Vapor−Liquid and Critical Behavior of Binary Systems of Hydrogen

Aug 4, 2007 - We have found that a unique binary parameter with a constant value for the whole family provides an excellent description of the behavio...
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J. Phys. Chem. B 2007, 111, 10180-10188

Vapor-Liquid and Critical Behavior of Binary Systems of Hydrogen Chloride and n-Alkanes: Experimental Data and Soft-SAFT Modeling F. Llovell,† L. J. Florusse,‡ C. J. Peters,‡ and L. F. Vega*,† Institut de Cie` ncia de Materials de Barcelona, Consejo Superior de InVestigaciones Cientı´ficas (ICMAB-CSIC), Campus de la UAB, Bellaterra, 08193 Barcelona, Spain, and Physical Chemistry and Molecular Thermodynamics, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ReceiVed: February 6, 2007; In Final Form: June 6, 2007

The purpose of this work is to check the capability of the crossover soft-SAFT equation of state to predict the phase behavior of hydrogen chloride/n-alkane mixtures based on experimental data. The hydrogen chloride parameters were optimized using the experimental information, while the parameters for the n-alkanes were obtained from published correlations to the molecular weight of the compounds. We have found that a unique binary parameter with a constant value for the whole family provides an excellent description of the behavior of hydrogen chloride + propane and hydrogen chloride + dodecane mixtures in a broad range of temperatures and pressures, as well as the critical line of the mixture. The model confirms that HCl + propane exhibits type-I critical behavior, while HCl + dodecane shows a type-II critical behavior. Taking advantage of the transferability of the parameters, the critical transition from type-II to type-III has been investigated with the equation in a predictive manner. Although results are very sensitive to the binary parameter value, there are indications to assert that type-III is achieved close to the HCl + heneicosane binary system.

Introduction Hydrogen chloride (HCl) is a very common compound used in several different industrial processes. In many cases, it appears as one of the major constituents of a mixture. For this reason, accurate basic thermodynamic data of the compound is needed. However, the corrosive nature of HCl makes it not easy to handle in experimental facilities, and as a result, thermodynamic information about hydrogen chloride and its mixtures is quite limited. In this sense, accurate models would be an attractive option for extracting information for mixtures containing HCl. However, from the modeling perspective, HCl is a complex system essentially due to its strong dipolar nature, which makes it behave as highly nonideal in mixtures. Analytical equations of state cannot take into account the directional nature of dipolar forces in a direct manner. An alternative modeling approach would be to use a molecular-based equation of state, in which the specific directional forces are explicitly taken into account. One of these equations is the SAFT equation (statistical associating fluid theory).1-5 Based on Wertheim’s first-order perturbation theory,6-9 the equation has been used to predict the phase behavior of several pure components and mixtures in a broad range of thermodynamic conditions. The key of the success of SAFT-based equations is their solid statistical mechanics basis, which gives a physical interpretation of the system. It provides a framework in which the effects of molecular shape and interactions on the thermodynamic properties can be separated and quantified. In addition, its parameters are few in number, with physical meaning, and transferable, which makes SAFT a powerful tool for engineering predictions. * To whom correspondence should be addressed. E-mail: [email protected]. Present address: MATGAS-Air Products, Campus de la UAB, Bellaterra, 08193 Barcelona, Spain. † Campus de la UAB. ‡ Delft University of Technology.

Soft-SAFT10-13 is a variant of the original SAFT equation; it uses a Lennard-Jones (LJ) model to describe the reference fluid, in contrast to the hard-sphere model of the original version. The predictive power and accuracy of soft-SAFT has been proved for several experimentally determined systems for which cubic-type EoSs fail, such as the solubility of hydrogen in heavy n-alkanes14 and the solubility of gases in perfluoroalkanes,15-17 among others. The underlying theory of the equation allows its systematic improvement and extensions in a sound manner. In this sense, the equation has been recently extended into several directions, (1) the calculation of second-order thermodynamic derivative properties18-20 and tricritical points,21 (2) the precise characterization of the critical region of pure fluids and mixtures22-24 through a crossover treatment based on White’s work25,26 from the renormalization group theory, and (3) the calculation of interfacial vapor-liquid and liquid-liquid properties by coupling the van der Waals density gradient theory to the original soft-SAFT equation.27-29 The purpose of this work is twofold, (1) to check the performance of the crossover soft-SAFT equation for mixtures of HCl with propane and dodecane versus experimental data and (2) to use soft-SAFT as a predictive tool to study the critical behavior of HCl + n-alkane binary mixtures, once the model is validated. The strong dipolar moment of HCl combined with the nonspherical shape of n-alkane molecules poses a challenge to any modeling approach. Given the molecular nature of SAFTtype equations of state, these mixtures are excellent candidates to check the validity of a SAFT-type equation. Experimental data for the HCl + ethane mixture was published by some of us in a previous work.30 We present here details on the experimental data measurements on the vapor-liquid phase equilibria of HCl + propane and HCl + dodecane mixtures, as well as the critical locus of the HCl + propane mixture. Bubble and dew points were measured in the whole mole fraction range

10.1021/jp071029t CCC: $37.00 © 2007 American Chemical Society Published on Web 08/04/2007

Binary Systems of HCl and n-Alkanes

J. Phys. Chem. B, Vol. 111, No. 34, 2007 10181

of the two binary systems from 273 up to 363 K and at pressures as high as 7 MPa. The behavior of the mixture was then described with the crossover soft-SAFT equation of state, which is used in a predictive manner for the rest of the HCl + n-alkanes series. Taking advantage of the predictive power of the equation and the availability of molecular correlations for the pure compounds, the effect of the n-alkanes chain length on the behavior of the mixture was also investigated in order to detect the transition in the critical behavior of the mixtures from typeII to type-III, passing through a possible type-IV, according to the classification of Scott and van Konynenburg.31 The remainder of the paper is organized as follows. In section 2, a short description of the experimental setup is provided; section 3 is devoted to a brief description of the soft-SAFT equation, while in section, 4 we present and discuss results obtained in this work. Finally, section 5 provides some concluding remarks. Experimental Section Experimental measurements were carried out in a highpressure Cailletet equipment. In this equipment, pressures of up to approximately 15 MPa can be allowed, and a temperature region from 250 up to 450 K can be covered. The design and principle of this equipment, as well as the experimental procedures, have been discussed elsewhere.32,33 The temperature was measured with an accuracy of 0.02 K, and the pressure could be determined within 0.002 MPa. On average, the accuracy of the mole fraction of the various fillings was as accurate as 0.001. The purity of hydrogen chloride had already been checked in a previous work,30 while the saturated vapor pressure curves of propane were measured and compared with correlated data from ref 34. Air Products was the supplier of hydrogen chloride, propane, and dodecane. Hydrogen chloride had a purity of 99.5 mol %, while propane and dodecane had a purity of 99.95 mol %. All chemicals were used without any further purification.

HCl propane dodecane heneicosane

1.000 1.776 4.975 8.197

3.566 3.831 3.971 3.997

257.2 225.8 286.0 296.6

A0 Aid ALJ Ach Aassoc ) + + + NkBT NkBT NkBT NkBT NkBT ∞

)

(

An-1

Across n

∑ Nk T + Nk T

n)1

B

B

)

φ 4.73 6.75 8.80 8.97

L/σ HB/kB (K) kHB (Å3) 1.00 1.16 1.64 2.16

1321

1137

ization group (RG) theory36 is applied. This term is needed to describe the long-range fluctuations produced in the properties of the fluid when approaching the critical region. The treatment, based on White’s work,25,26 is done by incorporating the scaling laws governing the asymptotic behavior close to the critical point while reducing to the original equation of state far from the critical point. The crossover term is expressed mathematically as a set of recursive equations that incorporate the fluctuations in a progressive way (see eq 2). We have confirmed22,23 that after 5 iterations (n ) 5), no further changes in the Helmholtz free energy are observed. It is important to remark that the value of An-1 for first iteration corresponds to the original soft-SAFT value. Details on the different terms and the implementation of the crossover term can be found in the original references.10-13,22,23 Since the Helmholtz free energy is calculated by adding different terms, each of them should be expressed as a function of the composition for mixtures. As in previous works, the van der Waals one-fluid theory (vdW-1f) is used to describe the monomer contribution ALJ and the crossover contribution Across, while the rest of the terms are explicitly written for mixtures. In this theory, the residual Helmholtz free energy of the LJ mixture is approximated by the residual Helmholtz free energy of a pure hypothetical fluid with conformal parameters σm and m

∑i ∑j xixjmimjσ3ij (

The soft-SAFT equation of state with the crossover term (crossover soft-SAFT) has been used to model the pure components and their mixtures.22-24 In this equation, the total free energy A of the system is written as

NkBT

σ (Å) /k (K)

m

σ3m )

Soft-SAFT Modeling

A

TABLE 1: Soft-SAFT Molecular Parameters Used for Hydrogen Chloride, Propane, Dodecane, and Heneicosane. The n-alkane Parameters Were Obtained from the Correlation with the Molecular Weight of the Compounds Proposed in Ref 22

mσ3m )

∑i

(3a) ximi)2

∑i ∑j xixjmimjijσ3ij (

(1) m)

∑i ximi)

(3b) 2

∑i ximi

(3c)

(2)

where Aid is the ideal term contribution. ALJ is the LennardJones (LJ) reference term which takes into account the repulsive and attractive interactions of the monomers forming the chain. We have used the accurate EOS of Johnson et al.35 to calculate the free energy and derivative thermodynamic properties of the LJ reference fluid. Ach, the chain term, comes from Wertheim’s theory, and it is formally identical in the different versions of SAFT. Aassoc is the association term, within the first-order Wertheim’s perturbation theory for associating fluids. The association term is expressed as the sum of contributions of all associating sites of a component. Finally, Across is the contribution obtained from a crossover treatment when the renormal-

m being the chain length of the conformal fluid. The cross parameters are calculated through the generalized LorentzBerthelot combining rules

(

)

σii + σjj 2

(4)

ij ) ξij (iijj)1/2

(5)

σij ) ηij

where ηij and ξij are adjustable binary parameters correcting the differences in size and energy, respectively, between the segments forming the two different compounds of the mixture. When these values are set to unity, the equation is used in a pure predictive manner for mixtures.

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TABLE 2: Experimentally Determined Bubble Point Data at Constant Composition in the Binary System Hydrogen Chloride(1) + Propane(2) T (K)

P (MPa)

x2 ) 1.0000 273 278 283 288 293 298 303 308 313 318 323 328 333 338 343 348 353 358 363 368 369.82

0.471 0.548 0.633 0.728 0.832 0.948 1.074 1.213 1.365 1.530 1.709 1.903 2.113 2.340 2.585 2.848 3.132 3.437 3.765 4.119 4.256

x2 ) 0.6132 273.71 283.26 293.31 303.29 313.09 313.26 323.17 333.43 343.25 348.28 349.24 349.83

1.712 2.112 2.602 3.147 3.757 3.767 4.442 5.197 5.927 6.197 6.183 6.148

x2 ) 0.2992 273.90 283.34 293.33 303.26 313.19 318.14 323.25 328.33 330.22 330.56 330.88 331.27 331.77 332.10

2.433 2.998 3.688 4.503 5.403 5.908 6.428 6.958 7.148 7.163 7.189 7.204 7.209 7.194

x2 ) 0.0988 274.06 283.28 293.22 302.97 303.07 303.18 303.28 313.25 313.30 323.13 323.25 324.53 324.69 324.79 324.86 325.05 325.09

2.674 3.314 4.134 5.084 5.094 5.104 5.124 6.260 6.260 7.550 7.571 7.741 7.757 7.767 7.777 7.774 7.769

T (K)

P (MPa)

x2 ) 0.8992 278.22 293.19 293.30 308.20 323.32 323.85 338.29 353.32 361.24 363.37 365.19 365.31

0.994 1.384 1.389 1.874 2.495 2.520 3.230 4.116 4.646 4.746 4.773 4.757

x2 ) 0.5495 273.85 288.16 303.57 310.68 318.29 325.79 333.28 335.83 340.80 345.45 345.85 346.05 346.09 346.17

1.843 2.523 3.423 3.898 4.443 5.023 5.628 5.833 6.213 6.424 6.404 6.392 6.392 6.387

x2 ) 0.1978 274.12 283.26 293.31 303.25 313.20 313.21 323.11 327.15 327.26 327.29 327.37

2.807 3.402 4.157 5.032 6.037 6.047 7.158 7.523 7.519 7.519 7.511

x2 ) 0.0541 273.73 278.39 288.38 298.18 308.26 318.27 323.11

2.718 3.044 3.824 4.739 5.839 7.135 7.821

T (K)

P (MPa)

x2 ) 0.8133 278.30 293.91 308.25 323.16 338.19 338.20 353.24 357.15 358.26 360.40

1.442 1.947 2.517 3.228 4.073 4.073 5.019 5.234 5.279 5.256

x2 ) 0.3916 274.58 288.32 295.77 303.26 310.83 318.27 325.80 330.79 333.17 337.02

2.182 2.977 3.477 4.037 4.657 5.322 6.037 6.522 6.732 6.911

x2 ) 0.1951 273.95 283.39 293.16 302.97 313.18 320.72 325.93 326.78 327.28 327.56 327.76

2.539 3.149 3.894 4.799 5.844 6.714 7.331 7.421 7.461 7.472 7.463

x2 ) 0.0496 274.22 283.22 293.27 298.22 303.37 313.33 323.39 324.27 324.38 324.41

2.729 3.379 4.244 4.724 5.274 6.474 7.887 8.008 7.998 7.998

T (K)

P (MPa)

x2 ) 0.7992 273.85 288.28 303.26 310.78 318.30 325.74 333.24 348.27 358.42 360.10 360.15

1.230 1.675 2.250 2.580 2.950 3.335 3.765 4.701 5.306 5.280 5.276

x2 ) 0.3067 273.90 283.33 293.34 303.22 313.38 323.19 328.24 331.84 332.43

2.382 2.947 3.642 4.432 5.362 6.373 6.899 7.184 7.172

x2 ) 0.0995 273.80 283.68 293.40 303.20 310.78 318.23 324.76

2.633 3.333 4.138 5.103 5.958 6.898 7.766

x2 ) 0.0000 274.07 283.20 283.23 298.18 298.26 313.22 313.25 323.25 323.29 324.40 324.44

2.677 3.377 3.382 4.787 4.792 6.602 6.602 8.092 8.088 8.275 8.273

Binary Systems of HCl and n-Alkanes

J. Phys. Chem. B, Vol. 111, No. 34, 2007 10183

TABLE 3: Experimentally Determined Bubble Point Data at Constant Composition in the Binary System Hydrogen Chloride(1) + Dodecane(2) T (K) x2 ) 0.8070 368.54 353.29 338.36 323.18 308.23 293.16 278.27

P (MPa) 1.880 1.670 1.470 1.265 1.070 0.8797 0.7047

x2 ) 0.1270 353.33 10.90 338.27 8.801 323.18 6.871 315.53 5.991 308.2 5.216 293.22 3.841 278.7 2.766 263.57 1.886 258.38 1.636

T (K)

P (MPa)

x2 ) 0.6010 368.27 353.28 338.13 330.65 323.18 308.17 295.97 293.23 277.63

4.284 3.774 3.269 3.014 2.764 2.284 1.919 1.834 1.414

x2 ) 0.1020 353.31 338.26 323.26 315.70 308.37 293.23 278.69 263.31 258.29

11.26 9.047 7.042 6.142 5.332 3.922 2.797 1.892 1.647

Before applying the soft-SAFT equation to mixtures, it is necessary first to model the pure components in order to check the performance of the equation for the pure fluids and to obtain the pure component parameters. Propane and dodecane are described, as the rest of the n-alkanes within the soft-SAFT approach, as homonuclear chainlike molecules, modeled as m Lennard-Jones segments of equal diameter σ and the same dispersive energy , bonded tangentially to form the chain. Two additional parameters appear when implementing the crossover approach, the cutoff length, L, related to the maximum wavelength fluctuations that are accounted for in the uncorrected (classical) free energy and φ, the average gradient of the wavelet function ψ(r). In our approach, L and φ are both treated as adjustable parameters; we have studied the influence of each of them on the phase envelope and the critical point estimation in our previous work.22 The molecular parameters of these two compounds and the rest of the n-alkane series are taken from the correlations provided in refer 22. HCl is modeled as a single Lennard-Jones segment of diameter σ and dispersive energy  with two square-well sites with volume and energy of association kHB and HB, respectively. These two square-well sites represent the dipole moment of the HCl molecule as an associative interaction. This approximation was also done in previous works of Galindo et al.37,38 using a different version of SAFT, SAFT-VR,39 obtaining accurate results for the studied mixtures. The molecular parameters of HCl used in this work were obtained by fitting to experimental saturated liquid densities and vapor pressures. They are provided in Table 1, along with those used for the n-alkane compounds investigated here. L and φ are used for the crossover version and have the physical meaning explained before. Results We first present, in a tabular form, the experimental data prior to modeling the systems with the crossover soft-SAFT equation. Tables 2 and 3 summarize all of the bubble point data obtained for the mixtures HCl + propane and HCl + dodecane, respectively. The dew point data for the HCl + propane mixture are presented in Table 4, while Table 5 summarizes the experimental critical points for the same mixture.

T (K)

P (MPa)

x2 ) 0.4120 368.38 353.35 338.32 323.24 308.34 293.19 278.22 263.38

7.232 6.277 5.327 4.397 3.542 2.757 2.072 1.497

x2 ) 0.0330 353.31 348.57 343.56 338.49 323.42 315.72 308.48 293.28 278.36 263.42 258.38

12.14 11.44 10.67 9.874 7.618 6.588 5.713 4.143 2.928 1.998 1.738

T (K) x2 ) 0.2210 368.97 353.64 338.32 323.42 316.12 308.29 293.29 278.67 263.36 258.33

P (MPa) 11.02 9.274 7.648 6.138 5.423 4.738 3.553 2.593 1.793 1.573

Figure 1 depicts the vapor-liquid equilibrium phase diagram for pure HCl. Symbols represent experimental data extracted from ref 30, while the solid line represents the soft-SAFT calculation. The soft-SAFT equation is able to describe both projections in an excellent manner. The crossover term enables an accurate description of the critical region with the same set of molecular parameters as those of the rest of the diagram. No need for rescaling, as was done in previous works,38 is necessary in this case. Moreover, the approximation made when modeling the dipole as an association contribution seems to be quite good for the pure fluid, although it is necessary to test its performance when dealing with mixtures. The phase envelope of propane is shown in Figure 2. The solid line represents soft-SAFT calculations, while symbols represent experimental data measured in our laboratory (circles) and correlations to experimental data from NIST (diamonds).34 Similarly, the phase envelope of dodecane is depicted in Figure 3. In this case, the circles represent correlations to experimental data from NIST,34 while the diamonds represent molecular simulation data.40 The phase envelope of both compounds is well reproduced by the equation, both far from and close to the critical point. Note that the phase envelope shows the right shape to capture the critical point. However, for the case of dodecane (see Figure 3), the curve seems to be too flat very close to the critical point. This has been previously observed by us and other authors (see, for instance, refs 22 and 41) when White’s crossover approach was implemented for chainlike molecules, with the flatness of the curve increasing as the chain length increased. It could be attributed to the way in which the crossover implementation is performed, applied only to the attractive part of the reference (spherical) fluid, but further investigations are needed before giving a final assessment. Note that, in any case, the crossover soft-SAFT is able to accurately describe the experimental data for the three phase envelopes, including critical points. It is important to remark that an accurate and physically sound modeling of the pure fluids is crucial to obtain reliable results when treating the mixtures. Once the pure fluids have been studied, the next step concerns the prediction of the phase behavior of the binary mixtures HCl

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TABLE 4: Experimentally Determined Dew Point Data at Constant Composition in the Binary System Hydrogen Chloride + Propane T (K)

P (MPa)

y2 ) 0.8992 353.28 358.29 359.25 362.22 364.64 365.35

3.602 4.009 4.073 4.327 4.604 4.754

y2 ) 0.5495 320.62 325.79 330.58 335.72 340.80 345.45 345.85

T (K)

P (MPa)

y2 ) 0.8133 323.20 328.09 333.22 333.30 338.31 343.21 348.08 348.24 353.16 356.19 359.10 360.21 360.69 360.71

2.182 2.430 2.680 2.714 3.033 3.360 3.726 3.751 4.145 4.453 4.803 4.958 5.047 5.231

3.040 3.438 3.911 4.394 4.969 5.745 5.718

y2 ) 0.3916 310.83 325.79 330.79 337.14 337.47 337.47 337.76 337.76

3.282 4.715 5.337 6.902 6.879 6.484 6.585 6.854

y2 ) 0.1978 313.20 323.11 327.15 327.53

5.207 6.565 7.281 7.386

y2 ) 0.1951 303.23 313.19 321.20 325.36 327.20

4.125 5.181 6.159 6.867 7.226

y2 ) 0.0541 283.20 288.22 293.14 298.29 303.28 308.17 313.22 318.05 323.77

3.182 3.607 4.064 4.543 5.085 5.639 6.276 6.955 7.863

y2 ) 0.0496 298.19 308.28 313.33 318.20 323.75 324.41 324.46

4.565 5.691 6.334 7.017 7.881 7.998 7.993

TABLE 5: Experimentally Determined Critical Points in the Binary System Hydrogen Chloride + Propane x2

T (K)

P (MPa)

0.0000 0.0496 0.0541 0.0988 0.0995 0.1951 0.1978 0.2992 0.3067 0.3916 0.5495 0.6132 0.7992 0.8133 0.8992 1.0000

324.42 324.41 324.39 325.05 325.01 327.76 327.15 332.10 332.43 337.02 346.17 349.83 360.10 360.40 365.31 369.82

8.274 7.998 7.983 7.774 7.786 7.463 7.523 7.194 7.172 6.911 6.387 6.148 5.276 5.256 4.757 4.256

+ propane and HCl + dodecane and to compare the model predictions with the measured data. The vapor-liquid equilibrium calculations were performed using the parameters for the

T (K)

P (MPa)

y2 ) 0.7992 340.81 348.33 355.68 355.84 360.15

3.209 3.757 4.451 4.469 5.016

y2 ) 0.3067 313.25 318.30 323.14 328.23 330.66

4.153 4.706 5.245 6.007 6.401

y2 ) 0.0995 308.26 315.78 323.13 324.84

5.366 6.317 7.405 7.663

T (K)

P (MPa)

y2 ) 0.6132 333.43 343.24 349.24 349.87 350.46 350.46

3.627 4.642 5.501 6.143 6.088 5.749

y2 ) 0.2992 313.20 323.25 328.33 330.56 332.10

4.271 5.378 6.116 6.476 6.811

y2 ) 0.0988 293.22 303.07 313.29 323.25 324.53 324.69 324.79 324.86 325.09

3.788 4.789 5.950 7.405 7.633 7.668 7.683 7.698 7.758

pure fluids. Although the soft-SAFT equation shows the qualitative trends of the diagrams (not shown here), quantitative agreement is obtained only if a binary interaction parameter ξ is used. Since our goal is to predict the phase behavior of the systems for which no experimental data is available, we decided to use this binary parameter for the existing mixtures. The procedure used to obtain the energy binary parameter was to fit it to a single Pxy diagram at an intermediate temperature. Once the adjusted value for ξ was obtained, it was used to predict the rest of the phase diagrams and the critical line as well. Because of the physical relevance of the equation, it is expected that the same binary parameter will also hold to model any other mixture of the homologous series HCl + n-alkanes. The selected data set for fitting the energy was the HCl + propane mixture at a constant temperature of 313 K, and a value of ξ ) 0.920 was obtained. Figure 4a depicts some Pxy diagrams of the mixture HCl + propane at constant temperatures in the range from 273 to 353 K. Circles, squares, diamonds, triangles, and crosses represent experimental data obtained in this study at 273, 293, 313, 333, and 353 K, respectively, and the solid lines are soft-SAFT

Binary Systems of HCl and n-Alkanes

J. Phys. Chem. B, Vol. 111, No. 34, 2007 10185

Figure 1. Vapor-liquid phase diagram of hydrogen chloride; (a) temperature-density diagram and (b) pressure-temperature diagram. Symbols represent the experimental data,37 and the solid lines represent the soft-SAFT calculations.

Figure 2. Vapor-liquid phase diagram of propane; (a) temperaturedensity diagram and (b) pressure-temperature diagram. Diamonds represent correlated experimental information from ref 34, while the circles are data from this work. The lines represent the soft-SAFT calculations.

predictions. The dashed line represents the mixture critical line as predicted by soft-SAFT. Quantitative agreement is observed for the whole range of temperatures and pressures. As can be seen, soft-SAFT is also able to predict the critical line in excellent agreement with the experimental data. In Figure 4b, a pressure-temperature projection of the mixture critical locus is presented. Symbols correspond to experimental data from Table 5, while the dashed line represents the soft-SAFT prediction. Again, it is observed that soft-SAFT is able to reproduce the critical line showing quantitative agreement for the whole composition range, with only slight deviations close to the critical point of hydrogen chloride. The equation confirms that the binary system HCl + propane exhibits a type-I fluid-phase behavior, that is, a continuous vapor-liquid critical line is connecting both critical points of the pure components. The HCl + dodecane mixture has been studied following the same procedure, and the results are depicted in Figure 5. Figure 5a represents several Px diagrams of these mixtures in a temperature range from 283 to 363 K. Circles, squares,

diamonds, triangles, and crosses correspond to experimental data at 283, 303, 323, 343, and 363 K, respectively. The solid lines are soft-SAFT predictions. As it has already been stated, the same value for the binary energy parameter ξ, fitted to a single Pxy isotherm for the HCl + propane mixture, is used here as a unique parameter. In general, very good agreement is obtained between soft-SAFT predictions and the experimental data. Even quantitative agreement is achieved at higher concentrations of HCl, while some small deviations are observed when increasing the mole fraction of dodecane. Although the results could be improved by fitting the value of the binary parameter to this mixture, this would result in a loss of predictive power of the soft-SAFT equation, which is intended to be used in a predictive manner for mixtures, including longer alkanes for which there is no experimental data available. As the obtained prediction seems accurate enough, we have decided to keep the same binary parameter value for all HCl + n-alkane mixtures investigated here. Figure 5b shows a pressure-temperature projection with the prediction of the continuous critical line for this mixture as obtained with the soft-SAFT equation of state,

10186 J. Phys. Chem. B, Vol. 111, No. 34, 2007

Figure 3. Vapor-liquid phase diagram of dodecane; (a) temperaturedensity diagram and (b) pressure-temperature diagram. Circles represent simulation data taken from ref 40, and diamonds stand for correlations to experimental data from ref 34. The lines are the softSAFT calculations.

which was also present in the HCl + propane binary system. In addition, however, in the binary HCl + dodecane system, a second critical line could be identified by the soft-SAFT model. This second critical line originates in the upper critical endpoint of a three-phase equilibrium liquid-liquid-vapor line and emerges at high pressures. Unfortunately, to the best of our knowledge, no experimental data are available for comparison. Apparently, the presence of a longer n-alkane has promoted the emergence of the second liquid-liquid critical line at lower temperatures. Hence, this mixture belongs to type-II fluid-phase behavior. Finally, taking advantage of the molecular nature of the equation and the transferability of the parameters, we have investigated how the phase diagram of the mixture evolves as the chain length of the n-alkane increases. To our knowledge, this is the first time that this transition in the systems HCl + n-alkane has been studied. It is expected that with an increasing carbon number of the n-alkane, both the gas-liquid and the liquid-liquid critical line will join, leading to type-III fluid-

Llovell et al.

Figure 4. (a) Pxy projections of the hydrogen chloride(1) + propane(2) mixture at five different temperatures, 273 (circles), 293 (squares), 313 (diamonds), 333 (triangles), and 353 K (crosses), plus the critical line. Symbols are the experimental data at each temperature, the filled squares represent the critical line points, the solid lines are the soft-SAFT predictions for each isotherm, and the dashed line is the equation prediction for the critical line. (b) Pressure-temperature diagram of the same mixture showing the critical line. Symbols represent the experimental data, solid lines are the pure fluid soft-SAFT calculations, while the dashed line is the critical line predicted by the equation.

phase behavior. However, it is unknown a priori for which carbon number this transition will take place. Moreover, the formation of a type-IV (a necessary transition between types II and III) could also be achieved for a certain carbon number of the n-alkane. Using the same value of the binary parameter as that mentioned before, we have determined that type-III fluidphase behavior is clearly obtained for the HCl + heneicosane mixture. Figure 6 shows the PT projection with the critical line of this mixture as obtained from the soft-SAFT equation of state. One should be aware that there is a strong influence of the selected binary parameter value on these diagrams since small modifications of it may cause the appearance of this characteristic critical behavior at larger or shorter chain lengths. In this sense, it is not clear if the HCl + eicosane mixture exhibits type-II, -IV, or -III behavior. Some experimental work would be really helpful in order to assess this type of behavior.

Binary Systems of HCl and n-Alkanes

J. Phys. Chem. B, Vol. 111, No. 34, 2007 10187

Figure 6. Pressure-temperature diagram of a mixture of hydrogen chloride(1) + heneicosane(2). The lines are as those in Figure 5b. The inset is also an enlargement of the region near the critical point of hydrogen chloride, showing the type-III behavior.

Figure 5. (a) Pxy projections of the hydrogen chloride(1) + dodecane(2) mixture at five different temperatures, 283 (circles), 303 (squares), 323 (diamonds), 343 (triangles), and 363 K (crosses). Symbols represent the experimental data at each temperature, and the solid curves are the soft-SAFT predictions for each isotherm. (b) Pressure-temperature diagram of the mixture, showing the critical line. The dotted line represents the liquid-liquid-vapor equilibria. The rest of the lines are as those in Figure 4. The inset shows an enlargement of the region near the critical point of the hydrogen chloride in order to highlight the three-phase region.

Conclusions The experimental results for binary mixtures of hydrogen chloride with propane and dodecane have been used to model the fluid-phase behavior of binary HCl + n-alkane mixtures with the crossover soft-SAFT equation of state, searching for the transition in the critical behavior of the mixture with increasing chain length of the second compound. Bubble and dew points were measured in a temperature range from 273 up to 363 K in the whole mole fraction region in both mixtures, while critical compositions for the HCl + propane mixtures were also provided. In order to model the data, a physically sound model has been proposed, that is, the crossover soft-SAFT equation of state approach. The molecular parameters of HCl were obtained from fitting experimental liquid densities and vapor pressures, while

the n-alkanes were modeled taking the parameters from previous work. All binary mixtures investigated here were modeled using a single-energy binary interaction parameter value obtained from fitting to only one isothermal HCl + propane mixture and used as a unique and transferable parameter for the other HCl + n-alkane systems. Excellent agreement has been obtained when comparing to the measured vapor-liquid equilibria for HCl + propane and HCl + dodecane mixtures over the whole range of conditions. The critical line of both mixtures HCl + propane and HCl + dodecane has been also calculated, showing type-I and type-II fluid-phase behavior, respectively. The study of the transition in the critical behavior of the HCl + n-alkanes family showed an evolution from type-II to type-III when the chain length of the n-alkane increased. Type-III fluid-phase behavior was established for the mixture of hydrogen chloride + heneicosane. Given the sensitivity of the shape of the various diagrams in relation to the particular value of the binary interaction parameter, further experimental work is suggested to accurately find the phase transition evolution in this series of binary systems. Acknowledgment. This research has been possible thanks to the financial support received from the Spanish Government (Project CTQ2005-00296/PPQ) and by the Generalitat de Catalunya (2005SGR-00288). F. Llovell acknowledges a predoctoral FPU grant from the Ministerio de Educacio´n y Ciencia (MEC). References and Notes (1) Jackson, G.; Chapman, W. G.; Gubbins, K. E. Mol. Phys. 1988, 65, 1. (2) Chapman, W. G.; Jackson, G.; Gubbins, K. E. Mol. Phys. 1988, 65, 1057. (3) Chapman, W. G. J. Chem. Phys. 1990, 93, 4299. (4) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Fluid Phase Equilib. 1989, 52, 31. (5) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Ind. Eng. Chem. Res. 1990, 29, 1709. (6) Wertheim, M. S. J. Stat. Phys. 1984, 35, 19. (7) Wertheim, M. S. J. Stat. Phys. 1984, 35, 35. (8) Wertheim, M. S. J. Stat. Phys. 1986, 42, 459. (9) Wertheim, M. S. J. Stat. Phys. 1986, 42, 477. (10) Blas, F. J.; Vega, L. F. Mol. Phys. 1997, 92, 135. (11) Blas, F. J.; Vega, L. F. Ind. Eng. Chem. Res. 1998, 37, 660.

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