

used. The sPC-SAFT-GV and sPC-SAFT-JC variants provide a similar and in some cases improved prediction compared to sPC-SAFT. To illustrate the accuracy of the predictions, consider the results for the methanol/ethanol system shown in Figure 6. The VLE predictions of alcohol/alcohol systems with sPCSAFT-GV and sPC-SAFT-JC are very similar with all three association schemes. For the methanol/ethanol system, the least accurate predictions are obtained with sPC-SAFT-GV-2B and sPC-SAFT-JC-2B (for both 2B parameters determined in this work and from Al-Saifi et al.12). The predictions based on the 2C and 3B parameters are slightly more accurate. More or less, the same discussion applies to the ethanol/1-octanol system. However, the predictions based on the 2C scheme are marginally more accurate compared to the predictions based on the 3B scheme. Again, only marginal differences are observed between the GV and JC models.

the binary mixtures containing methanol, where the 2C and 2B schemes appear to be better suited than the 3B scheme. Furthermore, the 2B parameters determined in this work provide slightly improved vapor−liquid equilibrium predictions compared to the parameters determined by Al-Saifi et al.12

4. PHASE BEHAVIOR OF ALCOHOL/ALCOHOL SYSTEMS In alcohol/alcohol systems, the like and unlike interactions are similar. Thus, it is expected that accurate predictions of these systems should be obtained with both sPC-SAFT-GV and sPCSAFT-JC, regardless of the association scheme used to model the alcohols. This is indeed the case, as verified by the results presented in Table 3 for sPC-SAFT-GV and sPC-SAFT-JC (details are provided in Tables S6 and S7 of the Supporting Information). The average %AAD in pressure/temperature for both models is approximately 1.5% with the 2C association scheme and approximately 2.0% when the other schemes are 6070

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Figure 6. VLE predictions for the methanol/ethanol system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Hall et al.33

Figure 7. VLE predictions for the methanol/water system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Kurihara et al.34

5. PHASE BEHAVIOR OF WATER/ALCOHOL SYSTEMS The results for alcohol/water systems presented in this section are crucial to this study. In a previous work,14 it was shown that improved VLE predictions for alcohol/water systems can be obtained when alcohols were modeled with the 2C scheme compared to the 2B and 3B schemes within the sPC-SAFT framework. This, however, came at the expense of accuracy in VLE predictions of alcohol/alkane systems, where the 2B and 3B association scheme were more accurate. In section 3 above, it was shown that the predictions of alcohol/alkane VLE with both models (GV and JC) using any of the association schemes were fairly similar and the disadvantage of the 2C scheme, as experienced with sPC-SAFT, was no longer encountered when the polar terms are incorporated into the model. Table 3 summarized the VLE predictions for alcohol/water systems using sPC-SAFT, sPC-SAFT-GV, and sPC-SAFT-JC (details are provided in Tables S8 and S9 of the Supporting Information). The results show that for all association schemes

the inclusion of the polar theories improves the prediction. The results also show that the best VLE predictions are obtained when the alcohols are modeled using the 2C scheme with both the JC and GV polar versions. In particular, major improvements are obtained for the methanol/water system. Similar to the results found for sPC-SAFT-2C without the inclusion of a polar term,14 the difference between the predictions of the various association scheme becomes less pronounced as the chain length of the alcohol increases. Now, consider the water/methanol binary system. Very little difference is observed between sPC-SAFT-GV and sPC-SAFTJC for the water/methanol binary system (Figure 7). For both models the best results are obtained when methanol is modeled using the 2C scheme. When methanol is modeled with the 2B scheme, it appears as if cross-association in the system is underestimated with both sPC-SAFT-JC and sPC-SAFT-GV. Conversely, when the 3B association scheme is employed, overestimation of cross-association is experienced. Similar 6071

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Figure 8. VLE predictions for the ethanol/water system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Kurihara et al.34

Figure 9. VLE predictions for the 1-propanol/water system with (a) sPC-SAFT-GV-XX and (b) sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data from Woerpel et al.35

poor VLE and LLE predictions. With the 2B scheme, the composition of the butanol-rich liquid phase is poorly predicted, but the solubility of 1-butanol in the water-rich liquid phase is predicted with fair accuracy. sPC-SAFT-GV-2C provides VLE predictions that are considerably more accurate compared to the predictions based on the 2B scheme. Improvement is also obtained in the LLE representation compared to the 2B scheme. The solubility of 1-butanol in the water-rich phase is, however, slightly overestimated. Considering sPC-SAFT-3B, accurate VLE representation of the system is obtained and the VLLE point is also predicted satisfactorily. However, the temperature dependency of the butanol-rich liquid phase composition is poor when compared to the trends generated with the 2B and 2C schemes. The solubility of 1butanol in the water-rich phase is also overestimated. The VLLE correlation of the 1-pentanol/water system (Figure 11) shows once again that the two polar theories provide similar VLE representation. Furthermore, it is noted

trends were previously observed for sPC-SAFT without the polar terms.14 Figure 8 shows that the same discussion is applicable to the ethanol/water system. Once again, for both models, the predictions based on the 2B scheme underestimate crossassociation, while sPC-SAFT-JC-3B overestimates cross-association. Good predictions are obtained for both models when the 2C scheme is used. Similar observations also apply to the 1propanol/water system (Figure 9). Importantly, the predictions based on the 2B scheme result in false vapor−liquid−liquid equilibrium (VLLE) predictions, although a BIP may be used to rectify the error, as indicated (See Table S10 of the Supporting Information). Figure 10 shows the VLLE and VLE predictions of the 1butanol/water system using sPC-SAFT-GV. Similar results are obtained with sPC-SAFT-JC. As with the results for the other alcohol/water systems presented thus far, cross-association seems to be underestimated by the 2B scheme, resulting in 6072

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Figure 10. (a) VLLE and (b) VLE predictions for the 1-butanol/water system with sPC-SAFT-GV-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Iwakabe and Kosuge36 and Sorensen and Artl.37

6. CONCLUSIONS The aim of this work was to incorporate the 2B, 2C, and 3B association schemes into the sPC-SAFT-GV and sPC-SAFT-JC thermodynamic models. New pure component parameters were regressed and the models were applied to alkane/alcohol, alcohol/alcohol, and water/alcohol systems. For all three types of systems, improved predictions were obtained for sPC-SAFTGV and sPC-SAFT-JC compared to sPC-SAFT. From the results presented, and within the boundaries of this study, the performances of sPC-SAFT-GV and sPC-SAFT-JC are very similar and the association schemes influence the performances of both models in a similar manner. Overall, the 2C association scheme offers improved VLE predictions compared to the 2B and 3B association schemes when incorporated in sPC-SAFTJC and sPC-SAFT-GV for alcohols. While results for alkane/ alcohol and alcohol/alcohol systems hint toward the 2C association scheme being best-suited, the true superiority of the 2C association scheme is observed when alcohol/water systems are modeled. The 2C association scheme thus appears to be the most appropriate association scheme for alcohols within the framework of sPC-SAFT-GV and sPC-SAFT-JC. In the future, other thermodynamic model frameworks may be investigated. Additionally, while linear alcohols were studied in this work, future work would also consider phase behavior involving branched alcohols.

Figure 11. VLLE correlations for the 1-pentanol/water system with sPC-SAFT-GV-XX and sPC-SAFT-JC-XX, where XX represents the association scheme used for the alcohol. Experimental data are from Iwakabe and Kosuge36 and Sorensen and Artl.37

that the best overall representation of the phase behavior is obtained with sPC-SAFT-GV-2C and sPC-SAFT-JC-2C. The correlations based on the 3B scheme provide the most accurate VLE representation, but the LLE representations are only moderate and cannot be corrected with a BIP. The correlations based on the 2B scheme also result in accurate VLE correlations, but the solubility of 1-pentanol in the water-rich phase is too high. For larger alcohols that exhibit VLLE behavior with water, the 2C and 3B association schemes provide accurate VLE representations. Unfortunately, the prediction of LLE is still problematic. Taking all these results into account, the correlations based on the 2C association scheme yield the best overall VLLE representation of alcohol (1-butanol or 1pentanol)/water systems with both sPC-SAFT-GV and sPCSAFT-JC.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S10, as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +27 21 808-4485. Fax: +27 21 808-2059. E-mail: [email protected]. Present Address †

Sasol Technology, 1 Klasie Havenga Avenue, Sasolburg, 1947, South Africa. 6073

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Notes

Equation of State for Highly Asymmetric and Associating Mixtures. Ind. Eng. Chem. Res. 2003, 42, 1098−1105. (7) Von Solms, N.; Kouskoumvekaki, I. A.; Michelsen, M. L.; Kontogeorgis, G. M. Capabilities, Limitations and Challenges of a Simplified PC-SAFT Equation of State. Fluid Phase Equilib. 2006, 241, 344−353. (8) Grenner, A.; Tsivintzelis, I.; Economou, I. G.; Panayiotou, C.; Kontogeorgis, G. M. Evaluation of the Nonrandom Hydrogen Bonding (NRHB) Theory and the Simplified Perturbed-Chain− Statistical Associating Fluid Theory (sPC-SAFT). 1. Vapor−Liquid Equilibria. Ind. Eng. Chem. Res. 2008, 47, 5636−5650. (9) Jog, P. K.; Chapman, W. G. Application of Wertheim’s Thermodynamic Perturbation Theory to Dipolar Hard Sphere Chains. Mol. Phys. 1999, 97, 307−319. (10) Gross, J.; Vrabec, J. An Equation-of-State Contribution for Polar Components: Dipolar Molecules. AIChE J. 2006, 52, 1194−1204. (11) Karakatsani, E. K.; Spyriouni, T.; Economou, I. G. Extended Statistical Associating Fluid Theory (SAFT) Equations of State for Dipolar Fluids. AIChE J. 2005, 51, 2328−2342. (12) Al-Saifi, N. M.; Hamad, E. Z.; Englezos, P. Prediction of Vapor− Liquid Equilibrium in Water−Alcohol−Hydrocarbon Systems with the Dipolar Perturbed-Chain SAFT Equation of State. Fluid Phase Equilib. 2008, 271, 82−93. (13) Kleiner, M.; Sadowski, G. Modeling of Polar Systems Using PCP-SAFT: An Approach to Account for Induced-Association Interactions. J. Phys. Chem. C 2007, 111, 15544−15553. (14) De Villiers, A. J.; Schwarz, C. E.; Burger, A. J. New Association Scheme for 1-Alcohols in Alcohol/Water Mixtures with sPC-SAFT: The 2C Association Scheme. Ind. Eng. Chem. Res. 2011, 50, 8711− 8725. (15) De Villiers, A. J.; Schwarz, C. E.; Burger, A. J. Improving Vapour−Liquid-Equilibria Predictions for Mixtures with Non-Associating Polar Components Using sPC-SAFT Extended with Two Dipolar Terms. Fluid Phase Equilib. 2011, 305, 174−184. (16) Grenner, A.; Schmelzer, J.; von Solms, N.; Kontogeorgis, G. M. Comparison of Two Association Models (Elliott−Suresh−Donohue and Simplified PC-SAFT) for Complex Phase Equilibria of Hydrocarbon−Water and Amine-Containing Mixtures. Ind. Eng. Chem. Res. 2006, 45, 8170−8179. (17) Errington, J. R.; Boulougouris, G. C.; Economou, I. G.; Panagiotopoulos, A. Z.; Theodorou, D. N. Molecular Simulation of Phase Equilibria for Water−Methane and Water−Ethane Mixtures. J. Phys. Chem. B 1998, 102, 8865−8873. (18) Koh, C. A.; Tanaka, H.; Walsh, J. M.; Gubbins, K. E.; Zollweg, J. A. Thermodynamic and Structural Properties of Methanol−Water Mixtures: Experiment, Theory, and Molecular Simulation. Fluid Phase Equilib. 1993, 83, 51−58. (19) DIPPR 801 Database; Design Institute for Physical Properties, Sponsored by AIChE. (20) Nath, A.; Bender, E. On the Thermodynamics of Associated Solutions. I. An Analytical Method for Determining the Enthalpy and Entropy of Association and Equilibrium Constant for Pure Liquid Substances. Fluid Phase Equilib. 1981, 7, 275−287. (21) Kontogeorgis, G. M.; Tsivintzelis, I.; von Solms, N.; Grenner, A.; Bøgh, D.; Frost, M.; Knage-Rasmussen, A.; Economou, I. G. Use of Monomer Fraction Data in the Parametrization of Association Theories. Fluid Phase Equilib. 2010, 296, 219−229. (22) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman and Co.: San Francisco, CA, 1960. (23) Pena, M. D.; Cheda, D. R. Liquid−Vapor Equilibrium II. Ethanol−n-Heptane System at 40 and 60 Deg. An. Quim. 1970, 66, 737−745. (24) Hiaki, T.; Taniguchi, A.; Tsuji, T.; Hongo, M. Isothermal Vapor−liquid Equilibria of Octane with 1-Butanol, 2-Butanol, or 2Methyl-2-propanol. Fluid Phase Equilib. 1998, 144, 145−155. (25) Wolff, H.; Höppel, H.-E. Die Wasserstoffbrückenassoziation von Methanol in n-Hexan Nach Dampfdruckmessungen. Ber. Bunsenges. Phys. Chem. 1968, 72, 710−721.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is based on the research supported in part by the National Research Foundation of South Africa (Grant specific unique reference number (UID) 83966) and Sasol Technology (Pty) Ltd. The authors acknowledge that opinions, findings, and conclusions or recommendations expressed in any publication generated by the supported research are those of the authors and that the sponsors accept no liability whatsoever in this regard.

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NOMENCLATURE BIP binary interaction parameter EOS equation of state GV Gross and Vrabec polar term Hvap heat of vaporization JC Jog and Chapman polar term kij binary interaction parameter KSE Karakatsani et al. polar term LLE liquid−liquid equilibria m segment number Mw molecular mass (g/mol) np Number of dipolar segments on a chain molecule in the dipolar term of Gross and co-workers np total number of data points in the data set P pressure PC-SAFT perturbed chain statistical association fluid theory Psat saturated vapor pressure SAFT statistical association fluid theory sPC-SAFT simplified perturbed chain statistical association fluid theory T temperature (K) VLE vapor−liquid equilibria VLLE vapor−liquid−liquid equilibria y molar fraction of the vapor phase xp fraction of dipolar segment on a chain molecule %AAD percentage average absolute deviation εAB/k association energy value (K) ε/k dispersion energy parameter (K) μ dipole moment (D) ρ molar density ρsat saturated molar density σ segment number (Å)

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