Freezing Point Depression of Electrolyte Solutions: Experimental

Ind. Eng. Chem. Res. 2008, 47, 3983–3989

3983

Freezing Point Depression of Electrolyte Solutions: Experimental Measurements and Modeling Using the Cubic-Plus-Association Equation of State Hooman Haghighi, Antonin Chapoy,* and Bahman Tohidi Centre for Gas Hydrate Research, Institute of Petroleum Engineering, Heriot-Watt UniVersity, Edinburgh EH14 4AS, Scotland, U.K.

New experimental freezing point depressions of six binary solutions (H2O-NaCl, H2O-CaCl2, H2O-MgCl2, H2O-KOH, H2O-ZnCl2, and H2O-ZnBr2) and four ternary solutions (H2O-NaC1-KCl, H2O-NaC1-CaCl2, H2O-KC1-CaCl2, and H2O-NaC1-MgCl2) have been measured by a reliable differential temperature technique. The available experimental literature data on the freezing point depression in addition to the vapor pressure data of aqueous electrolyte solutions for NaCl, KCl, KOH, CaCl2, MgCl2, CaBr2, ZnCl2, and ZnBr2 have been used to optimize binary interaction parameters between salts and water. The fugacity of water in salt-free aqueous phase has been modeled by the cubic-plus-association (CPA) equation of state. The Debye–Hückel electrostatic term has been used for taking into account the effect of salt on the fugacity of water when electrolytes are present. Model predictions are validated against independent experimental data generated in this work for both single and mixed electrolyte solutions and a good agreement between predictions and experimental data is observed, supporting the reliability of the developed model. 1. Introduction There are numerous calculations in chemical and petroleum engineering where reliable predictions of phase behavior of electrolyte solutions are required, from desalination units to gas hydrate inhibition in offshore/arctic drilling operations or in oil/ gas pipelines. Accurate models describing phase behavior of these systems are therefore necessary for analyzing, designing, and optimizing processes and equipment in the chemical and petroleum industry. The work presented in this communication is the result of a study on the phase equilibria of aqueous electrolyte solutions particularly in relation to drilling operations and subsea oil transmission lines where the proportion of salt in the aqueous phase could be significant. Studying the effect of electrolyte solutions on thermodynamic phase behavior of electrolyte solutions is the first step to gain a better understanding of the effect of salts on gas hydrate stability conditions. In this work, freezing point depressions of six single electrolyte aqueous solutions (H2O-NaCl, -CaCl2, -MgCl2, -KOH, -ZnCl2, and -ZnBr2) and four binary aqueous electrolyte solutions (H2O-NaC1-KCl, H2O-NaC1-CaCl2, H2O-KC1-CaCl2, and H2O-NaC1-MgCl2) were measured by using an apparatus and method developed at Heriot-Watt University.1 The accuracy and reliability of the new experimental measurements are demonstrated by comparing the measurements with reliable literature data from different researchers. Vapor pressure data of aqueous electrolyte solutions as well as freezing point depressions of nine aqueous electrolyte systems have been gathered from the literature to study the effects of salt on vapor-liquid and vapor–liquid–solid equilibria. The cubic-plus-association equation of state (CPA EoS) has been extended to predict fluid phase equilibria in the presence of single or mixed electrolyte solutions over a wide range of operational conditions. The equation of state (short-range interactions) is employed to calculate the effect of nonionic (molecular) species in the aqueous phase, and a Debye–Hückel electrostatic term (long-range interactions) is used to model the * To whom correspondence should be addressed. E-mail: [email protected]. Telephone: +44 (0)131 451 3564. Fax: +44 (0)131 451 3539.

effect of salts on the fugacity coefficients of molecular species in the solution. The predictions of the model have been compared with independent experimental data (vapor pressure and freezing point of ternary systems), demonstrating the reliability of the approach. 2. Experimental Details 2.1. Materials. Aqueous solutions of different salts used in this work were prepared gravimetrically in this laboratory. All the salts used were of analytical reagent grade and with reported purities of >99% for anhydrous NaCl and KCl (Aldrich) and >98% for anhydrous ZnCl2 and ZnBr2 (Aldrich). Dihydrate CaCl2 (Aldrich) and hexahydrate MgCl2 (Aldrich) with reported purities of >98% and 45 mass % KOH solution in water (Sigma-Aldrich) were also used without further purification. Solutions were prepared using deionized water throughout the experimental work. 2.2. Apparatus and Procedures. Freezing point measurements at atmospheric pressure were made using an apparatus and method developed at Heriot-Watt University.1 The apparatus is comprised of two cells each containing a platinum resistance temperature (PRT) probe ((0.1 K), surrounded by an aluminum sheath as shown in Figure 1, placed in a controlled temperature bath. One cell contains the aqueous electrolyte solution, while the second cell contains the bath fluid (as a reference fluid). The bath temperature can be ramped between different set points at a constant set rate. The similarity of construction and the level of filling fluids ensure that the two probes have very similar thermal time constants and will lag behind the bath temperature by nearly identical values, as long as there is no phase change. The temperature of each probe is measured during the ramp (either heating or cooling) by recording (with an appropriate interface board) the voltage generated across each PRT by a constant current generator. The resistance is sampled at determined intervals and digitally stored. 2.3. Procedures. The freezing point of a test solution is determined using an inflection point method. Initially the temperature of the test sample is reduced sufficiently to promote ice formation. This can be detected by a rise in sample

10.1021/ie800017e CCC: $40.75  2008 American Chemical Society Published on Web 05/09/2008

3984 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 Table 1. CPA Pure Compound Parameters for Water2 b (L/mol) a0 (bar L2/mol2) water

0.0145

1.2277

c1

ε (bar L/mol) β (× 103)

0.6736

166.55

69.2

Table 2. Optimized Water-Salt Interaction Coefficients for Different Salts (× 106)

NaCl KCl KOH CaCl2 MgCl2 CaBr2 ZnCl2 ZnBr2

A

B

C

D/K

E

-3879.89 -6427.25 -1465.19 -3566.60 -813.23 -3727.05 -1183.00 81.12

-6.09 -2.68 -13.31 -9.67 -14.41 -5.02 -1.37 -1.27

-45.95 -308.79 -2129.45 385.81 -76.81 -76.83 -39.08 -4451.44

-8137.28 -7445.30 -9338.45 -3960.14 -4469.65 -4392.45 -4481.42 -4741.98

10.43 6.16 23.58 16.19 20.12 17.12 24.21 6.08

Table 3. Freezing Point Depression (∆T) of Aqueous Single Electrolyte Solutionsa mass % of salt in ∆Texp ∆Tcal error aqueous solution ((0.1 K) σexp ((0.1 K) (∆Texp - ∆Tcal) NaCl

Figure 1. Schematic illustration of the freezing point measurement apparatus.

CaCl2

MgCl2

ZnCl2

ZnBr2

Figure 2. Typical freezing point measurement. (cooling) Ice formation can be detected by a rise in sample temperature as the latent heat of formation is released. (heating) Once the last crystal of ice has melted, the sample temperature converges with the bath temperature. The point at which the bath and sample temperatures begin to converge is taken as the freezing point of the sample or ice melting point.

KOH

a

1 5 10 15 18 4.7 9.4 14.1 18.8 23.5 2 5 9 12 15 5 10 20 30 5 10 20 30 45 1 5 10 25

0.58 3.04 6.79 11.02 14.29 2.50 5.51 10.21 16.53 25.9 1.14 3.13 6.79 10.73 15.58 2.09 4.56 9.31 17.61 1.24 2.76 7.32 12.76 25.09 0.69 3.74 8.46 38.55

0.0 0.2 0.3 0.0 0.1 0.1 0.0 0.1 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.0 0.2 0.0 0.1 0.1 0.2 0.0 0.2 0.0 0.0 0.2 0.1

0.56 3.07 6.68 11.12 14.36 2.47 5.57 10.04 16.73 26.65 1.19 3.32 7.01 10.71 15.55 2.09 4.46 7.12 18.66 1.24 2.76 6.51 11.82 25.18 0.61 3.50 8.43 37.76

0.02 -0.03 0.11 -0.10 -0.07 0.03 -0.06 0.17 -0.20 -0.75 -0.05 -0.19 -0.22 0.02 0.03 0.00 0.10 2.19 -1.05 0.00 0.00 0.81 0.94 -0.09 0.08 0.24 0.03 0.79

σexp is the average deviation between runs.

3. Thermodynamic Modeling temperature as the latent heat of formation is released. The temperature of the bath is then ramped up at a constant rate and the temperature of the bath, reference cell and the sample cells are recorded. The temperature of the sample will remain lower than the bath temperature as thermal energy is required to melt the ice. Once the last crystal of ice has melted the sample temperature will converge with the bath temperature. The point at which the bath and sample temperatures begin to converge can be easily identified and is taken as the freezing point of the sample or ice melting point (Figure 2). In fact in all experiments the melting point of ice in the presence of single or mixed aqueous electrolyte solutions is measured (i.e., correct thermodynamic equilibrium point) although this is commonly reported as freezing point depression of the above aqueous solutions. For each system, the freezing points were measured five times to check the repeatability and consistency. The final freezing point of the aqueous solution is taken as the average of all the runs.

For a system at equilibrium, from a thermodynamic viewpoint, the chemical potential of each component throughout the system must be uniform. For an isothermal system this will reduce to the equality of fugacity of each component in different phases. The fugacity of water in an aqueous electrolyte solution is equal to that in the ice phase at the freezing point of the solutions. The fugacity of water in salt free aqueous phase has been calculated by the well-proven cubic-plus-association (CPA) EoS.TheCPAEoScombinesthewell-knownSoave-Redlich-Kwong (SRK) EoS for describing the physical interactions with Wertheim’s first-order perturbation theory, which can be applied to different types of hydrogen-bonding compounds. Water parameters (water is the only associating component here) in the CPA EoS have been determined from pure liquid water by Kontogeorgis et al.2 When salt is present, the fugacity of nonelectrolyte compound in the aqueous phase is calculated by combining the EoS with the Debye–Hückel electrostatic contribution term.2 The CPA EoS has been selected for the modeling as it adequately describes the effect of alcohols and water on

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 3985

Figure 3. Freezing point depression in the presence of different concentrations of NaCl: model predictions (solid line); experimental data from Rivett11 (solid triangle), Rodebush12 (open circle), Schroeder et al.13 (solid square), Bergman and Vlasov14 (open triangle), Nallet and Paris15 (plus sign), Gibbard and Grossmann16 (open square), Potter et al.17 (open diamond), Hall et al.18 (grey square), Oakes et al.19 (solid diamond), Tohidi et al.20 (grey diamond), the CRC handbook21 (grey triangle), and this work (solid circle).

Figure 5. Freezing point depression in the presence of different concentration of MgCl2: model predictions (solid line); experimental data from Loomis25 (plus sign), Jones and Getman26 (open square), Jones and Pearce27 (open diamond), Rivett11 (solid square), Rodebush12 (solid diamond), Menzel23 (open triangle), Yanateva28 (solid square), Gibbard and Grossmann16 (solid triangle), Van’t Hoff and Meyerhoffer29 (grey square), and this work.

Figure 4. Freezing point depression in the presence of different concentrations of KCl: model predictions (solid line); experimental data from Hall et al.18 (solid square), Biltz22 (open triangle), Rodebush12 (open circle), Menzel23 (solid triangle), Assarsson24 (solid diamond), and the CRC handbook (solid circle).

Figure 6. Freezing point depression in the presence of different concentration of CaCl2 and CaBr2: model predictions for the CaCl2-water system (solid line); experimental data from Bakhuis Roozeboom30 (solid diamond), Jones and Getman26 (open triangle), Jones and Bassett31 (open diamond), Jones and Pearce27 (plus sign), Rodebush12 (solid square), Yanateva28 (open circle), Gibbard and Fong32 (grey outlined triangle), Oakes et al.19 (solid triangle), and this work (solid circle); model predictions for the CaBr2-water system (dotted line); experimental data from Jones and Getman26 (open triangle) and Jones and Bassett31 (open diamond).

phase equilibria.3 In the present work, the CPA EoS has been extended to take into account the effect of salt on freezing point depression (∆T) in the presence of aqueous electrolytes solution. 3.1. Modeling of the Ice Phase. The fugacity of a pure solid can (as for a supersaturated pure liquid) be calculated using the Poynting correction, i.e., assuming that the volume of the supersaturated phase is constant at the volume for the saturated phase.5,6 For ice, the expression becomes

(

)

VI(P - PIsat) exp (1) RT where fwI is the fugacity of water in the ice phase, φwsat is the water fugacity coefficient in the vapor phase at pressure equal to the ice vapor pressure, PIsat is the ice vapor pressure (Pa), VI is the ice molar volume (m3/mol), R is the universal gas constant, and P and T is the system pressure (Pa) and temperature (K), respectively. The ice molar volume, VI, (m3/mol) is calculated using the following expression:7 fwI ) φwsatPIsat

VI ) 19.629 × 10-6 + 2.2364 × 10-9(T - 273.15)

(2)

and the ice vapor pressure, PIsat, is calculated using8

( )

PIsat ) a1(1 - θ-1.5) + a2(1 - θ-1.25) Pn a1 ) -13.9281690 a2 ) 34.7078238 pn/Pa ) 611.657 Tn/K ) 273.16

ln

(3)

where θ is reduced temperature (T/Tn) and PIsat is the ice vapor pressure in pascal. 3.2. Modeling of Salt-Free Aqueous Phase. Species forming hydrogen bonds often exhibit unusual thermodynamic behavior due to the strong attractive interactions between molecules of the same species (self-association) or between molecules of different species (cross-association). These interactions may strongly affect the thermodynamic properties of the fluids. Thus, the chemical equilibria between clusters should be taken into

3986 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

Figure 7. Freezing point depression in the presence of different concentrations of ZnCl2, ZnBr2, and KOH: model predictions for the ZnCl2-water system (solid line); experimental data from the CRC handbook21 (grey square), Jones34 (grey diamond), Chambers and Frazer35 (solid square), Biltz22 (solid triangle), Jones and Getman26 (solid square), International critical tables36 (open circle), and this work (solid circle); model predictions for the ZnBr2-water system (dotted line); experimental data from this work (solid circle); model predictions for the KOH-water system (dashed line); experimental data from Linke and Seidell33 (open square), the CRC handbook21 (solid square), International critical tables36 (open circle), and this work (solid circle).

Figure 10. Vapor pressure of water in the presence of different concentrations of ZnCl2 at 398.15 K: model predictions for the ZnCl2-water system (solid line); experimental data from Safarov et al.39 (open circle). Table 4. Freezing Point Depression (∆T) of Aqueous Solutions of NaCl and 3 mass % CaCl2a error mass % of NaCl in aqueous solution ∆T ((0.1 K) σexp ∆Tcal ((0.1 K) (∆Texp - ∆Tcal) 1 5 10 15 18 a

2.14 5.38 9.97 14.81 20.72

0.1 0.4 0.5 0.5 0.4

-0.22 0.63 1.15 -0.26 0.41

2.36 4.75 8.82 15.07 20.31

σexp is the average deviation between runs.

Table 5. Freezing Point Depression (∆T) of Aqueous Solutions of CaCl2 and 3 mass % KCla error mass % of NaCl in aqueous solution ∆T ((0.1 K) σexp ∆Tcal ((0.1 K) (∆Texp - ∆Tcal) 5 10 15 20 25 a

Figure 8. Vapor pressure of water in the presence of different concentration of NaCl at 373.15 K: model predictions for the NaCl-water system (solid line); experimental data from Colin et al.37 (open circle).

4.63 8.67 15.38 23.37 33.7

0.2 0.3 0.6 0.6 0.3

4.17 8.02 13.96 23.05 36.46

0.46 0.65 1.42 0.32 -2.76

σexp is the average deviation between runs.

Table 6. Freezing Point Depression (∆T) of Aqueous Solutions of NaCl and 3 mass % KCla error mass % of NaCl in aqueous solution ∆T ((0.1 K) σexp ∆Tcal ((0.1 K) (∆Texp - ∆Tcal) 1 2 5 10 12 a

2.04 2.77 5.07 8.89 10.74

0.1 0.1 0.2 0.1 0.0

1.96 2.59 4.61 8.53 10.37

0.08 0.18 0.46 0.36 0.37

σexp is the average deviation between runs.

state that combines the cubic SRK equation of state and an association (chemical) term, is used here for fugacity calculations. The CPA can be expressed for pure compound in terms of pressure P, as9 P)

Figure 9. Vapor pressure of water in the presence of different concentrations of MgCl2 at 303.15 K: model predictions for the MgCl2-water system (solid line); experimental data from Patil et al.38 (grey circle).

account in order to develop a reliable thermodynamic model. The cubic-plus-association (CPA) model, i.e., an equation of

a RT RT + F V - b V(V + b) V

∑ [ X1

A

A

]

1 ∂XA 2 ∂F

(4)

where the physical term is that of the SRK EoS and the association term is taken from the SAFT EoS.10 The summation is over all association sites, and the mole fraction XA of molecules not bonded at site A can be rigorously defined as

(

XA ) 1 + F

∑X ∆ B

B

)

AB -1

(5)

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 3987 Table 7. Freezing Point Depression (∆T) of Aqueous Solutions of MgCl2 and 3 mass % NaCla error mass % of NaCl in aqueous solution ∆T ((0.1 K) σexp ∆Tcal ((0.1 K) (∆Texp - ∆Tcal) 1 2 5 10 15 a

2.82 3.57 6.24 12.44 20.98

0.2 0.2 0.5 0.5 0.3

2.41 3.09 5.44 11.14 20.45

0.41 0.48 0.8 1.3 0.53

σexp is the average deviation between runs.

1 1 - 1.9η where η is the reduced fluid density given as g(d)sim )

1 b η ) bF ) (8) 4 4V where F is the pure compound density. The energy parameter of the CPA EoS, a, is defined using a Soave-type temperature dependency: a ) a0[1 + C1(1 - √Tr)]

2

Figure 11. Freezing point depression of aqueous solutions of NaCl and 3 mass % CaCl2: model predictions (solid line); experimental data from this work (grey circle).

Figure 12. Freezing point depression of aqueous solutions of CaCl2 and 3 mass % KCl: model predictions (solid line); experimental data from this work (grey circle).

(7)

(9)

The covolume parameter b is assumed to be temperature independent, in agreement with most published equations of state. The selection of association scheme and the maximum number of association sites can be found for a compound by looking at the location of its constituting hydrogen atoms and lone pairs on acceptor atom (oxygen for water molecules). Huang and Radosz10 have classified eight different association schemes, which can be applied to different molecules depending on the number and type of associating sites. The four-site (4C) association scheme is used for highly hydrogen-bonded substances, such as water, which have two proton donors and two proton acceptors per molecule. The CPA pure compound parameters, used for the fugacity calculations in this paper, have been obtained by Kontogeorgis et al.2 and are listed in Table 1.

Figure 13. Freezing point depression of aqueous solutions of NaCl and 3 mass % KCl: model predictions (solid line); experimental data from this work (open circle).

where F is the molar density of the fluid, XA is related to the association strength between site A and site B on the molecule, and ∆AB, the association strength, is the key quantity in the CPA EoS. Both XA and ∆AB depend on the structure of the molecule and the number and type of sites. The association (binding) strength between site A and site B is given by

[ ( ) ]

εAB - 1 βb (6) RT where g(d)sim is the simplified expression for radial distribution function suggested by Kontogeorgis et al.,2 b is the covolume parameter from the cubic part of the model, β and ε are the association volume and energy parameters of CPA, respectively. The latter two could be obtained from spectroscopy data but are in most cases estimated along with the parameters of the physical term. The simplified expression for radial distribution function is given by2 ∆AB ) g(d)sim exp

Figure 14. Freezing point depression of aqueous solution of MgCl2 and 3 mass % NaCl: model predictions (solid line); experimental data from this work (solid circle).

3988 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

3.3. Modeling of Aqueous Electrolyte Solutions. When electrolytes are present, the fugacity of a nonelectrolyte compound is calculated by combining the equation of state with the Debye–Hückel electrostatic contribution for taking into the account the effect of salt:4 lnφi ) lnφEoS + lnγEL i ) 1, 2, ... , N i i

(10)

where N is the number of nonelectrolyte components, φi is the fugacity coefficient of component i, φiEoS is the fugacity coefficient of component i calculated by an EoS, neglecting the electrostatic effect, and γEL i is the contribution of the electrostatic term. Using the Debye–Hückel activity coefficient, the final form of the second term in eq 10 becomes lnγDH i )

2AMmhis 3

B

f(BI1⁄2)

(11)

where Mm is the salt-free mixture molecular weight determined as a molar average, and his is the interaction coefficient between the dissolved salt and a nonelectrolytic compound. The function f(BI1/2) is obtained from 1 - 2 ln(1 + BI1⁄2) (12) (1 + BI1⁄2) where I is the ionic strength. The parameters A and B are given by f(BI1⁄2) ) 1 + BI1⁄2 -

A)

1.327757 × 105dm1⁄2 (ηmT)3⁄2

B)

6.359696dm1⁄2 (ηmT)1⁄2

(13)

where dm is the density of the salt-free mixture and ηm is the salt-free mixture dielectric constant which can be calculated from ηm ) xwηw

(14)

xw and ηw are the salt-free mole fraction and dielectric constant of water, respectively. The dielectric constants of dissolved nonelectrolyte compounds have been neglected, relative to that of water. The binary interaction parameter, hws, between water and dissolved salt for nine electrolytes has been optimized by expressing hws as a function of salt concentration and temperature by using experimental freezing point depression data of aqueous solutions in the presence of salt, by optimizing constants A-E in the binary interaction parameter relation (shown below). hws )

A C + BW2 + 2 + DT + E W W

(15)

where T is temperature in degrees Celsius and W is salt concentration in weight percent. A, B, C, D, and E are fitting constants. The optimized interaction parameters are presented in Table 2. 4. Results and Discussion The available experimental data have been collected from the literature and were used for the tuning of the interaction coefficients. None of the experimental data generated in this laboratory have been used in the optimization process, thus providing independent data for validation of the model. The new experimental freezing point depressions of different concentrations of single salt measured in this work are given in Table 3. Figures 3–7 present the results of the thermodynamic modeling for freezing point depression as well as the new experimental freezing point depressions measured in this work as a reference for evaluation. Figures 8–10 present the predicted

vapor pressure of water for different concentrations of single salts against literature data. Experimental and calculated freeing point depression for four mixed electrolyte solutions (H2O-NaC1-KCl, H2O-NaC1CaCl2, H2O-KC1-CaCl2, and H2O-NaC1-MgCl2) measured by a reliable heating technique are presented in Tables 4–7. As shown in Figures 11–14, the model can accurately predict the freezing point depression; good agreement with the data generated in this work is observed. 5. Conclusions Literature data on water vapor pressure and ice freezing point depression in the presence of electrolyte solutions have been used in optimization of the water-salt interaction coefficient for eight common electrolyte solutions (NaCl, KCl, KOH, CaCl2, MgCl2, CaBr2, ZnCl2, and ZnBr2). The fugacity of saltfree aqueous phase was calculated by the CPA EoS, and the Debye–Hückel electrostatic term was used for taking into the account the effect of salt on water fugacity in the presence of electrolytes. A few freezing point measurements for aqueous mixed electrolyte solutions were performed in this laboratory. Model predictions are validated against these independent experimental data. Despite the wide range of temperature, salt concentrations, and type of data, the model was found to be very successful in predicting the phase behavior of electrolyte solutions, i.e. water vapor pressure and freezing point depressions due to the presence of salts. Acknowledgment This work is part of an ongoing Joint Industrial Project (JIP) conducted at the Institute of Petroleum Engineering, HeriotWatt University. The JIP is supported by Clariant Oil Services, Petrobras, Statoil, TOTAL, and the UK Department of Business, Enterprise and Regulatory Reform (BERR), which is gratefully acknowledged. Literature Cited (1) Anderson, R.; Llamedo, M.; Tohidi, B.; Burgass, R. W. Experimental Measurement of Methane and Carbon Dioxide Clathrate Hydrate Equilibria in Mesoporous Silica. J. Phys. Chem. B 2003, 107, 3507. (2) Kontogeorgis, G. M.; Yakoumis, I. V.; Meijer, H.; Hendriks, E. M.; Moorwood, T. Multicomponent Phase Equilibrium Calculations for WaterMethanol-Alkane Mixtures. Fluid Phase Equilib. 1999, 158, 201. (3) Folas, G. K.; Derawi, S. O.; Michelsen, M. L.; Stenby, E. H.; Kontogeorgis, G. M. Recent Applications of the Cubic-Plus-Association (CPA) Equation of State to Industrially Important Systems. Fluid Phase Equilib. 2005, 228, 121. (4) Aasberg-Petersen, K.; Stenby, E.; Fredenslund, A. Prediction of HighPressure Gas Solubilities in Aqueous Mixtures of Electrolytes. Ind. Eng. Chem. Res. 1991, 30, 2180. (5) Smih, J. M.; Van Ness, H. C. Introduction to Chemical Engineering Thermodynamics;McGraw-Hill Inc.: New York,1987. (6) Anderson, F. E.; Prausnitz, J. M. Inhibition of Gas Hydrates by Methanol. AIChE J. 1986, 32, 1321. (7) Tohidi, B.; Danesh, A.; Todd, A. C. Modelling Single and Mixed Electrolyte Solutions and its Applications to Gas Hydrates. Trans. Inst. Chem. Eng. 1995, 73, 464. (8) Wagner, W.; Saul, A.; Pruss, A. International Equations for the Pressure along the Melting and along the Sublimation Curve of Ordinary Water Substance. J. Phys. Chem. Ref. Data 1994, 23, 515. (9) Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An Equation of State for Associating Fluids. Ind. Eng. Chem. Res. 1996, 35, 4310. (10) Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 2284.

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ReceiVed for reView January 4, 2008 ReVised manuscript receiVed March 5, 2008 Accepted March 6, 2008 IE800017E