Can n-Propanol Form Hydrate? - Industrial & Engineering Chemistry

Feb 5, 2008 - Youngjun Lee , Seungmin Lee , Sungwon Park , Yunju Kim , Jong-Won Lee , and Yongwon Seo. The Journal of Physical Chemistry B 2013 ... Mo...
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Ind. Eng. Chem. Res. 2008, 47, 1689-1694

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Can n-Propanol Form Hydrate? Antonin Chapoy,† Ross Anderson,† Hooman Haghighi,† Terry Edwards,‡ and Bahman Tohidi*,† Centre for Gas Hydrate Research, Institute of Petroleum Engineering, Heriot-Watt UniVersity, Edinburgh EH14 4AS, Scotland, United Kingdom, and School of Oil and Gas Engineering, UniVersity of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia

Alcohols are generally considered hydrate inhibitors. The fact that 2-propanol, in addition to tert-butanol can form hydrates, suggests further investigation of this issue is required. In light of this, it was decided to assess the potential for hydrate formation by n-propanol. However, there are at present no data concerning its effects on hydrate stability available in the open literature. Here, we present freezing point data of n-propanol solutions (up to 80 mass %). These data suggest existence of a peritectic point at 263.05 K and formation of clathrate hydrate in the n-propanol-water system. To confirm whether n-propanol, like 2-propanol, forms mixed hydrates with structure I formers at elevated pressures, dissociation conditions were measured for aqueous solution of 10, 16.4, and 25 mass % n-propanol in the presence of methane at pressures up to 40 MPa and natural gas at around 10 MPa. The results show that n-propanol does not display a hydrate inhibition effect, which would be expected from an alcohol and may, in fact, take part in clathrate formation. Consequently, n-propanol has been modeled as a hydrate-forming compound by use of a thermodynamic model. Comparisons between experimental hydrate dissociation data and model predictions suggest that n-propanol may take part in structure II hydrate formation, occupying the large cavity of the hydrate structure. Introduction Alcohols are generally considered hydrate inhibitors. All available evidence suggests methanol, the most common alcohol used for hydrate inhibition, does not form clathrates, despite a favorable ratio of molecular size to simple hydrate cavity radii (see Table 1). However, the fact that 2-propanol, in addition to tert-butanol,1 can form hydrates suggests further investigation of this issue is required. The Centre for Gas Hydrate Research, Heriot-Watt University, recently demonstrated the formation of clathrate hydrate in systems of methane-2-propanol-water and natural gas-2-propanol-water. Modeling studies suggested that 2-propanol entered and stabilized the large 51264cavity of structure II (sII) hydrates.2 Subsequent independent Raman spectroscopy studies by Ohmura et al.3 confirmed these findings. In light of this, it was decided to assess the potential for hydrate formation by n-propanol. With respect to molecular size, n-propanol is certainly too small to stabilize the large cavity of structure H (sH) hydrates (the smallest guest known to stabilize the large cavity of sH is adamantane, with a radius of 3.7 Å), but n-propanol could be accommodated in the large cage of sII and potentially stabilize sII (see Table 1). Here, we present freezing point data for n-propanol solutions (up to 80 wt %). These data suggest the existence of a peritectic point at 263.05 K and formation of clathrate hydrate in the n-propanol-water system. To confirm whether n-propanol, like 2-propanol, forms mixed hydrates with small hydrate formers at elevated pressures, dissociation conditions were measured for aqueous solution of 10, 16.4, and 25 mass % n-propanol in the presence of methane at pressures up to 40 MPa and in natural gas around 10 MPa. Data were measured by equilibrium isochoric step-heating methods. The phase-equilibrium temper* To whom correspondence should be addressed. Tel.: +44(0) 131 451 3672. Fax: +44(0) 131 451 3127. E-mail: Bahman.Tohidi@ pet.hw.ac.uk. † Heriot-Watt University. ‡ University of Western Australia.

ature pressure conditions in the above measured systems were compared to the statistical-thermodynamics model predictions in which n-propanol was assumed to be a hydrate inhibitor, or a sII hydrate former, or a sH former. The experimental data were well represented by a model prediction based on the assumption that n-propanol is a sII hydrate former, thereby strongly suggesting the formation of sII hydrate with methane and n-propanol as guest substances. However, confirmation of sII hydrate formation with n-propanol by direct measurement of the hydrate phase is required for a final validation. Experimental Section Materials. Fluid samples used in the experiments were deionized water, methane of 99.99 vol % certified purity, and n-propanol of 99 mol % certified purity (Sigma-Aldrich). Aqueous solutions of water and n-propanol mixed at different ratio of 10, 16.4 and 25 mass % n-propanol aqueous solutions were prepared and used in the experiments. The natural gas mixture used in this work was purchased from BOC. The composition of the natural gas was measured by gas chromatography (GC) and is given in Table 2. Apparatus and Procedures. (A) Differential Temperature Apparatus. Melting point measurements at atmospheric pressure were made by use of an apparatus and method developed at Heriot-Watt University. The apparatus is composed of two platinum resistance temperature (PRT) probes, each surrounded by a 1-cm3 aluminum sheath as shown in Figure 1. The probes are inserted in a stainless steel block placed in a controlledtemperature fluid bath to ensure temperature homogeneity between samples. One probe contains the n-propanol-water mixture, while the second contains a low-temperature bath fluid (as a reference fluid) to measure the bath temperature, which can be ramped between different set points at a constant set rate. The similarity of construction and filling fluid ensures that the two probes have very similar thermal time constants and will lag behind the bath temperature by nearly identical amounts, when the contents of each probe are liquid. The temperature of each probe is measured during the ramp (either heating or

10.1021/ie071019e CCC: $40.75 © 2008 American Chemical Society Published on Web 02/05/2008

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Table 1. Ratios of Guest Radii to Cavity Radius ratio of guest radius to cavity radius sI hydrate

sII hydrate

sH hydrate

guest, radius

512 cavity, 2.55 Åa

512612 cavity,a 2.90 Åa

512 cavity, 2.51 Åa

51264 cavity, 3.33 Åa

512 cavity, 2.51 Åa

435663 cavity, 2.66 Åa

51268 cavity, 4.31 Åa

methanol, 2.3 Å ethanol, 2.8 Å n-propanol, 3.3 Å 2-propanol, 3.33 Åb

0.90 1.10 1.29 1.31

0.79 0.97 1.14 1.15

0.92 1.12 1.31 1.33

0.69 0.84 0.99 1.00

0.92 1.12 1.31 1.33

0.86 1.05 1.24 1.25

0.53 0.65 0.77 0.77

a

Cavity radius minus the van der Waals radius of the water molecule (1.4 Å). b From ref 2.

Table 2. Natural Gas Composition component

mol %

methane ethane propane i-butane n-butane i-pentane n-pentane nitrogen carbon dioxide

88.55 5.05 1.4 0.18 0.28 0.07 1.76 2.67 0.04

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. The melting point of a test solution is determined by an inflection point method. Initially the temperature of the test sample is reduced sufficiently to cause ice or hydrate formation. This can be detected by a rise in sample temperature as the latent heat of formation is released. The temperature of the bath is then raised at a constant rate and the temperature of the bath and the sample is recorded. The temperature of the sample will remain lower than the bath temperature as thermal energy is required to melt the ice and/or hydrate present. Once the last crystal of ice or hydrate 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 melting point of the sample. (B) High-Pressure Apparatus. Figure 2 shows the apparatus used to determine the phase equilibrium conditions. The phase equilibrium is achieved in a cylindrical cell made of stainless steel. The cell volume is about 500 cm3 and it can be operated up to 40 MPa between 243 and 323 K. The equilibrium cell is

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

Figure 2. Schematic illustration of the experimental setup.

held in a metallic jacket heated or cooled by a constanttemperature liquid bath. The temperature of the cell is controlled by circulating coolant from a cryostat within the jacket surrounding the cell. The cryostat is capable of maintaining the cell temperature to within 0.1 K. To achieve good temperature stability, the jacket is insulated with polystyrene board and the pipes (which connect it to the cryostat) are covered with plastic foam. A platinum resistance probe monitors the temperature and is connected directly to a computer for direct acquisition. The pressure is measured by means of a strain gauge pressure transducer mounted directly on the cell and connected to the same data acquisition unit. This system allows real-time readings and storage of temperatures and pressures throughout the different isothermal runs. To achieve a fast thermodynamic equilibrium and to provide good mixing of the fluids, a stirrer with a magnetic motor was used to agitate the test fluids. Prior to the tests, the equilibrium cell was cleaned and evacuated. The aqueous liquid solution of water and n-propanol was loaded into the cell and then the methane gas (or natural gas) was injected into the cell to achieve the desired starting pressure. Once the cell had been charged with the desired components, the mixing was started and the temperature was lowered to form hydrates, their presence being confirmed by pressure drop. The hydrate formation caused a rapid decline in the cell pressure as gas molecules were consumed during the process. The temperature was then increased stepwise, slowly enough to allow equilibrium to be achieved at each temperature step. As temperature increases inside the hydrate region, hydrates would dissociate, causing an increase in the pressure of the cell. This was not the case when the temperature was increased outside the hydrate region. Here, only a small pressure increase was seen, due to thermal expansion. Therefore, the point at which the pressure plotted as a function of the temperature changed sharply was considered the hydrate dissociation point. The procedure was repeated at different pressures in order to determine the hydrate phase boundaries over a wide temperature range. In this work, the hydrate dissociation data were measured for three different concentrations of n-propanol aqueous solutions.

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Thermodynamic Modeling. A general phase equilibrium model based on the uniformity of component fugacities in all phases has been extended to model n-propanol clathrate hydrate equilibria. A description of the thermodynamic model can be found elsewhere.4 In summary, the statistical thermodynamics model uses the Valderrama modification of the Patel and Teja equation of state5 (VPT-EoS) and non-density-dependent mixing rules4 (NDD) for fugacity calculations in all fluid phases. The VPT-EoS is given by

P)

aR(Tr)

RT V - b V(V + b) + c(V - b)

(1)

The NDD mixing rules are applied to describe mixing in the a parameter:

a ) a C + aA

(2)

Table 3. Phase Equilibrium Experimental Data for the Methane-n-Propanol and Water-n-Propanol Systems references

aC )

∑i ∑j xi xj aij

(3)

(4)

where kij is the standard binary interaction parameter (BIP). The term aA corrects for asymmetric interaction, which cannot be efficiently accounted for by classical mixing rules:

a ) A

∑p xp ∑i xi api lpi 2

Npts FOB, %

Dawe et al. (1973)15 Ziekiewicz and Konitz (1991)16 Gabaldon et al. (1996)17 this worka

1

1.55

5

1.66

10

4.96

1

0.00

Water-n-Propanol 360.7-371.3 around 0.1

16

2.91

313.40

0.008-0.011

25

4.12

331.8-372.8

0.03-0.1

82

5.19

264.55-271.55 0.101 325

12

3.50

Experimental liquidus data are for the binary system n-propanol-water.

Table 4. BIPs for the VPT-EoS and NDD Mixing Rules

and the aij parameter is expressed by

aij ) (1 - kij)xai aj

P, MPa

Boyer and Bircher (1960)11 Yaacobi and Ben-Nain 283.15-303.15 0.101 325 (1974)12 Suzuki et al. 313.40-333.40 1.4-0.2 (1990)13 Bo et al. 298.15 0.101 325 (1993)14

a

where aC is given by the classical quadratic mixing rules:

T, K

Methane-n-Propanol 298.15 0.101 325

system

k12 ) k21

l210

methane (1) + propanol (2) water (1) + propanol (2) methane (1) + water (2)

-0.0693

-0.0686

-0.1566

-0.576

0.5044

lpi ) lpi0 - lpi1(T - 273.15)

(7)

where p is the index of polar components and l is the binary interaction parameter for the asymmetric term. The hydrate phase is modeled by use of the solid solution theory of van der Waals and Platteeuw,6 as developed by Parrish and Prausnitz.7 The equation recommended by Holder and Hand8 is used to calculate the heat capacity difference between the empty hydrate lattice and pure liquid water. The Kihara model for spherical molecules is applied to calculate the potential function for compounds forming hydrate phases.9 The thermodynamic model was extended to include n-propanol by (1) modeling the phase behavior of pure n-propanol and introducing its physical constants, (2) optimizing the watern-propanol binary interaction parameter (BIPs) (by use of VLE data for the water-n-propanol system) and also the binary interaction parameters for n-propanol with methane, and (3) optimizing Kihara potential parameters for n-propanol by use of hydrate data. In this work, n-propanol has been added to the thermodynamic model by introducing its physical constants.10 The binary interaction parameter between methane and n-propanol has been optimized by use of aqueous n-propanol solubility data reported in Table 3. A Simplex algorithm and the objective function, FOB, displayed in eq 8 were used to optimize these binary

6.773 -28.31

0

51.72

l121 × 104 0 4.3 0

interaction parameters. The value of the FOB for each reference is listed in Table 3.

(5)

(6)

l211 × 104

-0.0235

1.8302

FOB )

api ) xapai

l120 0

∑| N 1 1

N

xi,exp - xi,cal xi,exp

|

(8)

where N is the number of data points, xi,exp is the measured solubility, and xi,cal is the calculated solubility. These optimized binary interaction parameters are reported in Table 4. The binary interaction parameters between water and npropanol have been optimized by use of VLE data and melting point data reported in Table 3. A similar Simplex algorithm and the objective function, FOB, displayed in eq 9 were used to optimize the binary interaction parameters. The value of the FOB for each reference is also listed in Table 3.

FOB )

1

NVLE

Pi,exp - Pi,cal

∑1 |

NVLE

Pi,exp 1 NM

| ∑|

+

NM

(Ti,expM)i,exp - (Ti,expM)i,cal

1

(Ti,expM)i,exp

|

(9)

where NVLE is the number of VLE data points, Pi,exp is the experimental pressure, Pi,cal is the calculated pressure, NM is the number of melting data points, Ti,exp is the measured melting point, and Ti,cal is the calculated melting point. These BIPs are reported in Table 4. The BIPs between methane and water are set to those reported previously18 (Table 4). The BIPs between other natural components and water are set to those reported previously by Tohidi-Kalorazi.19 The BIPs between the other natural components and n-propanol are set to zero. The hard-core radius, R, of the Kihara potential parameter for n-propanol was calculated from correlations given by Tee et al.20 This value was considered acceptable for hydrate

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Table 5. Experimental Liquidus and Peritectic Data for the Binary System n-Propanol-Water mass % n-propanol

peritectic T, K((0.1)

liquidus T, K((0.1)

5.0 5.0 10.1 10.1 16.4 16.4 16.4 16.4 16.4 16.4 20.0 20.0 30.2 30.2 40.0 50.0 50.0 60.0 70.0 75.0 80.0

262.95 263.05 263.05 263.05 263.05 263.05 263.05 263.05 262.95 263.05 263.05 263.15

271.55 271.65 269.55 269.65 266.75 266.75 266.65 266.75 266.65 266.65 264.35 264.35 262.85 262.75 262.35 261.95 261.85 261.25 259.55 257.65 254.35

modeling, given that predictions are not significantly affected by minor changes in the core radius. The two remaining Kihara potential parameters for n-propanolsthe collision diameter σ and the depth of the energy well swere optimized by use of the experimental hydrate dissociation data for n-propanol obtained in the present study (assuming sII and sH) by using the method of Tohidi-Kalorazi.19 The Kihara potential parameters for methane are taken from TohidiKalorazi.19 We have used the resulting model, as detailed above, to predict H-L-V equilibria for those systems investigated experimentally. Predictions are compared with experimental data in Figures 4-6. It can be seen that predictions are in good agreement with the experimental data, supporting the reliability of the thermodynamic model. Results and Discussions Binary n-Propanol-Water System at Atmospheric Pressure. There are considerable numbers of water-miscible polar organic compounds that are known to form clathrate hydrates in binary systems at atmospheric pressure [e.g., 1,4-dioxane/ tetrahydrofuran (THF)]. In such systems, sII hydrate formation is common, as this structure may form simple hydrates of quite large diameter molecules with only large (51264) cavities needing to be occupied. A good example of this is THF, which forms an essentially stoichiometric sII clathrate of formula THF‚17H2O at atmospheric pressure below temperatures of 278.25 K. As n-propanol is a similarly water-soluble polar organic liquid, it was speculated that evidence for n-propanol clathrate formation might be revealed by binary n-propanol-water data at low temperatures. The system was thus studied by use of the differential temperature-based freezing point apparatus, previously employed for freezing (melting) points of aqueous solutions. The binary n-propanol-water system was investigated up to concentrations of 80 mass % n-propanol (listed in Table 5 and plotted in Figure 3). As can be seen, for lower concentrations of n-propanol, ice is the more stable phase. As temperature is reduced, a peritectic solid-solid transition is reached at around 263.05 K where ice + liquid converts to hydrate + liquid or hydrate + ice. Note that for the purposes of interpretation, it is assumed that n-propanol, like 2-propanol, is forming sII clathrates, an assumption supported by ternary data presented in the next section. At higher n-propanol concentrations in

Figure 3. Experimentally determined binary phase diagram for the system n-propanol-water at atmospheric pressure. Table 6. Experimental Hydrate Dissociation Point for Methane in the Presence of 16.4 Mass % n-Propanol Aqueous Solutiona

a

T, K ((0.1)

P, MPa ((0.008)

295.2 291.05 285.95 281.3

37.60 21.32 10.52 5.77

One mole of propanol per 17 mol of water.

Table 7. Experimental Hydrate Dissociation Point for Methane in the Presence of 10 Mass % n-Propanol Aqueous Solution T, K ((0.1)

P, MPa ((0.008)

293.55 290.75 287.35 282.75

28.75 20.13 12.51 6.95

Table 8. Experimental Hydrate Dissociation Point for Methane in the Presence of 25 Mass % n-Propanol Aqueous Solution T, K ((0.1)

P, MPa ((0.008)

289.1 287.45 285.05 282.85 276.9

16.77 13.58 9.53 7.38 3.52

aqueous solutions (above ∼22 mass %), clathrates are the more stable phase, with very little depression in the dissociation temperature as a function of concentration until concentrations exceed ∼60 mass %. n-Propanol-Water-Methane and n-Propanol-WaterNatural Gas Systems. The data measured in the present study are tabulated in Tables 6-8. A total of 13 P-T equilibrium data points are reported for the n-propanol-water-methane systems for three different concentrations of 10, 16.4, and 25 mass % n-propanol aqueous solutions. It is clear from Figures 4-6 that there are significant deviations between experimental data and predicted hydrate phase boundaries for the n-propanol solutions if n-propanol is considered as a non-hydrate-forming inhibitor. Upon comparison with experimental data for the methane-distilled water system, it is clear that n-propanol has a considerably lower inhibition effect than what would be expected. This is a similar pattern to that seen for 2-propanol and supports formation of mixed methane-n-propanol clathrates. The only feasible explanation for the observed increase in the hydrate stability is that n-propanol enters and stabilizes hydrate structure; thus, it can be considered as a hydrate former. To better understand how n-propanol acts to stabilize hydrates, it is important to establish the particular cavity and structure it can enter. With respect to

Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1693 Table 9. Optimized Kihara Parameters for n-Propanol structure

R, Å

σ*,a Å

/k, Κ

sII sH

1.2664 1.2664

2.873 3.116

248.61 336.86

a R ) collision diameter; σ* ) σ - 2R;  ) depth of energy well; k ) Boltzmann’s constant.

Table 10. Experimental Hydrate Dissociation Point for Natural Gas in the Presence of X ) 10 and X ) 20 Mass % n-Propanol Aqueous Solution

Figure 4. Comparison of the sI methane hydrate equilibrium with the threephase equilibria involving sI hydrate by considering, in turn, n-propanol as non-hydrate former, as sII hydrate former, and as sH hydrate former (10 mass % n-propanol aqueous solution).

Figure 5. Comparison of the sI methane hydrate equilibrium with the threephase equilibria involving sI hydrate by considering, in turn, n-propanol as non-hydrate former, as sII hydrate former, and as sH hydrate former (16.4 mass % n-propanol aqueous solution).

X, mass %

T, K ((0.1)

P, MPa ((0.008)

10 20

289.35 290.55

10.007 9.917

dictions with the assumption that n-propanol is an inhibitor, are gathered in Figures 4-6. Kihara parameters are presented in Table 9. Where n-propanol is assumed to be an inhibitor, predictions are in significant disagreement with the measured experimental hydrate dissociation data (Figure 6). By contrast, the predictions where n-propanol is assumed to be a sII or sH former are close to experimental data. To further investigate the possibility that n-propanol stabilizes sII hydrates, tests were conducted on a natural gas (composition in Table 2) in the presence of 10 and 20 mass % n-propanol aqueous solutions. The measured hydrate dissociation points are presented in Table 10 and plotted in Figure 7. Three possible prediction scenarios are also shown in Figure 7: assumptions that n-propanol is an inhibitor, a hydrate sII former, and a hydrate sH former. Where n-propanol is assumed to be either an inhibitor or a sH former, predictions are in significant disagreement with the measured experimental hydrate dissociation data (Figure 7). By contrast, the closest prediction to experimental data assumes n-propanol to be a sII former.

Figure 6. Comparison of the sI methane hydrate equilibrium with the threephase equilibria involving sI hydrate by considering, in turn, n-propanol as non-hydrate former, as sII hydrate former, and as sH hydrate former (25 mass % n-propanol aqueous solution).

the molecular diameter, n-propanol is too large to fit into any of the cavities of sI hydrates, but it could be accommodated by the large cavities of sII hydrates, as illustrated in Table 1. In terms of sH, n-propanol is probably too small to stabilize the large cavity. It is important to note that size alone does not determine whether a component is a hydrate former because parameters such as the shape and chemical nature of the potential guest molecule are also important. The equilibrium pressure data obtained in the present study are used for tuning the Kihara parameters in the thermodynamic model. The results for hydrate dissociation data for methanewater-n-propanol aqueous solutions, compared to model pre-

Figure 7. Comparison of the sII natural gas hydrate equilibrium with the three-phase equilibria involving sII hydrate by considering, in turn, n-propanol as inhibitor, sII hydrate former, and sH hydrate former. (a) 10 mass % n-propanol aqueous solution; (b) 20 mass % n-propanol aqueous solution).

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Petrobras, Statoil, TOTAL, and the U.K. Department of Trade and Industry, and this support is gratefully acknowledged. We thank Colin Flockhart, Thomas McGravie, and Jim Allison for manufacture/maintenance of experimental equipment. Literature Cited

Figure 8. Experimental heating curve data for a 5.56 mol % (16.4 mass %) n-propanol aqueous solution in the presence of methane. Hydrate dissociation takes place over a very narrow range of temperatures on the hydrate phase boundary for the system: At temperatures below the point of complete dissociation, gas is released from decomposing hydrates (as well as thermal expansion), increasing the cell pressure with each temperature step. After the hydrate dissociation point, and all clathrates have dissociated, a further rise in the temperature will result only in a relatively small pressure rise due to thermal expansion.

This supports the proposal that n-propanol is a hydrate former, occupying the large cavity of sII hydrates. In addition the concentration of 5.56 mol % (16.4 mass %) n-propanol in water should represent the ideal concentration for complete large (51264) sII cavity filling by n-propanol. Figure 8 shows an example of step-heating curve data for the methane-watern-propanol system. As can be seen, hydrate dissociation takes place over a very narrow range of temperatures on the hydrate phase boundary for the system. This indicates essentially congruent melting; that is, the solid- and liquid-phase compositions are equal (with the methane component excluded) at each step. This supports stoichiometric (in terms of n-propanol:water ratios) sII clathrate formation with n-propanol occupying large cavities and methane occupying small (512) cavities to give a hydrate of formula xCH4.C3H7OH‚17H2O. Conclusions We have reported novel experimental incipient three-phase H-L-V equilibrium data for n-propanol clathrate hydrates. The results strongly suggest that n-propanol is a hydrate-forming compound. On the basis of these results, experimental data for n-propanol clathrates have been used in the optimization of Kihara potential parameters for n-propanol hydrates, reported here, facilitating extension of an existing thermodynamic model to predicting the hydrate phase boundary for systems containing n-propanol, taking into account its hydrate-forming and inhibition characteristics. Model predictions show the best agreement with the experimental data when n-propanol is considered as a hydrate former. Both experimental and modeling results suggest that n-propanol forms sII hydrates, occupying the large cavity of this structure. However, confirmation of sII hydrate formation with n-propanol by direct measurement of the hydrate phase is required for a final validation. 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,

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ReceiVed for reView July 26, 2007 ReVised manuscript receiVed November 30, 2007 Accepted December 5, 2007 IE071019E