Phase Equilibria and Excess Properties of Short-Alkane Mixtures

Article pubs.acs.org/jced

Phase Equilibria and Excess Properties of Short-Alkane Mixtures Estimated Using the SAFT-VR Equation of State Manuel M. Piñeiro,*,† Felipe J. Blas,‡ and María Carolina dos Ramos∥ †

Departamento de Física Aplicada, Universidade de Vigo, E36310, Vigo, Spain Departamento de Física Aplicada and Centro de Investigación de Física Teórica y Matemática FIMAT, Universidad de Huelva, E21071, Huelva, Spain ∥ Department of Chemical and Biomolecular Engineering Department, Vanderbilt University, Nashville, Tennessee 37235, United States ‡

ABSTRACT: Excess thermodynamic properties constitute excellent and valuable experimental information for determining if a theory or molecular model is able to predict the solution thermodynamic behavior of a given fluid mixture. Phase equilibrium, which is often used to test the applicability of a formalism in this context, does not always constitute a strong enough test to determine if the model or theory provides a sufficiently realistic description of the global thermodynamic behavior of the system. In this work we use a version of the statistical associating fluid theory (SAFT) to show how a simple model of alkanes, with a reduced number of molecular parameters, is able to predict simultaneously the general trends of phase equilibria and excess properties of mixtures of short n-alkanes. Despite the fact that alkane molecular models are simple, they are able to describe most of the features of phase and excess behavior of the mixtures considered. Theoretical predictions, at different thermodynamic conditions, are compared with experimental data taken from literature. Agreement between both results is at least qualitatively correct for a wide range of conditions, although deviations increase at higher temperatures and when pure compound critical points are approached.

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INTRODUCTION The estimation of complex fluid phase equilibrium has been one of the main objectives of the development and application of condensed matter theoretical descriptions, including thermodynamic models, equations of state (EoS), or molecular simulation techniques. An evident reason for this is the importance of the industrial applications where phase equilibrium is involved and plays a key role. Accordingly, the estimation of the various types known of phase equilibria has been a primary target and has constituted a motivation and guide to improve fluid state descriptions. Nevertheless, there are many other potential estimation objectives that are very insightful when describing the behavior of complex solutions of fluids. One of them is the complete set of excess properties, that account for the solution deviation from ideal behavior. From a theoretical perspective, excess properties often present subtle trends that are the result of the addition of several molecular scale effects, including the balance of energetic effects due to the type and intensity of the intermolecular interactions present within the fluid, and also structural effects as steric hindrance, creation or disruption of order, incomplete or partial mixing, etc. Thus, despite the fact that the calculation of excess properties is rather straightforward using, for instance, any EoS, the quantitative accuracy of the estimations is usually poor for the difficulty of accounting for the combination of effects involved. In this sense, the estimation of excess properties is a © 2014 American Chemical Society

demanding test for any thermodynamic model and can be used as benchmark and discriminatory tests in many cases. In addition, there is a large body of experimental data of multicomponent solution excess properties, as this has been an extremely active field of research during the last few decades. This fact allows establishing a comparison with experimental data, which in many cases are determined with great accuracy. The most usual laboratory conditions in the determination of fluid solution thermophysical properties are constant temperature and pressure, corresponding to the statistical isothermal− isobaric (or NPT) ensemble. The thermodynamic potential for this ensemble is the Gibbs free energy (G), and thus the excess properties related1,2 are excess Gibbs free energy, GE, entropy, SE, heat capacity, CEP, volume, VE, and enthalpy, HE. The last two of them are easily accessible from an experimental point of view using different standard volumetric or calorimetric techniques, which has caused that the available bibliography is very wide. From a theoretical perspective, among the plethora of EoS that have been developed to describe fluid state, one of the Special Issue: Modeling and Simulation of Real Systems Received: March 15, 2014 Accepted: July 8, 2014 Published: July 16, 2014 3242

dx.doi.org/10.1021/je500253h | J. Chem. Eng. Data 2014, 59, 3242−3249

Journal of Chemical & Engineering Data

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produced worse results for excess enthalpies, and a further correction accounting also for intramolecular effects was presented to solve this inconvenient. dos Ramos and Blas22 estimated excess volume and enthalpy of alkane solutions using soft-SAFT. While the trend of the first property with chain length and temperature was adequately described, again an explicit account of intermolecular interactions had to be included to describe properly the positive excess enthalpies at low temperatures, an experimentally demonstrated trend attributed to molecular conformational effects. With a slightly different approach, Blas et al.23 used SAFT-VR to describe phase equilibria and excess properties of solutions of short chain alkanes and compared the estimated excess properties with Monte Carlo simulations. The mixtures of almost symmetric mixtures of alike short chain alkanes present very small excess volume and enthalpy, but despite this the agreement between SAFT-VR estimation trends and experimental data was qualitatively correct and showed good correspondence with the united atom approach used for the Monte Carlo simulations. This work deals also with linear alkane mixtures, extending the previous calculations to estimate simultaneously phase equilibria and excess volume and enthalpy of mixtures of alkanes up to butane.

currently most widely used approaches is the so-called SAFT (statistical associating fluid theory) molecular model family of EoS. This theory is based on the first-order thermodynamic perturbation theory (TPT1), in the implementation proposed by Wertheim,3−6 intended to describe the thermodynamic properties of associating fluids. On this common basis, several different SAFT versions have been developed, all of them sharing some common features. In all cases the fluid Helmholtz potential is computed as the addition of a hard sphere monomer reference term, plus a monomer perturbation potential (square well, Lennard−Jones, etc.), a chain formation reference contribution, and an associating perturbation term (for systems with specific interactions, i.e., hydrogen bonding, reactive systems, etc.) This modular conception allows the inclusion of further terms accounting for additional effects, as Coulombic interactions, dipolar or higher order multipolar terms, etc. The original SAFT EoS was proposed by Chapman et al.7,8 and has been later extended and used to predict phase behavior and other thermodynamic properties of a wide variety of complex fluids. A number of different versions of SAFT have been developed during the last two decades, including softSAFT,9,10 SAFT-VR,11,12 or PC-SAFT,13 among others. Several reviews have been ever since devoted to the detailed analysis of the SAFT approach and its applications.14−18 In this context, the homologous series of linear alkanes represent an interesting case study. From a practical perspective, they are a basic building block in the composition of a wide range of oil derivatives, and they are present in many industrial applications, so they have been intensively studied from an experimental point of view. From a molecular modeling perspective, alkanes are often represented as flexible chains of monomers, each of them consisting in a single interacting unit representing a group of atoms. These representations may be either homo or heteronuclear depending on the degree of detail of the model, but in most cases the inter- and intramolecular interactions are purely dispersive and can be accounted for with acceptable accuracy using potentials as the square well (SW) or Lennard−Jones (LJ) expressions. The alkane molecules can be regarded then as weakly interacting, and so the alkane solutions present low deviations from ideality, which result in small absolute value excess properties, with a strong influence of structural microscopic effects. This situation, dominated by subtle effects, is poorly described by many molecular theories, and despite their sometimes vanishingly small excess properties, an even qualitative estimation is a demanding test. The fact that SAFT theory considers molecules as chains of segments fits fairly well the structure of this family, and although no associative effects are present the influence of variables as chain length, the monomer size and energetic interaction are welldescribed by the theory, so the estimation of excess properties of dispersive interacting chain molecules results in an interesting discussion. There are a few studies in literature concerning SAFT description of excess properties of dispersive chainlike molecules. Blas19 described the excess properties of binary LJ chains mixtures using soft-SAFT, studying the influence of segment size, dispersive energy, and chain length on excess volume and enthalpy. Vega et al.20,21 proposed an alkane molecular model based on mean field perturbation theory, following the Wertheim methodology, and estimated their excess properties. The authors found quantitative agreement for excess volumes and Gibbs potential, but the fact that the theory originally neglected conformational changes

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COMPUTATIONAL METHODS The theoretical approach used is SAFT-VR, as used previously by different authors,11,12,24 where alkanes are considered as fully flexible homonuclear chains of mi tangentially bonded hardsphere segments of diameter σii. Attractive interactions between segments i and j of either the same or different molecule are described using a square-well (SW) potential, ⎧+∞ if rij < σij ⎪ ⎪ uij(rij) = ⎨−ϵij if σij ≤ rij ≤ λijσij ⎪ ⎪0 if rij > λijσij ⎩

(1)

where rij is the distance between segments, σij is the contact distance between segment type i and segment type j, and λij and ϵij are the range and depth of the potential well for the i−j interaction, respectively. The original version of SAFT-VR11,12 EoS is used in this case. As other SAFT versions, the SAFT-VR approach needs a number of molecular parameters to describe the thermodynamic properties of real substances. In this work, each alkane molecule is characterized by four molecular parameters: the segment size (σii), the square-well dispersive energy parameter (ϵii), the range of the attractive interactions (λii), and the chain length (m1 or m2). We have used the model parameters for the n-alkanes as proposed by McCabe and Jackson.24 In addition to that, we have used the simple empirical relationship proposed previously in literature,25,26 which relates the number of spherical segments in the model chain to the number of carbon atoms C in the alkanes, m = (1/3)(C − 1) + 1. A number of cross or unlike parameters need to be specified as well. The usual Lorentz−Berthelot combining rules are considered for the segment diameter and potential well depth, σii + σjj σij = (2) 2 ϵij = (ϵiiϵjj)1/2 3243

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behavior at all temperatures except the highest one (199.93 K). This is the expected behavior since the critical temperature of pure methane is below the latest value, Tc = 190.6 K. The theoretical estimations obtained from the SAFT-VR approach are able to provide a very accurate description of the phase behavior of this binary mixture. This is not strange since the mixture is symmetric, as previously mentioned, and simple enough to be described by an EoS. Note that SAFT-VR calculations are predictions from molecular parameters of pure components since no further fitting has been used to calculate the properties of the mixture. Although the theory is able to provide an excellent description of the phase equilibrium of the methane (1) + ethane (2) mixture, SAFT-VR predicts wrongly subcritical behavior for the system at T = 199.93 K, in contrast with experimental data. This is due to the overestimation of the critical temperature of pure methane since SAFT is an analytical EoS that predicts a classical (mean-field) critical behavior. We now consider the effect of increasing the asymmetry of the mixture, i.e., increasing the number of carbon atoms of the less volatile component. Figure 2 shows the Px slice of the

while the unlike range parameter of the mixtures is obtained as λij =

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λiiσii + λjjσjj σii + σjj

(4)

RESULTS AND DISCUSSION We use the SAFT-VR approach presented in the previous section to predict the thermodynamic behavior of binary mixtures of short linear alkanes. In particular, we first consider the phase equilibria of six different mixtures involving methane, ethane, propane, and n-butane, in a wide range of temperatures and/or pressures. After considering the phase equilibrium of mixtures of methane with the next members of the n-alkane series, the mixtures including ethane, propane, and n-butane were analyzed. Once we have checked that the theoretical approach is able to account for the phase behavior of these simple mixtures, we apply the theory to estimation of excess volumes and enthalpies. Contrarily to phase equilibrium, whose estimation is generally accessible with any equation of state, especially in the case of mixtures with components of similar sizes and interaction energies, excess properties are more sensitive than phase equilibrium to molecular details, as their contribution to the thermodynamic potential arises from intermolecular interactions.1 The prediction of excess properties provides an excellent way to check if theoretical approaches are suitable for describing accurately the behavior of a given system. Phase Equilibrium. We first analyze the phase behavior of the simplest binary mixture of short alkanes, i.e., the methane (1) + ethane (2) system. As it is well-known, this mixture is symmetric, and both components have a similar molecular size and comparable intermolecular dispersive interactions. Under these conditions, the system only exhibits vapor−liquid phase separation at temperatures and pressures located between the vapor pressures of pure components and the continuous gas− liquid critical line running from the critical point of one component to the other. In other words, the mixture exhibits type I phase behavior according to the Scott and van Konynenburg27 classification, with the absence of liquid−liquid immiscibility. Figure 1 shows the Px slice of the phase diagram of the mixture at several temperatures, from 130 K to 199 K, approximately. As can be seen, the system exhibits subcritical

Figure 2. Pxy projection of the phase diagram for the methane (1) + propane (2) binary mixture. The symbols represent experimental data by Reamer et al.29 at 277.59 K (diamonds), 294.26 K (circles), 310.93 K (squares), 327.59 K (triangles up), 344.26 K (triangles down), and 360.93 K (crosses). Solid lines represent in each case SAFT-VR estimations.

phase diagram of the methane (1) + propane (2) binary mixture. As in the case of the previous system, it is still very symmetric (both components have similar molecular size and dispersive interaction energies), and hence it also exhibits type I phase behavior. We have analyzed the phase behavior at several temperatures, from 277 K to 360 K, approximately. Since the critical temperature of the most volatile component (methane) is well below the lowest temperature considered, and the critical temperature of propane is above 360 K (its critical temperature is 370 K, approximately), the Px slices of the system exhibit the shape corresponding to a mixture in which one of the components is supercritical (methane). The theoretical predictions from the SAFT-VR formalism are, in general, in good agreement with experimental data. This is especially true, at a given temperature, in the low pressure region, close to the vapor phase. Differences between theoretical predictions and experimental data increase with temperature, or in other words, when the temperature is close to the critical temperature of the mixture and the critical temperature of propane. As we have explained in the case of the previous mixture, this is a consequence of the analytical nature of a classical EoS as

Figure 1. Pxy projection of the phase diagram for the methane (1) + ethane (2) binary mixture. The symbols represent experimental data by Gomes de Azevedo and Calado et al.28 at 130.37 K (diamonds), 144.26 K (circles), 158.15 K (squares), 172.04 K (triangles up), 186.09 K (triangles down), and 199.93 K (crosses). Solid lines represent in each case SAFT-VR estimations. 3244



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chosen these mixtures because the main goal of this work is to show how that although is it relatively easy to predict the phase equilibria of simple mixtures of molecular systems (that exhibit the simplest phase behavior according to the classification of Scott and Konynenburg, i.e., type I behavior), it is difficult to predict with the same level of accuracy the excess thermodynamic properties of these mixtures. We turn now on the analysis of the phase diagram of the ethane (1) + propane (2) binary mixture. Figure 4 shows the

SAFT. It is important, however, to take into account that our theoretical results are predictions obtained only from molecular parameters of pure components, according to the combining rules described in the previous section. Obviously, it is possible to obtain a better agreement between theoretical results and experimental data using an adjustable unlike molecular parameter through any of the many existing combining rules, where adjustable parameters on mixing are fitted to provide the best quantitative description of the experimental data, but this is not the goal of this work. One of the strongest point of molecular theories, and this is particularly true in the case of SAFT, is their ability to predict mixture properties with input of limited experimental information, if any, as well as the use of the same molecular parameters in a transferable manner for the study of different mixtures. We have further increased the asymmetry of the system considering the phase behavior of the methane (1) + n-butane (2) mixture. As in the case of the two systems previously studied, this mixture also exhibits type I phase behavior. Figure 3 shows the Px slices of this mixture at several temperatures,

Figure 3. Pxy projection of the phase diagram for the methane (1) + butane (2) binary mixture. The symbols represent experimental data by Elliot et al.30 at 155.38 K (diamonds), 177.62 K (circles), 190.58 K (squares), 210.94 K (triangles up), 233.18 K (triangles down), 255.38 K (crosses), and 277.59 K (stars). Solid lines represent in each case SAFT-VR estimations.

Figure 4. (a) Pxy projection of the phase diagram for the ethane (1) + propane (2) binary mixture. The symbols represent experimental data by Blanc and Setier31 at 195 K (diamonds), 210 K (circles), 225 K (squares), 235 K (triangles up), 245 K (triangles down), 255 K (crosses), and 270 K (stars). Solid lines represent in each case SAFTVR estimations. (b) Txy projection at 0.101 MPa, experimental data by Watanabe et al.32 (diamonds), and SAFT-VR estimations (solid line).

from 155 K to 277 K, approximately. The three lowest temperatures are below the critical temperature of pure methane, and the rest of them are above. As can be seen, the predictions from the theory are able to provide a good agreement with experimental literature data, especially at the lowest temperatures, where the mixture does not exhibit a critical point. Agreement between theory and experiment is worse at the highest temperatures and pressures region, corresponding to the liquid phase. Critical points, at temperatures at which the methane is supercritical, are overestimated as expected since the theory does not take explicitly into account fluctuations of the system near the critical region. Once we have studied the phase equilibria of mixtures of methane with the next members of the n-alkane series, we consider the three mixtures with ethane, propane, and n-butane. Note that all the mixtures studied in this work, included the three previously analyzed, and the ethane (1) + propane (2) and + n-butane (2), and propane (1) + n-butane (2) systems exhibit type I phase behavior, i.e., only vapor−liquid exists in the region between the critical temperatures of the components of the mixtures (no liquid−liquid immiscibility is present in these mixtures). This selection is not accidental. We have

Px slice (4a), at several temperatures from 190 K to 270 K, and the Tx slice (4b), at atmospheric pressure. Since the range of temperatures considered are between the critical temperatures of both components (critical temperatures of ethane and propane are 305 K and 370 K, approximately), the Px and Tx slices at these conditions do not show critical points. As can be seen in both parts of the figure, theoretical estimations obtained from SAFT-VR are able to provide a good description of the phase behavior of the mixtures in the whole range of temperatures and pressures considered. The ethane (1) + n-butane (2) binary mixture, a similar system but with a slightly higher degree of asymmetry (the differences in chain length or number of chemical groups between both components is greater than in the previous case), is now studied. As in the former mixture, we consider both Px and Tx slices at different temperatures (from 273 K and 323 K, approximately) and pressures from 0.689 MPa to 5.516 MPa). Figure 5a shows the Px slice of the phase diagram. Unfortunately, only the compositions of the mixtures along 3245



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Figure 6. Txy projection of the phase diagram for the propane (1) + butane (2) binary mixture. The symbols represent experimental data by Watanabe et al.32 at 0.1 MPa, and solid lines represent SAFT-VR estimations.

Excess Thermodynamic Properties. We first consider the excess enthalpy of the methane (1) + propane (2) binary mixture at atmospheric pressure and different temperatures, from 243 K to 273 K, approximately. As can be seen in Figure 7, excess enthalpies are positive, nearly quadratic, and

Figure 5. (a) Pxy projection of the phase diagram for the ethane (1) + butane (2) binary mixture. The symbols represent experimental data by Kaminishi et al.33 at 273.15 K (diamonds), 283.15 K (circles), 293.15 K (squares), 303.15 K (triangles up), 313.15 K (triangles down), and 323.15 K (crosses). Solid lines represent in each case SAFT-VR estimations. (b) Txy projection experimental data by Kay34 at 0.689 MPa (diamonds), 1.379 MPa (circles), 2.068 MPa (squares), 2.758 MPa (triangles up), 3.447 MPa (triangles down), 4.137 MPa (crosses), 4.826 MPa (stars), and 5.516 MPa (X). Solid lines represent in each case SAFT-VR estimations.

the liquid phase are available in literature. As can be seen, the SAFT-VR formalism is able to provide an excellent description of the phase equilibrium at all thermodynamic conditions. We have also compared the experimental data from the literature with the theoretical predictions as obtained from SAFT. As can be seen in Figure 5b, the theory is able to describe very accurately the phase equilibria (both liquid and vapor phases), especially at low pressures. Unfortunately, as pressure increases, particularly at pressures equal or higher than 4.137 MPa, the predictions are not so accurate as they are at low pressures. This disagreement between theory and experiment is expected since the ethane (1) + n-butane (2) mixture, according to the experimental data from the literature, exhibits critical behavior at these conditions (pressures higher or equal than 4.137 K). As it has been previously mentioned, the behavior of the mixture is dominated by fluctuations that occur near the critical region, which cannot be predicted correctly by analytical equations of state. Finally, Figure 6 shows the Tx slice of the phase diagram of the propane (1) + n-butane (2) binary mixture at atmospheric pressures. As shown, theoretical predictions are able to provide a relatively good description of the compositions of both phases. Agreement between theory and experiment is better along the liquid side than the vapor side of the phase diagram. Also, the best description of the experimental data is obtained at low temperatures.

Figure 7. Excess molar enthalpies (HE, kJ·mol−1) for the methane (1) + propane (2) binary mixture. Symbols represent experimental data by Hutchings et al.,35 and lines represent SAFT-VR estimations, at 243.20 K (diamonds and solid line), 253.20 K (circles and dotted line), 263.60 K (squares and dashed line), and 273.20 K (triangles and dash−dot line).

approximately symmetric. The low excess heat values corresponding to this mixture become smaller as the temperature is increased. Agreement between theoretical predictions from the SAFT-VR formalism and experimental data taken from literature is only qualitative since the theory underestimates the experimental values. However, SAFT is able to account correctly for the trend displayed by the excess heat as a function of temperature. It is important to take into account two important aspects when comparing theoretical predictions of excess properties with experiments. First, excess properties are, in general, remarkably sensitive to molecular details. In addition, their absolute values are often very small. This makes their description much more difficult than other thermodynamic properties, including phase equilibrium. Second, one should take into account that although the SAFT-VR is only able to describe the behavior of the excess enthalpy in a qualitative 3246



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way, SAFT results have been obtained using only molecular parameters without any further fitting. In particular, the same set of parameters are able to provide a good estimate of both phase equilibria and excess properties. We now analyze the effect of increasing the molecular weight of one of the components in the previous mixture, the less volatile one, on the excess enthalpy at several temperatures. Figure 8 shows the excess heat of the methane (1) + n-butane

Figure 8. Excess molar enthalpies (HE, kJ·mol−1) for the methane (1) + butane (2) binary mixture. Symbols represent experimental data by Hutchings et al.,35 and lines represent SAFT-VR estimations, at 284.20 K (diamonds and solid line), 303.20 K (circles and dotted line), 328.70 K (squares and dashed line), 373.40 K (triangles up and dash− dot line), and 383.20 K (triangles down and dash−dot−dot line).

Figure 9. (a) Excess molar volumes (VE, cm3·mol−1), and excess molar enthalpies (HE, kJ·mol−1) for the ethane (1) + propane (2) binary mixture. Symbols represent experimental data by Ott et al.,36 and lines represent SAFT-VR estimations, at 363.15 K and 5.0 MPa (diamonds and solid line), 10.0 MPa (circles and dotted line), and 15.0 MPa (squares and dashed line).

(2) binary mixture at atmospheric pressure and temperatures from 284 K to 383 K, approximately. Unfortunately, the temperatures at which experimental data are available are not exactly the same as those corresponding to the previous mixture (methane (1) + propane (2)). The behavior of the excess enthalpy, as a function of composition of the more volatile component, is similar to that of methane (1) + propane (2) system: positive values at the whole range of compositions and nearly quadratic shape. In this case, excess enthalpy values are slightly higher than those corresponding to the previous mixture. This is an expected behavior since the asymmetry of the mixture increases. In particular, and although temperatures are not strictly the same, the maximum value of excess heat of the methane (1) + propane (2) system at 273 K is 0.018 kJ· mol−1, which is lower than the maximum value reached by the excess enthalpy of the methane (1) + n-butane (2) system at 284 K, around 0.045 kJ·mol−1 approximately. As in the previous case, agreement between theoretical predictions and experimental data taken from the literature is only qualitative since SAFT underestimates the excess values in the whole range of compositions. As shown, agreement between both results is better at higher temperatures. We now turn on to study the excess volume and enthalpy of the ethane (1) + propane (2) binary mixture. The excess behavior of this mixture is probably the richest considered in this work since both excess volume and enthalpy curves, as functions of composition, exhibit different shapes as pressure changes. Figure 9a shows the excess volume and Figure 9b the excess enthalpy of the mixture at 363.15 K and different pressures, from 5 MPa to 15 MPa. Both properties are negative and exhibit low absolute values at high pressures (10 MPa and 15 MPa). However, both curves exhibit interesting sigmoidal

shapes, as functions of composition, with discontinuous jumps indicated by straight lines, at the lowest pressure considered (5 MPa). The discontinuities are consequence of the vapor−liquid phase transition from the liquid to the vapor side of the phase envelope at this temperature and pressure. As mentioned before in this section, if we take into account the scenario at which these properties are calculated from the SAFT-VR formalism, although agreement between theory and experiment is only qualitative, the estimations from SAFT are remarkable. Finally, we consider the excess heat of the ethane (1) + nbutane (2) binary mixture at atmospheric pressure and at a range of temperatures running from 300 K to 363 K, approximately. As plotted in Figure 10, the excess enthalpy exhibits a similar behavior than previous systems. It is interesting to note that, although excess heat is again positive and nearly quadratic, the absolute magnitudes of the excess heat seem to be reduced with respect to the values corresponding to the methane (1) + n-butane (2) system shown in Figure 6. For instance, the maximum value of the excess heat of the methane (1) + n-butane (2) system, at 303 K, is approximately 0.04 kJ· mol−1, which is approximately twice the maximum value of the ethane (1) + n-butane (2) mixtures at nearly the same temperature (see Figures 6 and 10 for further details). Theoretical predictions from SAFT-VR are only qualitative and underestimate the experimental data taken from the literature, although they are able to predict qualitatively the behavior of the excess values as temperature changes. 3247



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any refitting intended to improve estimations has been done in this particular case. All these facts underline the ability of the SAFT-VR model to describe excess properties, even in cases a priori unfavorable as this one, providing a link between the excess thermodynamic magnitudes and the structure details of the microscopic molecular model. A comparison with molecular simulation estimations for the same molecular models can be meaningful as future work in this case, as well as an evaluation of the SAFT estimation performance concerning the complex effects induced by the presence of molecular association in the trends of fluid mixture excess magnitudes.

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AUTHOR INFORMATION

Corresponding Author

Figure 10. Excess molar enthalpies (HE, kJ·mol−1) for the ethane (1) + butane (2) binary mixture. Symbols represent experimental data by Wormald et al.,37 and lines represent SAFT-VR estimations, at 304.5 K (diamonds and solid line), 333.2 K (circles and dotted line), and 363.2 K (squares and dashed line).

*E-mail: [email protected]. Funding

We acknowledge financial support from project number FIS2011-13119-E, Red de Simulación Molecular (RdSiMol) of Subprograma de Acciones Complementaria del Ministerio de Ciencia e Innovación. F.J.B. acknowledges financial support from projects FIS2010-14866 and FIS2013-46920-C2-1-P, and M.M.P. from project FIS2012-33621 (this one cofinanced with EU FEDER funds), both from Ministerio de Economiá y Competitividad (Spain). Additional support from Universidad de Huelva and Junta de Andaluciá is also acknowledged.

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CONCLUSIONS The simultaneous estimation of phase equilibrium and excess properties (volume and enthalpy) of mixtures of short alkanes, up to n-butane, has been discussed using the SAFT-VR molecular EoS. Alkanes are described in the framework of this model as fully flexible homonuclear chains interacting through dispersive interactions. With this description, light alkanes are very similar to each other, the intermolecular interactions are weak, and in this situation their solutions are nearly ideal, and the estimation of their vanishingly small excess properties is a good benchmark for any thermodynamic model. The phase equilibria and excess properties of the mixtures studied have been estimated using only the alkane molecular characteristic parameters determined previously in literature, without considering any mixing rule parameter, trying to evaluate the performance and transferability of the pure molecule parameters. All mixtures studied show type I phase behavior, and the experimental data are reproduced with acceptable accuracy by SAFT-VR, taking into account the expected shift in the overestimation of the mixture critical line, as the original version of the EoS has been used without considering any additional treatment for the critical region. As a rule, the liquid side of the phase diagrams is estimated with less accuracy. Nevertheless, the overall representation of the phase equilibrium of this type of mixtures is satisfactory. We use the same scheme and molecular parameters to estimate excess volume and enthalpy, in the conditions where experimental data are available. Agreement between theory and experiment is qualitative in the case of enthalpy, while excess volumes are represented with higher accuracy. Estimations loose accuracy at higher temperatures, a fact that could have been also expected a priori. Nevertheless, these results have to be highlighted for several reasons. First, as explained the solutions are nearly ideal, and so excess magnitudes are remarkably small as mixtures containing almost identical molecules are considered. Despite this, the trends with temperature, pressure, and chain length are well-captured. This last in particular means that structural effects are to some extent accounted for even by such a simplified molecular model, that is not explicitly considering any conformational effect. In addition, no parameters on mixing are considered, nor

Notes

The authors declare no competing financial interest.

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Phase Equilibria and Excess Properties of Short-Alkane Mixtures

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