Examining the Consistency of Water Content Data in Alkanes Using

Article pubs.acs.org/jced

Examining the Consistency of Water Content Data in Alkanes Using the Perturbed-Chain Form of the Statistical Associating Fluid Theory Equation of State Wael A. Fouad, Deepti Ballal, Kenneth R. Cox, and Walter G. Chapman* Department of Chemical and Biomolecular Engineering, Rice University, Texas 77005, United States ABSTRACT: Experimental data available in the literature on the water content of alkanes (C5 and higher) is widely scattered. The accurate determination of water content in hydrocarbons is critical for the petroleum and natural gas industries due to corrosion and hydrate formation problems. A molecular theory with a single parameter fit to water content data is shown to accurately correlate water mole fraction in alkanes from C1 to C16 which are in equilibrium with liquid water or ice. Moreover, a list of experimental data is recommended to the reader based on its agreement with the fundamental equation of state used in this work. An empirical equation is proposed to accurately correlate water content in C5−C16 alkanes for temperatures ranging from 293.15 K to 323.15 K and as a function carbon number.

1. INTRODUCTION Modeling the equilibrium water content of gas and/or liquid hydrocarbons and their mixtures has proven to be of vital importance to the gas and petroleum industries for inherently safe design, operation, and efficient performance of process equipment. The prediction of water content is important in preventing corrosion problems caused by moisture condensation in pipelines or process equipment and in determining the dosage of chemical inhibitors designed to prevent hydrate crystal formation in subsea and terrestrial pipelines. Hydrates have been known to create blockages in fluid transmission lines, causing serious damage to plant equipment, and posing significant safety concerns. Despite the significant importance of these systems in many industries and the efforts to measure the mutual solubilities accurately, significant disagreement exists in the experimental data. The International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST) evaluated the solubility of water in alkanes containing five or more carbon atoms using a method developed by Góral1 based on the Redlich−Kwong equation of state (RK)2 with an additional term that accounts for hydrogen bonding.3 Other significant studies by researchers in this field include that by Tsonopoulos4,5 and Wagner6 in which experimental data for water solubility in hydrocarbons were correlated as a function of carbon number at ambient conditions, Mohammadi et al.7 for predicting water content in methane and ethane systems using the Valderrama modification of the Patel−Teja equation of state8 (VPT EoS) with the nondensity dependent (NDD) mixing rules,9 and Carroll10 for correlating the water content of acid gases using different empirical equations. Yarrison et al.11 followed a successful approach of combining the Peng−Robinson equation of state (PR)12 for modeling the hydrocarbon phase while using an accurate equation of state13 developed by the © 2013 American Chemical Society

International Association for the Properties of Water and Steam (IAPWS) for the pure water phase. Their comparison with data was limited to high pressure solubility data of water in pure supercritical methane and ethane gas. However, still there is a need for a molecular-based model to study the consistency of the experimental data sets across carbon numbers and to predict water content for temperatures, pressures, and hydrocarbons that have not yet been measured. Emborsky et al.14 extended Yarrison’s work by modeling water content in heavier hydrocarbons using the perturbed chainstatistical associating fluid theory (PC-SAFT)15,16 for the hydrocarbon phase instead of PR . Owing to the low solubility of water, hydrogen bonding can be neglected in the hydrocarbon phase, and therefore the proposed model suggested treating water as a nonpolar sphere surrounded by a sea of nonpolar hydrocarbon molecules. The nonpolar core of a water molecule is commonly modeled with a Lennard-Jones potential. The opportunity here is to use the accuracy of the PC-SAFT in modeling mixtures of nonpolar chainlike molecules to evaluate water content data over a range of carbon numbers. The aim is to find an optimum set of parameters for water that best fits water solubility data in normal alkanes (C5−C16) while setting the binary interaction parameter (kij) value as zero. The Lennard-Jones energy parameter, ε/k, was reduced from that commonly used with the PC-SAFT to a value of 207.3 K coming closer to simulation predicted values of around 74 K to 160 K.17 Taking advantage of the Emborsky et al.14 model, this work attempts to review most of the water solubility data in alkanes Special Issue: In Honor of Grant Wilson Received: August 15, 2013 Accepted: November 26, 2013 Published: December 9, 2013 1016

dx.doi.org/10.1021/je400749e | J. Chem. Eng. Data 2014, 59, 1016−1023

Journal of Chemical & Engineering Data

Article

where T is the temperature in Kelvin. Moreover, pure water saturated liquid density and vapor pressure are correlated using the following expression18

found in the literature and arrive to a list of recommended references that match the model predictions within ± 30 % deviation. In addition, this work extends that of previous authors by applying it to hydrocarbon phases that are in equilibrium with the ice phase. The assumption made of modeling water as a nonassociating fluid can be applicable at low temperatures. However, increasing the temperature will cause an increase in water content in the hydrocarbon phase making association and long-range polar interactions more significant. Therefore, we incorporate the association parameters of water in the PC-SAFT to overcome this situation.

⎛ p sat ⎞ T HO ln⎜⎜ 2 ⎟⎟ = c ( −7.8595τ + 1.8441τ1.5 − 11.7866τ 3 T ⎝ pc ⎠ + 22.6807τ 3.5 − 15.9619τ 4 + 1.8012τ 7.5) (5)

ρHsatO 2

2. THERMODYNAMIC MODELING For a water−alkane binary system, the phase equilibrium can be expressed as yH O ϕHsatOp 2 2

x HC)f H(TO, p),pure 2

= (1 −

ρc

− 1.7549τ16/3 − 45.5170τ 43/3 − 674694τ110/3 (6)

(1)

τ=1−

where yH2O is the mole fraction of water in the hydrocarbon rich phase, φHsat2O is the fugacity coefficient of water in the hydrocarbon rich phase, p is the total pressure, xHC is the hydrocarbon mole fraction in the water rich phase, approximated as zero in this work, and f (T,p),pure is the fugacity of pure H2O liquid water evaluated at temperature T and pressure p. Using the fact that the aqueous phase is dominantly water, the activity coefficient of water is assumed to be unity. The fugacity coefficient of water in the hydrocarbon rich phase is determined from the PC-SAFT equation of state (EoS) using ln(ϕHsatO) = 2

μHresO 2

kT

(7)

⎛ ⎛ 1 ⎞2 ρH O (p , T ) = ρHsatO (T ) + (p − pHsatO )⎜⎜2 × 106⎜ ⎟ 2 2 ⎝T ⎠ 2 ⎝ ⎞ ⎛ T − 0.819Tc ⎞ ⎛1⎞ − 464.022⎜ ⎟ + 3.947 exp⎜ ⎟ − 2.924⎟⎟ ⎝T ⎠ Tc ⎝ ⎠ ⎠ (8)

− ln(Z)

where pc, Tc, and ρc are the critical pressure, temperature, and density of liquid water, respectively. Equation 8 is a modification of the Wagner and Pruβ18 saturation pressure correlation that makes the density and, consequently, the liquid volume more accurate at pressures greater than the saturation pressure. 2.2. Ice−Gas Equilibria. The fugacity of water in the ice phase can be estimated in a similar fashion to that of liquid water. The main difference exits in correlating the ice molar volume and vapor pressure. The fugacity of ice can be calculated using the following relationship:19

(2)

⎛ fi = xiγipisat exp⎜ ⎝

ln f H(TO, p),pure = ln[ϕHsatO(T )pHsatO (T )] 2

2

2

⎛ V L (p , T ) ⎞ ⎜ H 2O ⎟ dp ⎜ ⎟ psat ⎝ RT ⎠

∫

p

ywHC =

⎡ ⎛ 274 ⎞⎟⎤ = 1 − 0.00134092747753865 exp⎢9.7⎜1 − ⎥ ⎣ ⎝ T ⎠⎦ + 1.95670·10−3

∫p

p sat

viice ⎞ d p⎟ RT ⎠

(9)

sat where xi, γi, vice i and pi refer to the mole fraction, the activity coefficient, the molar volume, and saturation pressure of component i in the ice phase. Since, the ice phase is assumed to be composed of pure water, the activity coefficient of water is equal to unity. Also, the fugacity coefficient of water in the hydrocarbon phase, φHC w , was taken to be equal to unity in this section. Consequently, the aforementioned equation can be simplified to the following form:19

(3)

where φHsat2O is the fugacity coefficient of water at saturation, VHL 2O is the liquid water molar volume, pHsat2O is the water saturation pressure, R is the universal gas constant, p and T are the pressure and temperature of the system, respectively. The fugacity coefficient of pure liquid water at saturation can be calculated using the following correlation by Yarrison et al.11 The correlation is valid in the temperature range of 274 K to 647 K. ϕHsatO 2

T Tc

The liquid water volume is just the reciprocal of the density which is fitted as a function of temperature in the range of 274 K to 510 K.11

where μHres2O is the chemical potential residual to an ideal gas at the same density as the fluid of interest, Z is the compressibility factor calculated using PC-SAFT, and k is the Boltzmann constant. 2.1. IAPWS Equation of State. Using the Wagner and Pruβ formulation18 allows an accurate water fugacity calculation with minimum parameters. From classical thermodynamics, the fugacity of pure water can be written as

+

= 1 + 1.9927τ1/3 + 1.0997τ 2/3 − 0.5108τ 5/3

vwice =

(4) 1017

⎡ v ice(p − psat ) ⎤ i ⎢ w ⎥ exp RT ⎢⎣ ⎥⎦ ϕwHCp sat pice

19.665 + 0.0022364(T − 273.15) 103

(10)

(11)



Article

Table 1. Fitted Pure Component Parameters for Water σ

molar mass −1

g mol water a

18.01528

ε/k

εAiBi/k

scheme

m

Å

K

K

4C

1.00

3.04

204.7

1920.02

% AADa κ

AiBi

0.0425

p

sat

2.69

% AADa ρsat 5.92

% AAD = (100/npts) ∑npts j |calcj − expj|/expj. sat pice = −5

10(−1032.558/ T + [51.056 log(T )] − 0.0977T + (7.0357·10 7600

)T 2 − 98.512)

(12)

In the aforementioned equations, T is given in Kelvin, vice w is expressed in units of m3 kmol−1, and psat is given in MPa. ice

3. RESULTS AND DISCUSSION The procedure taken in finding an optimized set of pure component PC-SAFT parameters for water combines fitting Figure 2. Model predictions (−) in comparison to experimental data on the solubility of water in (a) hexane by Burd et al.34 (○), Tewari et al.35 (△); (b) octane by Heidman et al.33 (○).

Figure 3. Model predictions (black line) in comparison to experimental data on the solubility of water in (a) heptane by Englin et al.25 (black open circle); Bittrich et al.36 (black open square); Black et al.23 (black open triangle); Budantseva et al.28 (red asterisk); Ghanem et al.37 (red plus sign); Polak et al.24 (red open circle); Schatzberg38 (bold black line); Zel’venskii et al.30 (black open triangle). (b) In hexadecane by Englin et al.25 (black open circle); Schatzberg38 (black open triangle); Hellinger et al.39 (black open square). Figure 1. Model predictions (black line) in comparison to experimental data on the solubility of water at a pressure of 1 atm in (a) pentane by Black et al.23 (black open circle); Polak et al.24 (black open triangle). (b) In hexane by Englin et al.25 (black open circle); Polak et al.24 (red open circle); Sugi et al.26 (∗); Tsonopoulos et al.27 (black open square); Budantseva et al.28 (plus sign); Black et al.23 (red open triangle); Charykov et al.29 (red line); Zel’venskii et al.30 (black open diamond); Roddy et al.31 (green open circle); Benkovski et al.32 (black open triangle). (c) In octane by Englin et al.25 (black open circle), Budantseva et al.28 (black open triangle), Heidman et al.33 (black open square), Polak et al.24 (red open circle), Black et al.23 (red plus sign). Figure 4. Model predictions (black line) in comparison to experimental data on the solubility of water in decane by Namiot et al.40 (black open circle), Economou et al.41 (black open square), Schatzberg et al.38 (red x), Becke et al.42 (black triangle), Hellinger et al.39 (bold green line).

saturated liquid densities and vapor pressures as well as liquid− liquid equilibrium data for the water−alkane binary system. First, water content in n-alkanes (C5−C16) was fitted to the three intrinsic PC-SAFT parameters (m, σ, and ε/k). Water is often modeled in molecular simulations as spherical with a diameter of nearly 3 Å; therefore, the segment chain length (m) 1018



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Table 2. Predictions for Water Content in Nonane, Undecane, Dodecane, and Tridecane at a Pressure of 1 atm T/K 298.15 303.15 298.15 313.15 298.15 313.15 298.15 313.15

104 xw,exp Nonane 5.638 3.232 Undecane 638 1138 Dodecane 6.138 1238 Tridecane 6.138 1338

104 xw,pred 5.6 7.1 6.0 12.4 6.2 12.8

Figure 6. PC-SAFT (black line) and PC-SAFT/IAPWS (red dashes) predictions in comparison to experimental data (black open circle) on the solubility of water in methane by (a) Yarrison et al.11 and (b) Olds et al.47

6.5 13.4

Table 3. The Data Categories for the Solubility of Water in C5+ n-Alkanes alkane

recommended

C6

J. Polak24 Sugi26 J. W. Roddy31 S. D. Burd34

C7

J. Polak24 P. Schatzberg38

C9 C10 C11 C12 C13 C16

doubtful

23

C5

C8

tentative

J. Polak24 L. S. Budantseva28 J. L. Heidman33 P. Schatzberg38 P. Schatzberg38 P. Schatzberg38 P. Schatzberg38 P. Schatzberg38 S. Hellinger39 P. Schatzberg38

C. Black J. Polak24 B. A. Englin25 C. Tsonopoulos27 L.S. Budantseva28 C. Black23 A. K. Charykov29 L. S. Budantseva28 N. A. Ghanem37 H.-J. Bittrich36 Ya. D. Zel’venskii30 J. F. McCants51 B. A. Englin25 B. A. Englin25

A. Yu. Namiot40 S. Hellinger39

Ya. D. Zel’venskii30 V. G. Benkovski32 Y. B. Tewari35

C. Black23

Figure 7. PC-SAFT (black line) and PC-SAFT/IAPWS (red dashed line) predictions in comparison to experimental data (black open circle) on the solubility of water in ethane by (a) Yarrison et al.11 and (b) Reamer et al.48

C. Black23

was set to be unity and the segment diameter was fixed to be 3.04 Å. Calculations showed a lack of sensitivity of water content to changes in the segment diameter. An optimized value for the potential well-depth (ε/k) of 204 K was found to fit the water solubility data in n-alkanes with the minimum possible error. Using an exponential-6 potential model, Errington et al.17 report a value of ε/k = 160 K based on molecular simulations. Taking the dipole moment of water into account using the nonprimitive mean spherical approximation (MSA),20 we found that the long-range polar interactions can be neglected when considering water content in n-alkanes at low temperatures and pressures. Association parameters were included in this work in order to capture hydrogen bonds formed by water in light hydrocarbons at high temperatures where the water content becomes significant. The two PCSAFT parameters for association (εAiBi and κAiBi) were fitted to pure saturated water densities and vapor pressures. Simulations performed by Koh et al.21 obtained a value of 1813 K for the association strength. The aim was to obtain a value of εAiBi that is as close as possible to the simulation value with the least possible error. Again, the association parameters can be safely neglected when considering water content in n-alkanes at low temperatures and pressures. Table 1 summarizes the optimized PC-SAFT parameters for water, fitted to solubility data in normal alkanes with carbon number of five and higher, along with the absolute average deviations (% AAD) in comparison to literature values by Wagner and Pruβ18 for the temperature range of 273.16 K to 606 K with a 2 K interval.

V. G. Benkovski32 A. Becke42 I. G. Economou41

B. A. Englin25

Figure 5. Water content in C5+ n-alkanes as a function of temperature and carbon number at a pressure of 1 atm. Correlation by this work (black line); Tsonopoulos5 (red line). 1019



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Table 4. Comparison between Predicted Values and Experimental Data49,50 for Water Content in Propane

Table 6. Summary of Results Obtained for the Binary System Ethane + Water

T/K

P/Mpa

YW,Exp

YW,Pred

AD %

310.928 310.928 338.706 338.706 338.706 360.928 360.928 360.928 369.65 369.65 369.65 383.15 383.15 383.15 383.15 399.817 399.817 399.817 399.817 422.039 422.039 422.039 422.039 292.65 299.65 AAD %

0.703 0.972 1.007 1.496 1.993 1.310 2.130 3.206 1.427 3.068 4.158 1.737 3.075 4.344 4.950 3.027 4.654 5.599 6.867 4.289 6.398 8.391 9.935 0.819 0.897

0.00954 0.00696 0.0265 0.0170 0.012 0.0497 0.0291 0.0172 0.0637 0.0264 0.0157 0.0809 0.0433 0.0266 0.0203 0.0786 0.0466 0.0360 0.0250 0.101 0.0635 0.0449 0.0388 0.00267 0.00349

0.00910 0.00647 0.0250 0.0164 0.0118 0.0484 0.0287 0.0174 0.0619 0.0265 0.0167 0.0819 0.0439 0.0282 0.0225 0.0788 0.0478 0.0371 0.0274 0.106 0.0670 0.0491 0.0423 0.00265 0.00369

4.606 7.074 5.768 3.918 1.433 2.456 1.454 1.145 2.802 0.272 6.397 1.198 1.508 6.225 10.883 0.361 2.495 3.145 9.552 4.651 5.491 9.361 9.276 0.726 5.654 4.314

ref

Yarrison et al.11 Olds et al.47 Chapoy et al.52 Mohammadi et al.7 Chapoy et al.53 Chapoy et al.54 Oellrich and Althaus55 Oellrich and Althaus55 Tabasinejad et al.56 Folas et al.57 Rigby and Prausnitz58 Yokoyama et al.59 Gillepsie and Wilson60 Kosyakov et al.61 Sultanov et al.62 Althaus et al.55 Kosyakov et al.61 total/AAD %

data points

p range (MPa)

AD %

In Equilibrium with Liquid Water 15 310.9 to 477.5 3.45 to 20.68 46 310.9 to 510.9 2.67 to 35.60 46 283.08 to 318.12 0.992 to 35.09 17 282.98 to 313.12 0.51 to 2.846

T range (K)

9.09 12.06 15.83 1.64

24 22 13

273.15 to 288.55 277.8 to 297.6 283.15 to 293.15

0.56 to 13.15 0.491 to 4.374 0.244 to 1.28

5.78 4.33 4.94

19

273.15 to 288.15

0.5 to 10

3.78

24

422.7 to 461.6

3.67 to 37.06

10.64

7 12

293.15 to 348.15 298.15 to 373.15

1.379 to 10 2.35 to 9.35

4.57 4.13

5

298.15 to 323.15

3.0 to 8.0

5.56

6

323.15 to 348.15

1.379 to 13.79

6.26

1.01 to 6.08 6.48 to 39.233

3.84 13.10

5 10

273.16 to 283.16 423 to 473 In Equilibrium with Ice 7 253.15 to 268.15 3 243.15 to 263.15 386

0.5 to 1.5 1.013 10.03

T range (K)

In equilibrium with liquid water Reamer et al.48 95 310.9 to 510.9 Yarrison et al.11 18 366.5 to 466.5 Mohammadi et 5 282.93 to 293.1 al.7 17 298.15 to 373.15 King and Coan63 Anthony and 9 310.98 to 377.65 McKetta64 Althaus et al.55 10 278.15 to 293.15 total/AAD % 177

p range (MPa)

AD %

1.38 to 68.95 3.45 to 110.32 0.506 to 2.99

8.89 14.14 5.97

2.28 to 3.63 3.42 to 27.85

4.36 5.88

0.5 to 3

1.17 10.12

liquid n-alkanes (C5−C16) are widely scattered. Since PC-SAFT has been shown to accurately model the phase behavior of long and short chain alkanes,22 the model can be used as a useful tool in examining the quality of the literature data. Experimental values that pass through the correlation curve or within ± 5 % deviation are recommended. In addition, data that are ± 30 % from the predicted values are tentative. Pure component parameters used for hydrocarbons throughout this work were obtained from Gross and Sadowski.16 Figure 1 panels a, b, and c show water mole fraction as a function of temperature, at atmospheric pressure, in pentane, hexane, and octane, respectively. Experimental data in Figure 1b,c are somewhat scattered, making it hard to verify that the perturbation theory is capable of capturing the physics behind the system. Moreover, a sensitivity analysis was carried out in Figure 1c to show the effect of varying ε/k on the solubility curve. It was realized that water solubility data in hexane and octane at elevated temperatures and pressures are more consistent with each other and the model. Figure 2 panels a and b show water solubility in hexane and octane at elevated temperature conditions, respectively. This can give an idea about the strength of the model used and supports recommendations made at lower temperatures. A thorough literature review showed that the liquid−liquid equilibrium data for the water−heptane and water−hexadecane systems were the most scattered. Deviations in experimental water mole fractions in the heptane and hexadecane system reached up to 54 % and 44 %, respectively. Figure 3 panels a and b depict the predicted water content as a function of temperature, at atmospheric pressure, in heptane and hexadecane, respectively. Figure 4 depicts water solubility in the hydrocarbon decane phase at elevated temperature and pressure conditions. The model appears to be predicting the solubility curve in an acceptable manner. Generally, deviations in the literature are minimal except for a couple of data points at low temperatures. Table 2 summarizes results obtained for water content in nonane, undecane, dodecane, and tridecane binary systems. Available data from the literature are few; however, they are still highly recommended based on the PC-SAFT prediction. We classify experimental data from the literature into three categories (according to their agreement with the model): recommended, tentative, and doubtful. Recommended data are points that almost lie on the model curve with an absolute average error of < ± 5 %. Tentative data are points that are within ± 30 % deviation from the model curve, otherwise, the data is doubtful. Table 3 summarizes our recommendations of

Table 5. Summary of Results Obtained for the Binary System Methane + Water up to a Pressure of 40 MPa ref

data points

3.11 3.81

3.1. Water Content in Liquid Alkanes (LLE). As previously stated, experimental data for water solubility in 1020



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data for liquid hydrocarbons. Data by Polak et al.,24 Schatzberg38 and Heidman et al.33 are considered the most recommended by this work. This agrees well with previous observations by Tsonopoulos5 and Maczynski et al.43 On the other hand, data by Englin et al.25 and Black et al.23 showed continuous deviations not only from our PC-SAFT predictions, but also from calculations done previously by other researchers.43,44 Finally, it would be useful for engineering applications to correlate water content in liquid hydrocarbons based on results predicted by the model. Tsonopoulos5 succeeded in developing an empirical equation for this purpose which is a function of carbon number at ambient condition. Moreover, this paper extends his work to temperature dependence. Figure 5 demonstrates how water solubility varies as a function of temperature and carbon number. As observed by Tsonopoulos,5 water mole fraction in alkanes increase slightly as a function of carbon number at ambient conditions. However, Figure 5 also shows that the solubility increases as a function of temperature too. The proposed equation for correlating water content in liquid alkanes (C5−C16) at temperatures ranging from 293.15 K to 323.15 K is as follows with an average absolute deviation of 0.86 % compared to PC-SAFT results:

content in ethane gas. Deviations by the PC-SAFT/IAPWS approach were calculated to be less than that in the water− methane binary system. Figure 7 panels a and b demonstrate the predicted water content in ethane gas under high temperature and pressure conditions. Furthermore, deviations in the PC-SAFT/IAPWS approach were found to be small in predicting water content in propane gas. Table 4 summarizes results and deviations (AD = average deviation) calculated for the water−propane binary system as predicted by the model. Tables 5 and 6 summarize results obtained for methane and ethane systems in equilibrium with liquid water and ice. The approach used diverges at high pressures owing to the aforementiond theory limitations. Therefore, errors were analyzed for methane systems up to 40 MPa only for fair comparison. A wide range of temperatures is covered from 243.15 K to 510 K. It can be seen that the consistency among experimental data for both methane and ethane systems is reasonable and the agreement with model predictions is high.

4. CONCLUSION We modeled water content in normal alkanes as a nonpolar sphere surrounded by a sea of hydrocarbon molecules. Because the water solubility is low, self-association and long-range polar interactions between water particles can be neglected at low temperatures and pressures. Lack of agreement among experimental data obtained from different sources is studied, and a set of data is recommended to the reader based on the molecular theory used. Overall, results show that PC-SAFT equation of state can be used as a rigorous engineering tool for various natural gas processing applications.

x w ·104 = exp( −80.8136 + 14.427 ln(T ) + 0.04CN ) (13)

3.2. Water Content in Light Alkanes (VLE). Prediction of the vapor−liquid equilibrium of water-light hydrocarbon systems is critical for industrial applications including natural gas dehydration and hydrate inhibition. As a commonly used pipeline specification, water content in dry natural gas should not exceed a maximum of 7 lb/MMCF, which is equivalent to a dew point temperature of 14 °F.45,46 Therefore, a powerful thermodynamic tool like PC-SAFT can be useful for predicting the above conditions. Pure component parameters used for modeling light hydrocarbons in this work were obtained from Gross and Sadowski.16 Fortunately, most of the data found in the literature for water solubility in light alkanes are consistent with each other with acceptable deviations. As a result, forming a list of recommended references for light hydrocarbon systems will not be attempted. Hydrocarbons in equilibrium with liquid water or ice phase are covered in this section. Figure 6 panels a and b demonstrate the predicted water content in supercritical methane gas under high temperature and pressure conditions. In reference to Figure 6a,b, it is shown that the PC-SAFT/ IAPWS model starts diverging at a relatively high pressure of about 40 MPa. On the other hand, PC-SAFT alone for both the water-rich and alkane-rich phases was able to model the whole range of pressure with the least error. The accuracy of the IAPWS EoS in modeling water liquid is of no doubt as shown previously by Yarrison et al.11 Therefore, the source of error introduced in the PC-SAFT/IAPWS approach can be attributed to the failure of the perturbation theory in calculating the water partial molar volume in the hydrocarbon phase accurately. Also, the dispersion energy parameter (εij) between water and methane might be underestimated as a result of setting the interaction parameter (kij) to zero. Furthermore, the assumption taken to consider the solubility of alkanes in water as negligible is weakest in the case of light hydrocarbons. On the other hand, both errors in calculating water partial molar volume in the hydrocarbon and water phase appear to cancel each other when PC-SAFT alone was used, hence a better prediction. The same discussion can be applied to water

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 1-713-348-4900. Funding

W.A.F. gratefully acknowledges the Abu Dhabi National Oil Company (ADNOC) for financial support through a Ph.D. scholarship. We gratefully acknowledge the financial support of the Robert A. Welch Foundation (Grant No. C-1241) and of RPSEA (Grant No. 10121-4204-01). Notes

The authors declare no competing financial interest.

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REFERENCES

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