Phase Equilibria, Excess Properties, and Henry's Constants of the

15924

J. Phys. Chem. C 2007, 111, 15924-15934

Phase Equilibria, Excess Properties, and Henry’s Constants of the Water + Carbon Dioxide Binary Mixture† Marıá Carolina dos Ramos,‡ Felipe J. Blas,*,‡ and Amparo Galindo§ Departamento de Fı´sica Aplicada, Facultad de Ciencias Experimentales, UniVersidad de HuelVa, 21071 HuelVa, Spain, and Department of Chemical Engineering and Chemical Technology, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom ReceiVed: May 15, 2007; In Final Form: July 9, 2007

The high-pressure phase diagram and other thermodynamic properties of the water + carbon dioxide binary mixture are examined using the SAFT-VR approach. The carbon dioxide molecule is modeled as two spherical segments tangentially bonded. The water molecule is modeled as a spherical segment with four associating sites to represent the hydrogen bonding. Dispersive interactions are modeled using the square-well intermolecular potential. The polar and quadrupolar interactions present in water and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Galindo and Blas (Fluid Phase Equilib. 2002, 194-197, 502; J. Phys. Chem. B 2002, 106, 4503) and Clark et al. (Mol. Phys. 2006, 22-24, 3561) for carbon dioxide and water, respectively. The phase diagram of the mixture exhibits a number of interesting features: type-III phase behavior according to the classification of Scott and Konynenburg, three-phase behavior at low temperatures with its corresponding upper critical end point, a gas-liquid critical line at high temperatures and pressures that continuously changes from gas-liquid to liquid-liquid as the pressure is increased and gas-gas immiscibility of second kind. Only one unlike interaction parameter is fitted to give the best possible representation of the temperature minimum of the gas-liquid critical line of the mixture. This unlike parameter is then used in a transferable manner to study the complete pressure-temperature-composition phase diagram. The phase diagram calculated with SAFT-VR is in excellent agreement with the experimental data taken from the literature in a wide range of thermodynamic conditions. The theory is also able to predict a good qualitative description of the excess molar volume and enthalpy of the mixture as well as the most important features of the Henry’s constants at different temperatures.

I. Introduction In the last few years, the use of supercritical carbon dioxide (CO2) has gained great chemical and industrial interest. The supercritical CO2 is being considered as a substitute solvent for the conventional organic solvents that generally are hazardous and dangerous for health and for the environment.1 In this case, the advantages that CO2 displays against other solvents are the following: relatively nontoxic, nonflammable, relatively inert in most of the processes, very inexpensive, economically profitable, and nonpolluting, it has a greater solvation power, is readily recovered and recycled, and hence the industrial processes are more efficient. There are several areas in which processes are using CO2 as a solvent, including the separation in the food industry, coatings, polymer production, and drycleaning.2 Other applications and uses of CO2 are of interest within the oil and gas industries. For instance, enhanced oil recovery uses carbon dioxide to inject it in order to extract more crude. Another important field in which an accurate knowledge of the thermodynamic properties for the H2O + CO2 binary mixtures is essential is found in geochemistry and environmental technology because of the increasing concern to reduce the †

Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. E-mail: [email protected]. ‡ Universidad de Huelva. § Imperial College London.

amount of carbon dioxide in the atmosphere by storing it in geological formations. The methods to dispose the CO2 are under examination. The storage of carbon dioxide by means of sequestering it into depleted hydrocarbon reservoirs, by injecting it into saline aquifers, or using industrial fixation into inorganic carbonate are being considered.3-5 Unfortunately, CO2 is a low-dielectric-constant fluid, and, consequently, a relatively poor solvent of many polar and organic compounds, including water. Experimental data from different sources, including analysis of rocks and minerals, fluid inclusion studies, and laboratory measurements, among others, indicate that aqueous and carbonic fluids (such as CO2, methane, and other components) have played a key role in the genesis of hydrocarbon reservoirs. In addition, most of fluids in these reservoirs contain water + carbon dioxide mixtures. The importance of the water + carbon dioxide mixtures comes not only from a practical point of view but also from a theoretical point of view. Both components are particularly complex to model. Water is one of the most important and complex substances in life. It has a permanent electric dipole moment and can associate with other water molecules and/or other polar substances through hydrogen bonding. Carbon dioxide is a linear molecule, and although it has no electric dipole moment (because its symmetry), it has an important electric quadrupole moment. Although several authors6,7 have suggested possible specific interactions between carbon dioxide molecules and other

10.1021/jp073716q CCC: $37.00 © 2007 American Chemical Society Published on Web 08/24/2007

Water + Carbon Dioxide Binary Mixture polar substances, such as water, there is no clear and definitive evidence of such a specific interaction. It is clear from the previous discussion that it would be desirable to have an accurate description of the thermodynamic behavior of the water + carbon dioxide binary mixture in a wide range of temperatures and pressures. There has been an important number of experimental and modeling studies to determine its thermodynamic properties, including the phase behavior, of the water + carbon dioxide binary mixture. See the excellent reviews of Blencoe and co-workers8,9 for a detailed account of the theoretical approaches undertaken over the last 50 years. From an experimental point of view, most of the interest has been focused on the mutual solubilities, and as a result a large number of experiments have been conducted, as shown in the excellent reviews of Larryn and Akinfiev,10 Spycher et al.,11 and Chapoy et al.12 More recently, the vaporliquid equilibria has been studied by Valtz et al.6 From a theoretical point of view, the binary mixture of carbon dioxide and water exhibit the interesting type-III phase behavior according to the classification of Scott and van Konynenburg.13,14 These types of mixtures exhibit liquid-liquid-vapor (LLV) three-phase coexistence at low temperature, an upper critical end point (UCEP), and two different gas-liquid critical loci, one running from the critical point of the more volatile component (CO2 is this case) to the UCEP of the mixture, and a second one that departs from the other component (in our case H2O) and continues to high pressures turning into a fluidfluid critical line. Some mixtures exhibit the so-called gas-gas immisciblity of the second kind, in which the critical line that departs from the less-volatile component has a negative slope as the pressure increases, passing through a temperature minimum, and then develops a positive slope at higher pressures. Another interesting feature that this mixture presents is the barotropic inversion, in which there is an inversion of density due to the pressure effect.15 Most of the theoretical approaches mainly concern the solubilities,7 hydrates,16 VLE in a small range of temperatures,6 and excess properties.17 Despite of this, there is a little information about the global description of the phase behavior and other properties of such a binary system. In this work, we use the SAFT-VR approach to examine the high-pressure phase behavior, excess functions, and other thermodynamic properties of the water + carbon dioxide binary mixture. We have adjusted only one crossed interaction parameter by fitting the temperature minimum observed in the gas-liquid critical line. We have then used the same parameters to the study other conditions of pressure and temperature as well as other thermodynamic properties. In particular, we investigate the global pressure-temperature-composition (PTx) phase diagram of the mixture. We analyze in detail the “peculiar” behavior of the mutual solubilities of CO2 and H2O. The ability of the theoretical approach is also tested by comparing the calculated excess volume and enthalpy and the infinite-dilution Henry’s constant of the mixture with the corresponding experimental data. This is a very stringent test because excess properties and Henry’s constant are very sensitive to the molecular details of the model. The rest of the paper is organized as follows. We present the molecular model and theory in Section II, where we also highlight the most-relevant features of the molecular parameters used in this work. The results and discussion are presented in Section III; and the conclusions are made in Section IV. II. Molecular Model and Theory The water molecules are modeled based on the four-site model first proposed by Bol18 and Nezbeda et al.19 The

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15925 molecules are modeled as square-well segments of hard-core diameter σ11, with four off-center short-range attractive sites, which mediate the hydrogen-bonding interactions. Two of the sites (of type H) represent the hydrogen atoms in the water molecule, and the other two sites (of type O) represent the lone pairs of electrons of the oxygen atom. The sites are placed at a distance rd/σ11 ) 0.25 from the center of the sphere and have a cutoff range of rc so that an attractive energy, HB, is realized if sites are closer than rc. Only O-H bonding is considered; that is, no H-H or O-O interactions are allowed. The squarewell interaction is characterized by a depth 11 and a range λ11. This model has been used previously in many studies6,20-26 and has been shown to describe the phase behavior of aqueous mixtures accurately. Carbon dioxide is a linear symmetrical molecule with a zero dipole moment but with a large quadrupole moment. Following our previous works,27,28 we model carbon dioxide with a simple united-atom approach in which m2 ) 2 square-well segments of equal hard-core diameter σ22 are bonded tangentially. The square-well segments are further characterized by a depth 22 and range λ22. It is important to note at this point that the models proposed correspond to an effective treatment of the polar and quadrupolar interactions present in water and carbon dioxide via squarewell potentials of variable range. The SAFT approach has been extended in a number of works to incorporate explicit polar interactions (both dipoles and quadrupoles).29-36 These approaches can be very successful in modeling real polar and associating fluids, but they require the addition of polar parameters, such as the molecular dipole or quadrupole moments. These are usually taken from experimental data, if available, although care should be taken to note that the value of the dipole moment is state-dependent. A Boltzmann averaging of the dipole-dipole interaction energy over all orientations leads to an angleaveraged (i.e., angle-independent) free energy varying as the sixth inverse power of intermolecular distance, usually called the Keesom interaction,37 which can be treated as contributing to the overall van der Waals intermolecular interaction. We take this view, and treat orientation-independent polar interactions effectively as dispersion forces using square-well potentials of variable range. As we will show below, the model is perfectly adequate to describe the phase behavior of the compounds of interest, and we reduce the need to add polar parameters. Related to this discussion are also the works of Ji et al.25 and Valtz et al.6 who have considered the use of association-like interactions between CO2 and H2O. Ji et al.25 have modeled carbon dioxide as an associating molecule with three sites to take into account self-association in CO2 and the association of CO2 and H2O molecules. In particular, these authors use the SAFT1 equation, which is directly comparable with the SAFT-VR approach we use in this work. They find the need to incorporate association sites in CO2 and to use temperaturedependent parameters in order to reproduce the phase equilibria of the mixture to the desired accuracy. Valtz et al. also considered incorporating association sites to model CO2, but found that the unlike water-carbon dioxide association energy parameter takes very-small values when fitted, and hence concluded that this was not necessary. In agreement with their work, we find that we can predict the most-important features of the H2O + CO2 phase behavior and other thermodynamic properties without incorporating association sites in the CO2 model and with unlike parameters that are not temperaturedependent. Because the SAFT-VR theory has already been presented in a number of works,38,39 here we give only an overview of the

15926 J. Phys. Chem. C, Vol. 111, No. 43, 2007

dos Ramos et al.

main expressions. The equation is written in terms of the Helmholtz free energy. In the case of mixtures containing both chain-like and hydrogen-bonding molecules, the free energy can be expressed as a sum of four microscopic contributions: an ideal contribution AIDEAL, a monomer term AMONO, which takes into account the attractive and repulsive forces between the segments that form the molecules, a chain contribution ACHAIN, which accounts for the connectivity of the molecules, and an association term AASSOC, which takes into account the contribution to the free energy due to hydrogen-bonding interactions. The Helmholtz free energy is then written as

A AIDEAL AMONO ACHAIN AASSOC ) + + + NkBT NkBT NkBT NkBT NkBT

A

n

)

NkBT

xi ln(FiΛi3) - 1 ∑ i)1

A1 A2 A A ) + + NkBT NkBT NkBT NkBT

(3)

NkBT

n

)-

xi(mi - 1) ln ySW ∑ ii (σii) ) i)1 -x2(m2 - 1) ln ySW 22 (σ22) (4) -ii/kBT. gSW ii (σii)e

where ) The contact pair radial distribution function for a mixture of square-well molecules corresponding to the i-i interaction, gSW ii (σii), is obtained from the high-temperature expansion.41-43 Further details can be found in refs 38 and 39. The contribution to the free energy due to the association of si sites on molecules of species i is obtained from the theory of Wertheim47-50 as ySW ii (σii)

AASSOC NkBT

n

)

) ]

(6)

where the fraction of water molecules not bound is given by the mass action equation.51,52 For a general site a in molecule i it can be written as

1

Xa,i )

n

1+

sj

(7)

∑ ∑ Fxj Xb,j ∆a,b,i,j j)1 b)1

and in the case of only water-water bonding the mass action equation is simply given by

X)

1 1 + 2Fx1∆

(8)

The function ∆a,b,i,j characterizes the association between the site a on a molecule i and the site b on a molecule j. This can be written in general as38,39

∆a,b,i,j ) Ka,b,i,j Fa,b,i,jgSW ij (σij)

(9)

HS

where the residual free energy of the reference hard sphere fluid AHS/NkT is calculated using the expression of Boublı´k and Mansoori et al.44,45 A1/NkT corresponds to the mean attractive energy of the mixture and is obtained in the context of the M1Xb mixing rules.38,39 The second-order fluctuation term A2/NkT is calculated using the local compressiblity approximation. Details of each of these terms and of the mixing rules can be found in the original works.38,39 The chain contribution to the free energy of a mixture of chain model molecules formed by square-well segments can be written as21,39,46

ACHAIN

[(

(2)

where Fi ) Ni/V is the number density, xi is the molar fraction, and Λi is the thermal de Broglie wavelength of species i. The contribution to the free energy due to the monomermonomer interactions is obtained as a high-temperature perturbation expansion up to second order41-43 mono

AASSOC X ) x1 4 ln X - + 2 NkBT 2

(1)

where N is the total number of molecules, T is the temperature, and kB is the Boltzmann constant. The free energy of the ideal mixture is given by40 IDEAL

equivalent and the subscripts can be dropped; that is, Xa,i ) X. This, together with the absence of water-carbon dioxide association, greatly simplifies the analysis, and the contribution to the free energy due to the water-water association is obtained as

[ ( si

xi ∑ ∑ i)1 a)1

ln Xa,i -

) ]

Xa,i 2

+

si 2

(5)

The first sum is over species i and the second over all si sites of type a on a molecule i. Because there is only one type of hydrogen bond (O-H) for the water molecule, the fractions, X, of water molecules not bound at any of the four sites are

or specifically here as

∆ ) K11F11gSW 11 (σ11)

(10)

Here, the Mayer f-function of the a-b site-site interaction φa,b,i,j is given by Fa,b,i,j ) exp(-φa,b,i,j/kBT) - 1, and Ka,b,i,j is the available volume for bonding.53 Because in the mixture there is only one type of water-water hydrogen bond, the only subscripts remaining indicate that the only association is between the molecules of component 1. The corresponding Mayer f-function is then given by F11 ) exp(HB 11 /kBT) - 1. The rest of the thermodynamic properties, such as the chemical potential µ, compressibility factor Z, and other thermodynamic derivatives needed in our calculations, can be obtained easily from the Helmholtz free energy using standard thermodynamic relations. III. Results In this section, we present the main predictions we have obtained using the SAFT-VR approach to describe different thermodynamic properties of the water + carbon dioxide binary mixture. We aim at understanding the phase behavior, excess thermodynamic properties, and Henry constants of this mixture as well as providing a sound approach to predict the thermodynamic properties of the mixture accurately. The SAFT-VR approach, as other versions of SAFT, requires the determination of the intermolecular parameters of the model to describe the properties of real substances. In particular, each nonassociating substance is characterized by four parameters: a parameter m associated with the molecular aspect ratio or with the number of spherical segments forming the model chain, the hard-core diameter of the segments, σ, and the depth, , and range, λ, of the square well used to model the long-range attractive interactions. In the case of associating compounds, the number and type of bonding (or association) sites, the site cutoff range, rc, for each site and the site-site energy, HB, are

Water + Carbon Dioxide Binary Mixture

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15927

TABLE 1: Optimized and Rescaled Square-Well Intermolecular Potential Parameters for Water26 and Carbon Dioxide27,28 substance

m

σ (Å)

/kB (K)

λ

HB/kB (K)

KHB (Å3)

σc (Å)

c/kB (K)

HB c /kB (K)

3 KHB c (Å )

H2O CO2

1 2

3.033 2.7864

300.4330 179.27

1.718250 1.515727

1336.951

0.893687

3.469657 3.136386

276.2362 168.8419

1229.273

1.337913

further needed to characterize the molecules. Parameter values are obtained by comparison with experimental data, usually vapor pressure and saturated liquid densities. In this work, we use the values published previously both for carbon dioxide27,28 and for water26 (the parameters are also given in Table 1 here for completeness). Both sets of parameters together with the SAFT-VR approach provide a very-good description of the vapor pressures and coexistence densities for a large range of temperatures, with the exception of the near-critical region. This is an expected behavior because SAFT-VR, as any classical equation of state, does not consider the density fluctuations that occur near the critical point. However, because we have an interest in the high-pressure phase equilibria and the critical behavior of the binary mixture, here we used here conformal parameters (σc and c) rescaled to the experimental critical temperature and pressure (see the corresponding values in Table 1). Note that the change in the values of the conformal parameters also results in different values for the nonconformal paramters (λ, Kc, and HB c ) when they are reported in experimental units. The calculation of mixture properties also requires us to know a number of cross or unlike parameters. The arithmetic mean is used for the unlike hard-core diameter

σ12 )

σ11 + σ22 2

MPa) extending to higher pressures, first with a negative slope, through a temperature minimum (540 K and 190 MPa), and then continuing with a positive slope to higher temperatures and pressures. At lower temperatures and pressures, a muchshorter critical line starts at the critical point of pure carbon dioxide (304.21 K and 7.383 MPa) and ends at slightly higher pressures at an upper critical end point (UCEP), where the GL region, richer in CO2, disappears into the region of LL immiscibility. The three-phase line, characteristic of type-III phase behavior, can be seen in the inset of the figure. As can be seen, it runs from very-low temperatures and pressures to the UCEP; it corresponds to pressures and temperatures where the two immiscible liquid phases coexist with a gaseous phase. As can be seen, the theory is able to provide an excellent

(11)

and the unlike square-well range is given by

λ12 )

λ11σ11 + λ22σ22 σ11 + σ22

(12)

The unlike dispersive energy of the system is defined as

12 ) ξ12(1122)1/2

(13)

where ξ12 describes the departure of the system from the geometric mean; it is usually determined by comparison with mixture data and then used to predict properties at different conditions. In this work, we have adjusted ξ12 to give the bestpossible representation of the temperature minimum of the fluid-fluid critical line of the mixture. The value obtained (ξ12 ) 0.9742) is treated as temperature-independent and used to study the complete pressure-temperature-composition (PTx) phase behavior of the mixture in a wide range of conditions. In addition, as we will show later, a number of thermodynamic properties are also predicted using these model parameters without the need for further adjustment. A. High-Pressure Phase Behavior and Critical Phenomena. In this section, we study the phase behavior of the mixture. Using the molecular parameters of the pure components and the unlike mixture parameter mentioned in the previous section, we have obtained the PT projection of the PTx surface for the H2O + CO2 mixture (Figure 1a). As can be seen, the phase behavior of the system is dominated by a large region of liquidliquid (LL) immiscibility. This is a direct consequence of the self-association interaction between water molecules (hydrogen bonding).20 The system shows two separate gas-liquid (GL) critical lines. At high pressures and temperatures, a critical line starts from the critical point of pure water (647 K and 22.03

Figure 1. PT projection of the phase diagram for the water(1) + carbon dioxide(2) binary mixture. The circles correspond to the experimental vapor pressure data of pure water,57-65 the squares correspond to the experimental vapor pressure of pure carbon dioxide,66-71 the stars72 and plusses73 correspond to the experimental gas-liquid critical line, and the triangles correspond to the three-phase line.6 The continuous curves are the SAFT-VR predictions for the vapor pressures, the dashed curves for the critical lines, and the long-dashed curve for the LLV three-phase line. The inset of part a shows the region close to the critical point of pure CO2. Part b shows a larger scale on the P axis of the PT representation, and the inset shows the Tx projection of the gas-liquid critical line of the mixture.

15928 J. Phys. Chem. C, Vol. 111, No. 43, 2007 description of the PT projection of the PTx surface of the phase diagram at low and high temperatures and pressures, including the critical lines and the three-phase line of the mixture. Particularly interesting is the prediction of the type of phase behavior and the existence of the GG immiscibility of second kind, a characteristic directly associated to the presence of a temperature minimum in the gas-liquid critical line running from the less-volatile component to high pressures and temperatures. It is important to note that only one mixture parameter is necessary in order to describe the phase behavior for the entire fluid range. It is also important to mention that the theory is able to predict the existence of GG immiscibility of second kind with ξ12 ) 1, that is, with no correction to the geometric mean for the unlike energy parameter of the mixture, although agreement between theoretical predictions and experimental data is in this case only qualitative. The GL critical line can be seen extended to very high pressures in Figure 1b, where a comparison of the experimental critical compositions and those calculated can also be seen in the inset. We have used a larger scale on the P axis of the PT representation to have a better perspective of the GL critical line of the mixture. Here we can clearly observe not only the temperature minimum of the critical line (∼540 K) but also how this line reaches temperatures above the critical temperature of water at sufficiently high pressures. This is a distinct feature of the phase behavior exhibited by the water + carbon dioxide mixture and an example of the gas-gas immiscibility mentioned in the introduction. As can be seen in the inset of the figure, the theory is also able to provide excellent agreement with the experimental data term of composition as shown in the Tx projection. It is important to note that we have used two different sets of experimental data taken from different references in the literature. Different GL and LL coexistence regions of the phase diagram of the mixture become clearer in constant-temperature Px and constant-pressure Tx slices of the PTx surface. We first concentrate on constant-temperature Px slices at high temperatures. Five Px slices are presented in Figure 2a. The three lowest temperatures, 523, 533, and 538 K, correspond to temperatures below the temperature minimum (540 K, approximately) of the GL critical line (usually also referred to as fluid-fluid critical line), but still above the UCEP of the mixture. At these temperatures, the system exhibits a continuous coexistence region, with GL character at low pressures that changes continuously to LL character at high pressures. The corresponding Px slices are seen to exhibit the peculiar shape characteristic of the LL immiscibility at high pressures in mixtures exhibiting type-III phase behavior. At the two highest temperatures, 543 and 573 K, which correspond to temperatures between the temperature minimum of the GL critical line and the critical point of pure water (647 K, approximately), the system exhibits a GL coexistence region extending from the vapor pressure curve of pure water and ending at the GL critical point of the mixture at the corresponding temperature. It is interesting to note that at this range of temperatures (above the temperature minimum), the Px slices have a second two-phase coexistence region, a fluid-fluid coexistence region at very high pressures. This two-phase region exists even at temperatures above the critical temperature of pure water. This phenomenon is usually referred to as gas-gas immiscibility of the second kind. This two-phase envelope becomes wider as the pressure is increased, and it is bound by a minimum pressure associated to a second fluid-fluid critical point of the mixture at the corresponding temperature. The pressure minimum is seen to

dos Ramos et al.

Figure 2. Px projection of the phase diagram for the water(1) + carbon dioxide(2) binary mixture at high temperatures. Part a shows the Px projection in a larger scale on the P axis, and part b shows the same results on a smaller scale. The symbols represent the experimental data taken from the literature, and the curves are the predictions from SAFT-VR at different temperatures: 523.15 K (circles72 and continuous curve), 533.15 K (squares72 and dotted curve), 538.15 K (diamonds72 and dashed curve), 543.15 K (triangles72 and long-dashed curves), and 573.23 K (crosses72 and dot-dashed curves).

move toward higher pressures and lower compositions of water as the temperature is increased. Figure 2b shows the same constant-temperature Px slice of the phase diagram in a different scale. The theory is able to describe correctly the most important features of the two-phase envelope as the temperature and pressure are varied. In particular, at fixed temperature the theory predicts quantitatively the water composition in the H2O-rich (liquid) phase. In contrast, only a qualitative agreement between theory and experiments is seen in the CO2-rich (gas) phase. As can be seen, the theory overestimates the compositions at which the gas phase is in equilibrium with the liquid phase, although is able to provide a reasonable description of the phase envelope. Agreement between theoretical predictions and experimental data can be considered remarkable if we take into account that only one thermodynamic state, that corresponding to the minimum in temperature of the GL critical line, has been used to fit the unlike parameter ξ12. We now turn our attention to the phase behavior at muchlower temperatures, close to the UCEP of the mixture and the critical point of pure carbon dioxide. In Figure 3a, a constanttemperature Px slice at 298.15 K is shown. Because this temperature is below the UCEP temperature of the mixture, VL equilibria is observed at the lower pressures (below the pressure at which the three-phase coexistence occurs), LLG coexistence at P ≈ 6.3974MPa (the pressure corresponding to the LLG three-phase line at this temperature), and LL immiscibility at high pressures. Although the theory overestimates the water molar fractions along all of the phase envelopes, agreement between experimental data and theoretical predictions is good


J. Phys. Chem. C, Vol. 111, No. 43, 2007 15929

Figure 4. Px projection of the phase diagram for the water(1) + carbon dioxide(2) binary mixture at low temperatures. The symbols correspond to the experimental data taken from the literature, and the curves correspond to the predictions obtained from SAFT-VR at 278.22 K (circles6 and continuous curves), 288.26 K (squares6 and dotted curves), 298.28 K (diamonds6 and dashed curves), 308.20 K (triangles6 and longdashed curves), and 318.23 K (pluses6 and dot-dashed curves).

Figure 3. Px projection of the phase diagram for the water(1) + carbon dioxide(2) binary mixture at temperatures close to the UCEP point. The continuous curves and the open circles are the phase envelopes from SAFT-VR and experimental data taken from the literature, respectively at (a) 298.15 K,74-79 (b) 304.2 K,74,75 and (c) 308.2 K.6,74,76 The solid circles and the dashed lines in a and b represent the LLV three-phase coexistence line. The inset in a shows the vapor-liquid coexistence region above the three-phase pressure at the corresponding temperature.

in terms of pressures. At a temperature of 304.2 K, which is below the UCEP temperature of the mixture but near (and below) the critical temperature of pure CO2 (304 K approximately), the mixture exhibits similar behavior (Figure 3b.) Because the temperature is slightly below the temperature at which LLG coexistence occurs, the system still exhibits VL equilibria at low pressures and LL equilibria at high pressures. At even higher temperatures, 308.2 K, now above the UCEP temperature of the mixture (and also above the critical point of pure carbon dioxide), the system exhibits fluid-fluid coexistence, with VL character at low pressure that changes continuously to LL character as the pressure is increased (Figure 3c). This is the expected behavior when the temperature is increased in systems that exhibit type-III phase behavior. It is interesting to note how the distinctive shape of the phase envelope associated to the CO2-rich fluid phase resembles the corre-

sponding envelope shown previously in Figure 2a and b. As in the previous figures, agreement between theory and experiment is remarkable in all cases. The GL phase behavior in the low-temperature 278.22318.23 K low-pressure (below the three-phase coexistence pressures) region can also be examined in Figure 4. The data and calculations correspond essentially to the solubility of carbon dioxide in the water-rich phase (Figure 4a) and the solubility of water in the carbon dioxide-rich phase (Figure 4b) at low temperatures and pressures. Note that we have only represented the phase behavior at low pressures (below 5MPa) because we are now interested in the GL phase behavior. It is important to remember that for the temperatures considered (below the UCEP temperature of 305 K), the three-phase equilibrium and LL immiscibility must emerge from the phase diagram at higher pressures. To check the accuracy of the theory in predicting the GL phase behavior at these conditions, we have compared the results with experimental data taken from the literature. Although the water content of both the water-rich and the carbon dioxide-rich phases is overpredicted by the theory, considering that only one unlike mixture parameter has been fitted, for a very different set of conditions a surprisingly good agreement with experimental data is found. In addition, the theory is able to provide the correct trends as the temperature and pressure are varied. We have also studied a number of constant-pressure Tx slices of the PTx phase diagram of the mixture. Figure 5 shows the phase envelopes at different pressures, from 20 up to 200 MPa. The lowest pressure, 20 MPa, lies below the critical pressure of pure water. This results in a coexistence with VL character at high temperatures and a region of LL character at low temperatures. At higher pressures (50, 100, 150, and 200 MPa), the differences between the gas and liquid phases are more difficult to identify because the two phases in coexistence are liquids with different densities. To assess the accuracy of the theoretical predictions, we have compared the results from SAFT-VR with experimental data taken from the literature. As can be seen in the figure, the theory is seen to capture the essential features of the phase envelopes in a wide range of pressures. In particular, the theory is able to provide a nearly quantitative description of the envelope in the H2O-rich liquid phase. However, significant deviations from experimental data are seen in the CO2-rich liquid phase, where the theoretical predictions overestimate the coexistence molar fraction of water.


Figure 5. Tx projection of the phase diagram for the water(1) + carbon dioxide(2) binary mixture at high pressures. The symbols correspond to the experimental data taken from the literature, and the curves are the predictions from SAFT-VR at 20 MPa (circles72 and continuous curve), 50 MPa (squares72 and dotted curve), 100 MPa (diamonds72 and dashed curve), 150 MPa (up triangles72 and long-dashed curve), and 200 MPa (right triangles72 and dot-dashed curve).

Before finishing this section dedicated to examine the phase behavior of the water + carbon dioxide mixture, it is interesting to study in detail the mutual solubilities of water and carbon dioxide. The experimental data for the phase equilibria of the mixture is usually provided as mutual solubilities of H2O in a CO2-rich gas (or liquid) phase and CO2 in an H2O-rich liquid phase (see the work of Spycher11 and references therein for a detailed revision of the experimental data available in the literature). The solubility curve associated with the H2O in the CO2-rich phase (gas or liquid depending of the thermodynamic conditions), as function of pressure, exhibits a number of different shapes depending on the temperature of the system. The key point for understanding this behavior is to recognize the existence of a LLG three-phase line and its corresponding UCEP at 305.5 K and 7.45 MPa. Thus, different shapes of the solubility curves are expected and observed if the temperature of the mixture is below or above the UCEP temperature of the mixture. If T ) 305.5 K, then the curve associated to the solubility of H2O in CO2-rich phases, as a function of pressure, exhibits a sharp discontinuity at the three-phase coexistence pressure. At low pressures, the solubility is seen to decrease as the pressure is increased. At higher pressures, or more precisely, at pressures above the three-phase coexistence pressure (at the corresponding temperature), the solubility of H2O in CO2-rich phases is seen to increase as the temperature and pressure are increased, as expected. This scenario is exactly the behavior obtained in the corresponding constant-temperature Px slices shown in Figure 3a-c. The apparently “anomalous” discontinuity of the solubility of H2O in the CO2-rich phase is essentially due to the presence of the LLG three-phase line of the mixture. And also related with the same phenomenology, if the temperature of the system is above the UCEP temperature of the mixture, then the solubility curve does not exhibit a discontinuity but shows a minimum at low pressures, which smoothly diminishes as the temperature is increased. The particular pressure value at which the minimum occurs is seen to increase as the temperature is raised. The presence of this minimum in the solubility curve of H2O in the CO2-rich phase is a direct consequence of the type of phase behavior exhibited by the mixture. The solubility of CO2 in the H2O-rich liquid phase also exhibits an interesting behavior because it decreases with rising temperature, but increases sharply with increasing pressure up to the pressure corresponding to the three-phase coexistence, and at a lesser rate thereafter. A discontinuity in the slope exists for the CO2 solubility because of the presence of two different

dos Ramos et al. curves, one corresponding to the solubility of CO2 in the H2Orich phase (in coexistence with a CO2-rich vapor phase) and another corresponding to the solubility of CO2 in the H2O-rich phase (in coexistence with a CO2-rich liquid). Above the UCEP temperature, the CO2 solubility is given by one curve (CO2 in the H2O-rich liquid phase), with a curvature that smoothly diminishes as the temperature is increased. To recap, if we follow the phase envelopes corresponding to the H2O-rich (liquid) phase and the CO2-rich (gas and liquid) phase, then we find that the peculiar mutual solubility behavior associated to CO2 and H2O is essentially the scenario observed in the vicinity of the vapor-pressure curve of the more-volatile component (in this case CO2) and the UCEP of a mixture that exhibits type-III phase behavior according to the classification of Scott and Konynenburg. In fact, the discontinuities observed in the solubility of H2O in the CO2-rich phase and in the slope of the solubility of CO2 in the H2O-rich phase is a consequence of crossing the three-phase coexistence line as the pressure is varied. In addition, the existence of a minimum in the solubility of H2O in the CO2-rich phase below the UCEP temperature is a reminiscence of the disappearance of the small GL coexistence region located in the CO2-rich zone of the phase diagram, which is still present at temperatures as high as 538 K, as shown previously in Figure 2a and b. B. Excess Thermodynamic Properties of the Mixture. In this section, we examine two of the most-important excess thermodynamic functions, namely, the excess volume and the excess enthalpy, for the water + carbon dioxide binary mixture. We apply the SAFT-VR approach with the same molecular parameters and the same unlike parameter, ξ12, to predict these two important excess properties without further adjustment. The investigation of excess thermodynamic properties of the mixture, such as excess volume and enthalpy, is useful to assess the validity of our model because it is a very-stringent test of any theory and molecular model. We first consider the excess thermodynamic volume of the mixture at different conditions. The excess volume is one of the most-important functions. It gives, by definition, an idea of the difference between the real molar volume of the mixture and the ideal volume of the mixture, and it is therefore one indicator of the degree of nonideality in the mixing of dissimilar species. Positive values suggest net repulsive interactions between components, and negative values suggest net attractive interactions. The excess molar volume of the mixture is calculated from the theoretically determined molar volumes of the pure fluids (Vi ) and the molar volume of the mixture (Vm) using the standard thermodynamic relationship n

VE ) V m -

xiVi ∑ i)1

(14)

where the index i runs for all of the n components of the mixture. Note that the ideal volume of mixing is zero so that this excess property is also equal to the mixing volume. We study first the excess volume of the mixture at fixed T ) 573.15 K and several pressures ranging from 29.94 up to 99.93 MPa. It is useful to note that the temperature selected is below the critical temperature of pure water (647 K approximately). The two lowest pressures considered, 29.94 and 39.93 MPa, correspond to states below the high temperature gas-liquid critical line, and therefore the system exhibits fluidfluid phase separation at these thermodynamic conditions. The theoretical predictions and experimental data taken from the literature are shown in Figure 6a. As can be seen, at 573.15 K


Figure 6. Excess molar volume for the water(1) + carbon dioxide(2) binary mixture at different pressures. The symbols correspond to the experimental data taken from the literature, and the curves are the predictions from SAFT-VR at: (a) 573.15 K and 29.94 MPa (triangles80 and continuous curve), 39.94.4 MPa (squares81 and dotted curve), 49.93 MPa (diamonds81 and dashed curve), 69.93 MPa (circles81 and thin continuous curve), and 99.93 MPa (crosses81 and dotted curve); (b) 673.15 K and 29.94.4 MPa (circles9 and continuous curve), 34.94 MPa (pluses9 and dash-dash-dotted curve), 39.94 MPa (squares9 and dotted curve), 49.93 MPa (diamonds9 and dashed curve), 59.93 MPa (right triangles9 and dot-dashed curve), 79.93 MPa (left triangles9 and dotdot-dashed curve), and 99.93 MPa (down triangles9 and dot-dashed curve). At T ) 673.15 K and P ) 29.94 MPa, the molar volumes of pure H2O and CO2 are 56.07 and 191.09 cm3/mol, respectively. The theoretical predictions at the same conditions are 74.15 and 223.10 cm3/mol, respectively. The thinner lines in a correspond to the theoretical predictions at the two-phase fluid-fluid phase region.

the excess volume curves exhibit sigmoidal behavior, with V E < 0 for mixtures rich in water and V E > 0 for those rich in carbon dioxide. V E is positive in a wide range of compositions, an expected result because the water + carbon dioxide mixture is highly nonideal due to the specific interactions (extensive hydrogen bonding) between water molecules. This behavior is in agreement with the trends observed by the isobaric density data obtained by Seitz and Blencoe (see Figure 3 of ref 8). At each pressure, the composition range for which positive values of V E are observed is characterized by the existence of a maximum, which is seen to displace toward lower water compositions as the pressure is increased. It is also important to note that the curves at the two-lowest pressures (29.94 and 39.94 K) exhibit discontinuities in the slope of the excess volume. In particular, these discontinuities are located at molar compositions of water x1 ≈ 0.65 (at 29.94 MPa) and x1 ≈ 0.70 (at 39.94 MPa), which correspond to the compositions at which the homogeneous liquid phase disappears. As can be seen in Figure 6a, this means that the system exhibits vapor-liquid (or fluid-fluid) phase separation in the range x1 ≈ 0.65 - 0.94 (at 29.94 MPa) and x1 ≈ 0.70 - 0.97 (at 39.94 MPa). An inspection of the constant-pressure Tx slices of the phase diagram presented in Figure 5 corroborates the behavior observed in the excess

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15931 thermodynamic property (note that these particular pressures are not shown in Figure 5, but one can clearly see that the corresponding phase envelopes should lie between those shown in the figure). We now consider the excess volume of the mixture at higher temperatures. In particular, we study the V E at fixed T ) 673.15 K and several pressures in the same range of pressures previously considered (P ) 29.94 - 99.93 MPa). The selected temperature now lies above the critical temperature of pure water, and the mixture exhibits a homogeneous fluid phase in the whole range of compositions at all of the pressures considered. Figure 6b shows the theoretical predictions and experimental data taken from the literature for the excess volume, as a function of water molar compositions. V E is seen to exhibit positive values at all pressures considered, with a pseudo-quadratic shape. As mentioned previously, positive values are expected because they are identified with an expansion in the system due to weak interactions between the components of the mixture, which is the particular case of the water + carbon dioxide binary mixture. The V E curves show relatively large maximum values at different pressures, with a sharp decrease of V E as the pressure is increased. In terms of shape, the curves are very asymmetric at lower pressures, and become more symmetric as the pressure is increased, with the maximum displaced toward mixture compositions rich in carbon dioxide. In a preliminary study of the thermodynamic properties of the water + carbon dioxide mixture,54 we have predicted the opposite behavior for V E at the same temperature but at lower range of pressures (9.94 - 29.94 MPa). This phenomenon is related to the fact that the highest degree of asymmetry occurs where the maximum values are achieved, at 29.94 MPa, which is very close to the PT condition of the critical isochore for pure water (∼29.2 MPa at 673.15 K). From an experimental point of view, the existence of a maximum in the V E versus pressure curve (at constant composition) has been accurately determined and characterized in the works of Seitz and Blencoe8 and Blencoe and Seitz.9 It is remarkable that the SAFT-VR approach is able to provide an excellent description of a property so sensitive to molecular details as V E. In particular, the theory accounts for the behavior of the excess volume at two different temperatures (in a range of 100 K) and in a wide range of pressures (from relatively low pressures up to high pressures). We should emphasize again that no single additional binary mixture parameter has been adjusted, and although a truly quantitative agreement is not seen, the SAFT-VR equation of state provides an excellent picture of the most-relevant physical features exhibited by the excess volume of the water + carbon dioxide binary mixture. We have also studied the excess enthalpy of the water + carbon dioxide binary mixture at different temperatures and pressures. This excess function is defined in the same way as V E (see eq 14). We first consider the behavior of the excess enthalpy as a function of pressure. In Figure 7a, the excess enthalpy is seen to exhibit a peculiar shape, which is due to the existence of large regions of LL immiscibility in the phase diagram. As can be seen, the excess function is positive in the entire composition range and increases in magnitude as the pressure is decreased. Because all of the curves at different pressures exhibit the same qualitative behavior, we analyze in detail the behavior observed for one of the pressures studied. For the intermediate pressure, P ) 12.4 MPa, the experimental excess enthalpy shows three different regions along the entire range of compositions. In a first region, which goes from x1 ) 0.0 to x1 ≈ 0.416 water compositions, the system exhibits one


Figure 7. Excess molar enthalpies for the water(1) + carbon dioxide(2) binary mixture. The symbols correspond to the experimental data taken from the literature, and the curves are the predictions from SAFT-VR at (a) 523.15 K and 10.4 MPa (circles82 and dotted curve), 12.4 MPa (squares82 and long-dashed curve), and 15.0 MPa (diamonds82 and continuous curve); (b) 12.4 MPa and 498.15 K (circles82 and continuous curve), 523.15 K (squares82 and dotted curve), 548.15 K (diamonds82 and dashed curve), and 573.15 K (diamonds82 and dotdashed curve). The thinner lines and the open symbols correspond to the theoretical predictions and experimental data at the two-phase fluidfluid phase region, respectively.

homogeneous (liquid) phase. Note that the theory overestimates the size in compositions of this region (the theoretical prediction estimates the end of the liquid region at x1 ≈ 0.53). Although the shape of the H E curve appears to be a straight line, the function exhibits a slightly convex shape, ending at the composition corresponding to a two-phase boundary. A second region exists, from x1 ≈ 0.416 to x1 ≈ 0.987, at which the system exhibits two-phase fluid-fluid phase separation. Note that the theoretical predictions underestimate the size of the immiscibility region, as stated in the comment mentioned above. In this case, both the experimental data and the theoretical predictions describe a straight line that connects the values of the excess enthalpy at the coexistence compositions of the two-phase region. Finally, from x1 ≈ 0.987 to x1 ) 1.0, the system again exhibits one homogeneous phase, although in this case correspond to a gas phase. See the inset of the figure, which shows in detail the region close to x1 ) 1.0. In this context, the sharp turning point at molar compositions of water x1 ≈ 0.416 and the change in the slope of the excess enthalpy at molar fractions close to 1, represent the points, in terms of compositions, at which the homogeneous liquid-phase disappears and the gas homogeneous phase appears again as the water composition is increased. This means that for water molar fractions between approximately 0.416 and 0.987, the system is in the VL twophase region. Theoretical predictions are able to provide an excellent description of the excess enthalpy at the three pressures

dos Ramos et al. considered, including the trend observed when the pressure is varied. The theory is seen to underestimate the values of the excess enthalpy at all compositions and to overestimate the range of compositions at which the water + carbon dioxide mixture exhibits a homogeneous liquid phase. This is due to the overestimation of the coexistence molar fraction of water in the CO2-rich liquid phase. It is also interesting to mention that the excess enthalpy (and also the excess volume) of a mixture that exhibits two-phase coexistence can be measured directly from experiments. This is done by measuring the enthalpy exchanged in the measurement cell from the moment at which the second component is added to the first one until the system stabilized (including the stabilization of the two phases and the interface). The data presented correspond to the experimental data taken from the literature with the exact measurement of the enthalpy of the system in this setup. In the case of the theory we have just calculated, the excess enthalpy in the two regions in which the system exhibits one homogeneous phase, and the straight line joins the boundary points of these regions. We have also studied the excess enthalpy of the mixture at different temperatures. As can be seen in Figure 7b, the SAFT-VR approach is able to provide an excellent description of this property in a wide range of temperatures, from approximately 498 to 573 K. Agreement between experimental data and theoretical predictions is excellent at all compositions. The theory not only gives the correct shape of the excess enthalpy but also predicts the expected behavior when the temperature is varied, keeping the rest of thermodynamic variables constant. Unfortunately, the theory is unable to predict quantitatively the molar fraction range at which the mixture is homogeneous. C. Henry’s Law Constants. We now consider the infinitedilution mixture property of the Henry’s law constant of a solute in a solvent. An accurate prediction of this kind of property is difficult to obtain because it is very sensitive to small molecular detail. McCabe et al.55 have shown that the SAFT approach can be used in a predictive way to study this property in aqueous mixtures. This is of special interest because Henry’s law constant can also be straightforwardly related to the free energies of hydration of the solute in the solvent of interest. Here, we use the theory, with the same intermolecular model parameters, including the same binary interaction parameter values, to predict Henry’s constant of carbon dioxide in water under saturated vapor pressure. We compare our theoretical predictions with experimental data taken from the literature as well as with predictions obtained by Lı´sal et al.56 using molecular simulation of different molecular models of water and/or carbon dioxide. These authors use two models for CO2, the Harris and Yung model (EPM2) and the Errington and Panagiotopoulos model (EP-CO2), and five models for water, SPC, SPC/E, the Errington and Panagiotopoulos model (EP-H2O), TIP4P, and TIP5P. As can be seen in Figure 8a, this property exhibits an interesting behavior as a function of temperature: it is an increasing function at low temperatures, and a decreasing function at high temperatures, exhibiting a temperature maximum at approximately 450 K. The equivalent ln H2,1 versus T representation has also been included in Figure 8b. As can be seen from the figures, the simulation data are in qualitative agreement with the experimental values; they predict the correct temperature dependence of the Henry’s constant. With the exception of the EP-H2O + EP-CO2 molecular model used by Lisal et al.56 (see the down triangles in Figure 8a and b), all simulation molecular models predict the maximum of


Figure 8. (a) Henry’s coefficients and (b) ln H2,1 vs T representation for the water(1) + carbon dioxide(2) binary mixture under saturation vapor pressure. The continuous (ξ12 ) 1.0) and dotted (ξ12 ) 0.9742) curves are the predictions from SAFT-VR, and the solid circles are the experimental data taken from the literature.83-85 The rest of symbols correspond to the simulation data results obtained by Lı´sal et al.56 using different models for both substances: open circles (EPM2 and SPC models), up triangles (EPM2 and SPC/E models), diamonds (EPM2 anc MSPC/E models), down triangles (EP-CO2 and EP-H2O models), squares (EPM2 and TIP4P models), and asterisks (EPM2 and TIP5P models). See the work of Lı´sal et al. and the text for the nomenclature used to denote the different models.

the Henry’s constant at temperatures lower (∼400 K) than the one observed experimentally. We have used two different unlike parameter ξ12 values: ξ12 ) 1, which corresponds to the usual geometric mean, and ξ12 ) 0.9742, which is the value obtained previously by fitting the theoretical results to the temperature minimum of the gas-liquid critical line of the mixture. As can be seen, both values overestimate Henry’s constant at low temperatures and underestimate it at high temperatures. Both values result in the prediction of the same value of the temperature maximum, which is also below the experimental value. Although the predictions from the SAFT-VR are only qualitative, it is encouraging to see that a simple approach, without a further adjustment, is able to predict the main features of this property. It is also noticeable that, in the comparison with the experimental data, the error of the SAFT-VR predictions is of the same order of magnitude as that of the simulation data. IV. Conclusions We have studied the thermodynamic properties of the water + carbon dioxide binary mixture using the SAFT-VR equation of state. We use the simple united-atom approach to model the carbon dioxide molecule, which is represented as a chain formed by attractive spherical segments tangentially bonded together interacting via square-well potentials. The water molecule is modeled as spherical with four off-center association sites (two sites are of type H and two of type O). Because in this work

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15933 we are interested studying the phase behvior for a wide range of pressures and temperatures, including the near critical, critical, and supercritical regions, we have used intermolecular parameters rescaled to the experimental critical points of the pure components. Standard geometric and arithmetic combining rules are used to obtain unlike mixture parameters, and in addition an unlike energy parameter is adjusted according to the modified geometric mean rule to give the best representation of the minimum temperature of the gas-liquid critical line. This parameter is then used in a transferable manner to study other thermodynamic properties at different conditions. In the first part of this work, we have studied the high-pressure phase behavior of the mixture. The theoretical results correspond to type-III phase behavior according to the classification of Scott and Konynenburg,13 in agreement with experimental data. In particular, the theory accounts for the gas-gas immiscibility of second kind and the temperature minimum of the gas-liquid critical line of the mixture. We have also studied the phase equilibria at high and low pressures and temperatures. All of the calculations show good qualitative agreement with experimental data. We have provided an analysis of the mutual solubilities of H2O and CO2 and find that the theory is able to reproduce the peculiar behavior of these properties. In particular, it predicts the discontinuity at low temperatures and the minimum at higher temperatures observed in the solubility curve of H2O in the CO2-rich phase, as well as the change of the slope of the CO2 solibility in the H2O-rich liquid phase. All of these features are a consequence of the presence of a three-phase boundary chracteristic of mixtures that exhibit type-III phase behavior. In the second part, we examine two of the most-important excess thermodynamic functions, namely, the excess volume and the excess enthalpy. We use the same molecular parameters and unlike interaction parameter (ξ12) to predict the key features of these properties. Agreement between experimental data and theoretical predictions for both magnitudes, in a wide range of temperatures and pressures, is nearly quantitative. This result is remarkable because excess properties are characterized by very-small values and are very sensitive to the molecular details of the theory used. Finally, we have analyzed the behavior of Henry’s law constant of carbon dioxide in water as a function of temperature. The SAFT-VR theory is able to predict in good qualitative agreement with experimental data, and with some molecular simulation data, the most important features of this property. In particular, the theory predicts the existence of the maximum shown by this function at intermediate temperatures. It is interesting as a final comment to emphasize how a simple molecular approach, such as SAFT-VR, is able to predict a number of different thermodynamic properties of the water + carbon dioxide binary mixture, including the phase behavior, excess functions, and Henry’s law constants, relying on verylimited experimental mixture information (in this case a single point in the high-temperature GL critical line) and a unique adjustable mixture parameter. The components of the mixture studied in this work, water and carbon dioxide, are not particularly easy to model. In particular, water has a strong electric dipole moment and carbon dioxide has a permanent electrical quadrupole moment. As we have mentioned, it is possible to introduce additional contributions to the free energy to treat these interactions explicitly; we have, however, taken the view that the orientationally averaged interactions can be treated in an effective way via square-well potentials of variable range and hence implemented the SAFT-VR approach in its

15934 J. Phys. Chem. C, Vol. 111, No. 43, 2007 original form. The excellent overall agreement we observe in the comparison with experimental data suggests that the approach used in this work contains the essential ingredients to predict the most-important features of the properties studied. Acknowledgment. M.C.dR. acknowledges the Programme Alβan from European Union Programme of High Level Scholarships for Latin America (identification no. E03D21773VE) for a Fellowship. We also acknowledge financial support from project no. FIS2004-06627-C02-01 of the Spanish Direccioń General de Investigacioń. Additional support from Universidad de Huelva and Junta de Andalucıá is also acknowledged. We also thank Eduardo J. M. Filipe and Manuel M. Pin˜eiro for useful discussions concerning to the excess enthalpy experimental results. References and Notes (1) Kenan Center Web Page. http//www2.ncsu.edu/champagne, 2006. (2) DeSimone, J. M. Science 2002, 297, 799-803. (3) IPCC Special Report Carbon Dioxide Capture and Storage http:// www.ipcc.ch/index.html, 2005. (4) CO2 sequestration http://www.princeton.edu/∼chm333/2002/fall/ co_two/intro/, 2002. (5) The U.S. Department of Energy. Fossyl Energy http://www. fossil.energy.gov/sequestration/, 2006. (6) Valtz, A.; Chapoy, A.; Coquelet, C.; Paricaud, P.; Richon, D. Fluid Phase Equilib. 2004, 226, 333. (7) Ji, X.; Tan, S. P.; Adidharma, H.; and Radosz, M. Ind. Eng. Chem. Res. 2005, 44, 7584. (8) Seitz and, J. C.; Blencoe, J. G. Geochim. Cosmochim. Acta 1999, 63, 1559. (9) Blencoe, J. G.; Seitz, J. C.; and Anovitz, L. M. Geochim. Cosmochim. Acta 1999, 63, 2393. (10) Diamond, L. W.; Akinfiev, N. N. Fluid Phase Equilib. 2003, 208, 265. (11) Spycher, N.; Pruess, K.; Ennis-King, J. Geochim. Cosmochim. Acta 2003, 67, 3015. (12) Chapoy, A.; Mohammadi, A. H.; Chareton, A.; Tohidi, B.; Richon, D. Ind. Eng. Chem. Res. 2004, 43, 1794. (13) Scott, R. L.; van Konynenburg, P. H. Discuss. Faraday Soc. 1970, 49, 87. (14) van Konynenburg, P. H.; Scott, R. L. Philos. Trans. 1980, A298, 495. (15) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3d ed.; Butterworth Scientific: London, 1982. (16) Sun, L.; Zhao, H.; Kiselev, S. B.; McCabe, C. J. Phys. Chem. B 2005, 109, 9047. (17) Kiselev, S. B.; Ely, J. F.; Tan, S. P.; Adidharman, H.; Radosz, M. Ind. Eng. Chem. Res. 2006, 45, 3981. (18) Bol, W. Mol. Phys. 1982, 45, 605. (19) Nezbeda, I.; Kolafa, J.; Kalyuzhnyi, Y. V. Mol. Phys. 1989, 68, 143. (20) Galindo, A.; Whitehead, P. J.; Jackson, G.; Burgess, A. N. J. Phys. Chem. 1996, 100, 6781. (21) Galindo, A.; Whithead, P. J.; Jackson, G.; Burgess, A. N. J. Phys. Chem. B 1997, 101, 2082. (22) Garcıá-Lisbona, M. N.; Galindo, A.; Jackson, G.; Burges, A. N. Mol. Phys. 1998, 93, 57. (23) Garcıá-Lisbona, M. N.; Galindo, A.; Jackson, G.; Burgess, A. N. J. Am. Chem. Soc. 1998, 120, 4191. (24) Patel, B. H.; Paricaud, P.; Galindo, A.; Maitland, G. C. Ind. Eng. Chem. Res. 2003, 42, 3809. (25) Ji, X.; Tan, S. P.; Adidharma, H.; Radosz, M. Ind. Eng. Chem. Res. 2005, 44, 8419. (26) Clark, G. N. I.; Haslam, A. J.; Galindo, A.; Jackson, G. Mol. Phys. 2006, 104, 3561. (27) Blas, F. J.; Galindo, A. Fluid Phase Equilib. 2002, 194-197, 501. (28) Galindo, A.; Blas, F. J. J. Phys. Chem. B 2002, 106, 4503. (29) Walsh, J. M.; Guedes, J. R.; Gubbins, K. E. J. Phys. Chem. 1992, 96, 10995. (30) Kraska, T.; Gubbins, K. E. Ind. Eng. Chem. Res. 1996, 35, 4727. (31) Kraska, T.; Gubbins, K. E. Ind. Eng. Chem. Res. 1996, 35, 4738. (32) Tang, Y.; Wang, Z.; Lu, B. C.-Y. Mol. Phys. 2001, 99, 65. (33) Dominic, A.; Chapman, W. G.; Kleiner, M.; Sadowski, G. Ind. Eng. Chem. Res. 2005, 44, 6928. (34) Eirini, Karakatsani K.; Theodora, Spyriouni.; Economou, G. E. AIChE J. 2005, 51, 2328. (35) Spyriouni, T.; Economou, I. E. AIChE J. 2005, 51, 2328.

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