Methane and Carbon Dioxide Hydrate Phase Behavior in Small

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Methane and Carbon Dioxide Hydrate Phase Behavior in Small Porous Silica Gels: Three-Phase Equilibrium Determination and Thermodynamic Modeling Yongwon Seo,† Huen Lee,*,† and Tsutomu Uchida‡ Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea, and Gas Hydrate Research Group, Institute for Energy Utilization, National Institute of Advanced Industrial Science and Technology (AIST), 2-17-2-1 Tsukisamu-higashi, Toyohira-ku, Sapporo, Hokkaido 062-8517, Japan Received March 28, 2002. In Final Form: August 6, 2002 Hydrate phase equilibria for the binary CH4 + water and CO2 + water mixtures in silica gel pores of nominal diameters 6.0, 15.0, and 30.0 nm were measured and compared with the calculated results based on van der Waals and Platteeuw model. At a specified temperature, three phase H-LW-V equilibrium curves of pore hydrates were shifted to the higher pressure region depending on pore sizes when compared with those of bulk hydrates. The activities of water in porous silica gels were expressed with a correction term to account for both capillary effect and activity decrease. By using the values of interfacial tension between hydrate and liquid water phases which were recently presented by Uchida et al.,5 the calculation values were in better agreement with the experimental ones. The structure and hydration number of CH4 hydrate in silica gel pores (6.0, 15.0, and 30.0 nm) were found to be identical with those of bulk CH4 hydrate through NMR spectroscopy.

Introduction Gas hydrates are nonstoichiometric crystalline compounds formed when “guest” molecules of suitable size and shape are incorporated in the well-defined cages in the “host” lattice made up of hydrogen-bonded water molecules. These compounds exist in three distinct structures I (sI), structure II (sII), and structure H (sH), which contain differently sized and shaped cages. The sI and sII hydrates consist of two types of cages, whereas the sH hydrate consists of three types of cages.1 Gas hydrates are of particular interest in the petroleum industry as well as in energy and environmental field. Initial interest in gas hydrates began with the discovery that hydrate formation could plug natural gas pipelines. Large masses of natural gas hydrates exist both on-shore buried under the permafrost and off-shore buried under the oceanic and deep lake sediments. Because each volume of hydrate can contain as much as 170 volumes of gas at standard temperature and pressure conditions, naturally occurring gas hydrates in the earth containing mostly CH4 are regarded as future energy resources.1 Recent investigations consider the possibility of sequestering industrially produced carbon dioxide as crystalline gas hydrates in the deep ocean to prevent further release into the atmosphere as greenhouse gas.2 Despite the importance for truly understanding the phase behavior of hydrates in porous media, only a few works have been reported in the literature. Handa and Stupin3 first studied the effect of porous media on equilibrium pressures of CH4 and C3H8 * To whom correspondence should be addressed. Phone: 8242-869-3917. Fax: 82-42-869-3910. E-mail: [email protected]. † Korea Advanced Institute of Science and Technology (KAIST). ‡ National Institute of Advanced Industrial Science and Technology (AIST). (1) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd ed.; Revised and Expanded; Dekker: New York, 1998. (2) Teng, H.; Yamasaki, A.; Chun, M. K.; Lee, H. Energy. 1997, 22, 1111. (3) Handa, Y. P.; Stupin, D. J. Phys. Chem. 1992, 96, 8599.

hydrates. They showed that the equilibrium pressures of CH4 and C3H8 hydrates in silica gel pores were higher than those of the bulk hydrates. Uchida et al.4,5 experimentally determined the equilibrium pressures of CH4, C3H8, and CO2 hydrates in porous glasses of different pore sizes. Seshadri et al.6 and Smith et al.7 reported the pore equilibrium pressure-temperature data of C3H8 and CH4 hydrates, respectively, in silica gels by using the same experimental method suggested by Handa and Stupin.3 Henry et al.8 and Clarke et al.9 reported calculations based on the earlier statistical thermodynamic model to predict hydrate phase equilibria in porous media. They added a correction term to the bulk hydrate model developed by van der Waals and Platteeuw to account for the capillary effect. Recently, Wilder et al.,10 Klauda and Sandler,11 and Smith et al.7 also proposed the calculation methods considering the pore-size distributions because the large discrepancies between the experimental values of Handa and Stupin3 and calculated ones of Henry et al.8 and Clarke et al.9 might be attributed to the assumption of single pore size. However, the pore hydrate equilibrium data experimentally determined and particularly approaching the lower quadruple point were not consistent with the generally expected phase behavior, and therefore, there existed a difficulty for developing the proper pore hydrate model. In this study, to confirm and overcome the inconsistency between experimental and model values, (4) Uchida, T.; Ebinuma, T.; Ishizaki, T. J. Phys. Chem. B 1999, 103, 3659. (5) Uchida, T.; Ebinuma, T.; Takeya, S.; Nagao, J.; Narita, H. J. Phys. Chem. B 2002, 106, 820. (6) Seshadri, K.; Wilder, J. W.; Smith, D. H. J. Phys. Chem. B 2001, 105, 2627. (7) Smith, D. H.; Wilder, J. W.; Seshadri, K. AIChE J. 2002, 48, 393. (8) Henry, P.; Thomas, M.; Clennell, M. B. J. Geophys. Res. 1999, 104, 23005. (9) Clarke, M. A.; Pooladi-Darvish, M.; Bishnoi, P. R. Ind. Eng. Chem. Res. 1999, 38, 2485. (10) Wilder, J. W.; Seshadri, K.; Smith, D. H. Langmuir, 2001, 17, 6729. (11) Klauda, J. B.; Sandler, S. I. Ind. Eng. Chem. Res. 2001, 40, 4197.

10.1021/la0257844 CCC: $22.00 © 2002 American Chemical Society Published on Web 11/01/2002

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Figure 1. Pore-size distributions of silica gels used in this study. (a) 6.0 nm SG, (b) 15.0 nm SG, and (c) 30.0 nm SG.

the equilibrium dissociation pressures for CH4 and CO2 hydrates confined in silica gel pores of nominal diameters 6.0, 15.0, and 30.0 nm were carefully measured and compared with the proposed model calculations considering the interfacial tension between hydrate and liquid water phases for capillary effect. Finally, to check the possible structure transition and the pore size effect on composition change the crystalline structure and hydration number of hydrates formed in silica gel pores of various sizes were identified by using the 13C NMR. Experimental Section Materials. CO2 gas used for the present study was supplied by World Gas (Korea) and had a stated purity of 99.9 mol %. CH4 gas with a minimum purity of 99.95 mol % was supplied by Linde Gas U.K. Ltd (U.K.). The water with ultrahigh purity was supplied from Merck (Germany). Silica gels of nominal pore diameter 6.0 nm (6.0 nm SG) and 15.0 nm (15.0 nm SG) were purchased from Aldrich (USA), and 30.0 nm silica gel (30.0 nm SG) was from Silicycle (Canada). All materials were used without further treatment. The properties of silica gels having three different pore diameters were measured by ASAP 2000 (Micromeritics, USA) and are listed in Table 1. Their pore-size

Table 1. Physical Properties of Silica Gel Samplesa sample

6.0 nm SG

15.0 nm SG

30.0 nm SG

mean particle diameter (µm) mean pore diameter (nm) pore volume (cm3/g) surface area (m2/g)

(33-74) 6.8 (6.0) 0.84 (0.75) 497 (480)

(33-74) 14.6 (15.0) 1.13 (1.15) 308 (300)

(40-75) 30.5 (30.0) 1.17 (-) 111 (100)

a

Values in the parenthesis are vendor data.

distributions were also determined and shown in Figure 1. The used silica gels were first dried at 373 K for 24 h before water sorption. Then, the pore saturated silica gels were prepared by placing these dried silica gels in a desiccator containing degassed and distilled water, evacuating the desiccator, and allowing more than 5 days in order to establish the solid-vapor equilibrium. The total amount of sorbed water in the silica gel pores was confirmed by measuring the mass of silica gels before and after saturation and was found to be almost identical with the pore volume of each silica gel. Apparatus and Procedure. A schematic diagram and detailed description of the experimental apparatus for hydrate phase equilibria was given in the previous papers.12,13 The apparatus was specially constructed to measure accurately the hydrate dissociation pressures and temperatures. The equilib-

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Seo et al. Table 2. Kihara Potential Parameter for Guest-Water Interaction CH4

a (Å)

σ (Å)

/k (Å)

0.3

3.2408

153.2

CO2

a (Å)

σ (Å)

/k (Å)

0.72

2.9925

168.3

component i in all phases which coexist simultaneously

ˆf H f Li ) ˆfVi () f Iw) i ) ˆ

(1)

where H stands for the hydrate phase, L for the waterrich liquid phase, V for the vapor phase, and I for the ice phase. The chemical potential difference between the empty H hydrate and filled hydrate phases, ∆µMT-H () µMT w w - µw ), is generally derived from statistical mechanics in the van der Waals and Platteeuw model14

νm ln(1 - ∑θmj) ∑ m j

H ) µMT ∆µMT-H w w - µw ) -RT

Figure 2. P-T trace for determination of final equilibrium dissociation point (15.0 nm SG). rium cell was made of 316 stainless steel and had an internal volume of about 50 cm3. The experiment for hydrate-phase equilibrium measurements began by charging the equilibrium cell with about 25 cm3 of silica gels containing pore water. After the equilibrium cell was pressurized to a desired pressure with CO2 or CH4, the whole main system was slowly cooled to 263 K. When pressure depression due to hydrate formation reached a steady-state condition, the cell temperature was increased at a rate of about 0.1 K/h. The nucleation and dissociation steps were repeated at least two times in order to reduce hysteresis phenomenon. The equilibrium pressure and temperature of three phases (hydrate (H)-water-rich liquid (LW)-vapor (V)) were determined by tracing the P-T profiles from hydrate formation to dissociation. Unlike the bulk hydrate, in the case of hydrates in porous silica gels, a gradual change of slope around the final hydrate dissociation point was observed due to the pore-size distribution. As a consequence, it becomes, of course, very difficult to determine the unique equilibrium dissociation point in the P-T profile measured for the porous silica gels. To overcome the inherent difficulties the dissociation equilibrium point in porous silica gels was chosen in the present study as the cross point between the maximum inclination line and complete dissociation line (Figure 2). As indicated by Uchida et al.,4 this unique point corresponds to the dissociation one in the pores of the mean diameter of used silica gels. To identify crystalline structure and hydration number of CH4 hydrate formed in silica gel pores and compare them with those of the CH4 hydrate formed in the bulk state, a Bruker 400 MHz solid-state NMR spectrometer was used in this study. The NMR spectra were recorded at 200 K by placing the hydrate samples within a 4 mm o.d. Zr-rotor that was loaded into the variable temperature (VT) probe. All 13C NMR spectra were recorded at a Larmor frequency of 100.6 MHz with magic angle spinning (MAS) at about 2-4 kHz. The pulse length of 2 µs and pulse repetition delay of 20 s under proton decoupling were employed when the radio frequency field strengths of 50 kHz corresponding to 5 µs 90° pulses were used. The downfield carbon resonance peak of adamantane, assigned a chemical shift of 38.3 ppm at 300 K, was used as an external chemical shift reference.

Thermodynamic Model The equilibrium criteria of the hydrate-forming mixture are based on the equality of fugacities of the specified (12) Seo, Y.; Lee, H. Environ. Sci. Technol. 2001, 35, 3386. (13) Seo, Y. T.; Lee, H. J. Phys. Chem. B 2001, 105, 10084.

(2)

where νm is the number of cavities of type m per water molecule in the hydrate phase and θmj is the fraction of cavities of type m occupied by the molecules of component j. This fractional occupancy is determined by a Langmuirtype expression

θmj )

CmjˆfVj 1+

∑k

(3)

CmkˆfVk

where Cmj is the Langmuir constant of component j on the cavity of type m and ˆfVj the fugacity of component j in the vapor phase with which the hydrate phase is in equilibrium. The Langumuir constant, Cmj, is

Cmj )

4π kT

∫0∞ exp[

]

-ω(r) 2 r dr kT

(4)

where k is the Boltzmann’s constant, r is the radial distance from the cavity center, and ω (r) is the spherical-core potential. In the present study, the Kihara potential with the spherical-core is used for the cavity potential function because it has been reported to give better results than the Lennard-Jones potential for calculating the hydrate dissociation pressures.15 The optimized Kihara potential parameters used in this study are presented in Table 2. Holder et al.16 suggested the method to simplify the chemical potential difference between empty hydrate and reference state as follows

∆µ0w ∆µMT-I w ) RT RT ∆µ0w ∆µMT-I w ) RT RT

∆hMT-I w dT + T0 RT2

∫

∫T

T 0

T

∫0

P

∆υMT-I w dP RT

(5)

∆hMT-I + ∆hfus w w

dT + RT2 MT-I + ∆υfus P ∆υw w dP - ln aw (6) 0 RT

∫

where T0 is 273.15 K, the normal melting point of water, (14) van der Waals, J. H.; Platteeuw, J. C. Adv. Chem. Phys. 1959, 2, 1. (15) Mckoy, V.; Sinanoglu, O. J. Chem. Phys. 1963, 38, 2946. (16) Holder, G. D.; Corbin, G.; Papadopoulos, K. D. Ind. Eng. Chem. Fundam. 1980, 19, 282.

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∆µ0w is the chemical potential difference between empty hydrate and water at T0 and zero absolute pressure, and ∆hwfus and ∆υwfus are respectively the molar difference in enthalpy and volume between ice and liquid water. As pointed out by Parrish and Prausnitz,17 the molar difference in enthalpy and volume between empty hydrate and ∆υMT-I , is assumed to be independent and ice, ∆hMT-I w w of temperature and pressure, but only depends on the type of hydrate structure. The fugacity of water in the filled hydrate lattice, ˆf H w, is calculated by either of the following two expressions depending on the equilibrium temperature

(

)

(

)

∆µMT-H ∆µMT-I w w RT RT

I ˆf H w ) f w exp

(7)

or L ∆µMT-H ∆µMTw w RT RT

L ˆf H w ) f w exp

(8)

Using the Clausius-Clapeyron equation, the fugacity of ice is related to that of pure liquid water by the following equation

(

f Iw ) f Lw exp -

∫T

T 0

∆hfus w RT2

dT +

∫0

P

)

∆υfus w dP RT

VL2 cos θ σHW rRT

Table 3. Equilibrium Pressure-Temperature Data for CH4 Hydrate in Silica Gel Pores

(9)

6.0 nm SG

This equation does not need the expression of the vapor pressure of ice and only uses the physical property difference between the ice and supercooled liquid water. When we insert this equation into eq 7, the resulting expression for the fugacity of water in the filled hydrate phase is exactly equal to eq 8. Therefore, regardless of temperature range of the hydrate system considered, we can obtain a unique expression for the fugacity of water in the filled hydrate phase. All of the parameter values in eq 9 were obtained from the literature. Here, the fugacities of supercooled water and all components in the vapor phase, f Lw and ˆfVj , were calculated using the SoaveRedlich-Kwong (SRK) equation of state incorporated with the modified Huron-Vidal second order mixing rule.18,19 Any appropriate excess Gibbs energy model for the VLE calculations can be used for the Huron-Vidal mixing rules. However, in the present study, the modified UNIFAC group contribution model was used with the structural and interaction parameters given elsewhere.20 The details of the model description were given in our previous paper.21 In the present study, the pores of silica gels were completely saturated with water, and thus, in the H-LW-V equilibrium, the pores are completely filled with liquid water and hydrate in equilibrium with bulk gas. The decrease of water activity in porous silica gels mainly due to capillary effect occurring by the presence of geometrical constraints can be expressed as8,9

ln aw ) ln(xwγw) -

Figure 3. Hydrate phase equilibria of the binary CH4 + water mixtures in silica gel pores.

(10)

where VL is the molar volume of pure water, θ is the wetting angle between pure water and hydrate phases, σHW is the (17) Parrish, W. R.; Prausnitz, J. M. AIChE J. 1972, 11, 26. (18) Dahl, S.; Fredenslund, A.; Rasmussen, P. Ind. Eng. Chem. Res. 1991, 30, 1936. (19) Soave, G. Chem. Eng. Sci. 1972, 27, 1197. (20) Dahl, S.; Michelsen, M. L. AIChE J. 1990, 36, 1829. (21) Yoon, J. H.; Chun, M. K.; Lee, H. AIChE J. 2002, 48, 1317.

15.0 nm SG

30.0 nm SG

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

275.30 276.65 277.95 279.35 279.95 280.95

5.17 6.19 7.20 8.275 9.326 10.5

277.15 279.15 280.45 281.75 282.88 283.70

4.825 6.06 7.16 8.243 9.275 10.285

276.33 278.30 280.55 282.15 283.33 284.53

4.012 4.948 6.175 7.30 8.285 9.638

interfacial tension between hydrate and liquid water phases, and r is the pore radius. Results and Discussion Three-phase H-LW-V equilibria of CH4 and CO2 hydrates confined in silica gel pores with nominal diameters 6.0, 15.0, and 30.0 nm were measured between lower and upper quadruple point temperatures. Hydrate equilibrium data of the binary CH4 + water mixtures were presented along with model calculations in Figure 3 and listed in Table 3. All H-LW-V lines of CH4 hydrates in silica gel pores were shifted to the lower temperature and higher pressure region when compared with that of bulk hydrate. As expected, the decrease of pore diameter made the equilibrium line more shifted toward lower temperature at constant pressure. This inhibition behavior that occurred in silica gel pores was also observed in several recent investigations3-7 and can appear similarly for melting point depression of ice confined in small pores.24 For a close comparison, the pore hydrate data reported in the literature were all included in Figure 3: Handa and Stupin3 for 15.0 nm pores, Uchida et al.5 for 6.0 and 30.0 nm pores, and Smith et al.7 for 6.0 and 15.0 nm pores. The present experimental data were found to be in good agreement with those of Uchida et al.5 but largely deviated from those of Handa and Stupin3 and Smith et al.,7 even (22) Deaton, W. M.; Frost, E. M. U.S. Bur. Mines Monogr. 1946, 8, 1. (23) Larson, S. D. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 1955. (24) Handa, Y. P.; Zakrzewski, M.; Fairbridge, C. J. Phys. Chem. 1992, 96, 8594.

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Figure 4. Hydrate phase equilibria of the binary CO2 + water mixtures in silica gel pores. Table 4. Equilibrium Pressure-Temperature Data for CO2 Hydrate in Silica Gel Pores 6.0 nm SG

15.0 nm SG

30.0 nm SG

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

274.30 275.30 276.15 276.71 277.65

2.215 2.664 3.072 3.44 3.89

272.30 274.25 275.65 276.93 278.34 278.98 279.70

1.447 1.865 2.283 2.662 3.216 3.598 3.918

271.80 273.65 276.05 277.95 279.25 280.45 281.35

1.13 1.433 1.95 2.418 2.913 3.40 3.88

though Uchida et al.5 used Vycor porous glasses as porous media in the case of 30.0 nm pores. In addition, hydrate equilibrium data of the binary CO2 + water mixtures were presented along with model calculations in Figure 4 and listed in Table 4. Figure 4 also includes the hydrate equilibrium data obtained by Uchida et al.5 for 30.0 nm pores. The overall trend observed in the binary CO2 + water mixtures was qualitatively the same as that in the binary CH4 + water mixtures. Although the experimental determinations of the binary CO2 + water mixtures in porous silica gels were restricted to the H-LW-V phase boundary, the model calculation could be extended to two different three-phase boundaries of hydrate (H)-ice (I)-vapor (V) and hydrate (H)-waterrich liquid (LW)-carbon dioxide-rich liquid (LCO2). The upper quadruple points (Q2) where two H-LW-V and H-LW-LCO2 phase boundaries intersect and thus four phases (H, LW, LCO2, and V) coexist were located very closely along the saturation vapor pressure curve of CO2. In addition, the apparent equilibrium pressure shifts representing the equilibrium pressure difference between pore and bulk hydrates at a specified temperature were shown in Figure 5. As the pore size decreases and equilibrium temperature increases, the equilibrium pressure shifts were found to be larger. Inside porous media, the thermodynamic potential of chemical components can change with respect to bulk conditions as a consequence of (1) molecular interactions at the pore walls, usually attraction of the fluid molecules by hydrophilic surfaces, and (2) the energy required to

Figure 5. Equilibrium pressure shifts between pore and bulk hydrates. (a) CH4 hydrate and (b) CO2 hydrate.

maintain capillary equilibrium.25 Furthermore, partial ordering and bonding of water molecules with hydrophilic pore surfaces depress water activity. The decrease of water activity leads to hydrate formation conditions either much higher in pressure at a specified temperature or much lower in temperature at a specified pressure. This phenomenon is also observed in the mixtures containing inhibitors such as salts and alcohols which cause a depression in the freezing point of water thereby reducing its activity. Therefore, the pore effect of geometrical constraints on water activity can be considered to be equivalent to a change in activity as caused by the inhibitors3. Figures 3 and 4 also demonstrated that the overall P-T behavior in silica gel pores followed similar trend as that observed in the mixtures containing inhibitors. A significant proportion of water in the wall of confined spaces has been often found to exist as bound water without undergoing complete freezing transition.24 This bound water will not also participate in hydrate formation under the same pressure-temperature conditions as the pore water. In the present experiments, the pores of silica

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Table 5. Percent AAD between the Experimental and Calculated Values system

pore diameter (nm)

%AAD

CH4 + water

6.0 15.0 30.0 6.0 15.0 30.0

9.30 3.92 2.24 14.03 6.32 2.33

CO2 + water

gels were first completely saturated with water, and after reaching the H-LW-V equilibrium, the pores are filled only with hydrate and liquid water. It is assumed that the wetting angle (θ) is 0°. Even though the operative interface of hydrate and liquid water phases plays a key role in understanding the pore effect on hydrate formation, no reliable data of the interfacial tension between hydrate and liquid water phases (σHW) have been reported in the literature except those suggested by Uchida et al.4,5 According to previous works, the interfacial tension between hydrate and liquid water phases was assumed to be equivalent to that between ice and liquid water phases (σHW ) σIW ) 0.027 J/m2),7,8,10,11 which resulted in large discrepancies between the experimental and calculated values. Recently, Uchida et al.5 presented the values of σHW from fitting their experimental values by the Gibbs-Thomson equation: 0.017 J/m2 for CH4 hydrate and 0.014 J/m2 for CO2 hydrate. By using the values suggested by Uchida et al.,5 the predicted H-LW-V values were in much better agreement with the present experimental ones although a little deviation was found for both binary CH4 + water and CO2 + water mixtures in 6.0 nm SG. Though the present pore hydrate model was proven to be quite reliable in both qualitative and quantitative manners, the percent average absolute deviations (%AADs) between experimental and calculated H-LW-V values were listed in Table 5 for reference. A little deviation at the smaller pores might be attributed to the fact that the much larger proportion of bound water, not converted to hydrate, exists in the smaller pores rather than in the larger pores as also indicated by Handa et al.24 In the present work, for the prediction of the H-I-V equilibrium line the interfacial tension between ice and hydrate phases (σIH) was assumed to be zero for both CH4 and CO2 hydrates. At the present time, the exact nature of σIH still remains unsolved, and thus to clarify this point, the more sensitive and accurate experimental H-I-V measurements will be required for several different pore sizes. The melting points of ice in porous silica gels are affected by their pore sizes and estimated by25,26

[

Tpore ) Tbulk 1m m

2σIW Fw∆Hfwr

]

(11)

where Tbulk is the bulk melting temperature (273.15 K), m σIW is the interfacial tension (0.027 J/m2) between ice and liquid water phases, Fw is the specific density of water (1000 kg/m3), ∆Hfw is the specific enthalpy of fusion of water (333 kJ/kg), and r is the pore radius. The lower quadruple point (Q1) where four phases (H, I, LW, and V) coexist appears normally adjacent to the corresponding melting point of ice. Accordingly, the lower quadruple temperature (TQ1) could be expected to decrease from its bulk one as the pore size decreased. In the present modeling, an initial guess of TQ1 was obtained from eq 11, (25) Clennell, M. B.; Hovland, M.; Booth, J. S.; Henry, P.; Winters, W. J. J. Geophys. Res. 1999, 104, 22985. (26) Jallut, C.; Lenoir, J.; Bardot, C.; Eyrand, C. J. Membr. Sci. 1992, 68, 271.

Table 6. Calculated Lower and Upper Quadruple Points of Hydrates in Silica Gel Pores

system CH4 + water

CO2 + water

Q1

Q2

pore diameter (nm)

T (K)

P (MPa)

T (K)

P (MPa)

6.0 15.0 30.0 bulk 6.0 15.0 30.0 bulk

263.4 269.2 271.0 272.9 264.3 269.1 270.6 272.1

1.874 2.258 2.388 2.536 0.807 0.972 1.029 1.089

276.8 280.6 281.9 283.1

3.826 4.230 4.410 4.522

and the final TQ1 was determined as the intersection point of two calculated H-LW-V and H-I-V phase boundaries after iterative calculations. The calculated quadruple points of the binary CH4 + water and CO2 + water mixtures in silica gel pores were listed in Table 6. For the CH4 hydrate (CH4‚n H2O), the hydration number, n, has been determined by various calorimetric and spectroscopic methods.27-29 However, in the present study, the NMR spectroscopy was adopted to determine the hydration numbers of CH4 hydrates confined in silica gel pores because the NMR spectroscopy has been recognized as a powerful tool for identifying hydrate structures and compositions, determining guest and host dynamics, and monitoring hydrate formation kinetics.30 Figure 6 shows a stacked plot of 13C MAS NMR spectra of CH4 hydrates in porous silica gels and bulk state. All of the spectra demonstrated two peaks at the same chemical shifts of -6.9 and -4.6 ppm, respectively. Because the ideal stoichiometric ratio of the small 512 to the large 51262 cages in the unit cell of structure I is 1:3, the peak at -4.6 ppm can be assigned to CH4 molecules in the small 512 cages and the peak at -6.9 ppm to CH4 molecules in the large 51262 cage. For determination of hydration number, the relative integrated intensities of 13 C MAS NMR spectra must be combined with the following statistical thermodynamic expression representing the chemical potential of water molecules in structure I in order to determine the occupancies of CH4 molecules in the small and large cages. In the absence of guest-guest interactions and host-lattice distortions, the chemical potential difference of the empty lattice to ice when the hydrate is in equilibrium with ice, ∆µ0w, is given by14

∆µ0w ) -

RT [3 ln(1 - θL,CH4) + ln(1 - θS,CH4)] 23

(12)

where θS and θL are the fractional occupancies of small and large cages, respectively. The value of ∆µ0w was determined to be 1297 J/mol for structure I hydrate.31 From Figure 6, the relative area ratios of large to small cages were found to be 3.89 (6.0 nm SG), 3.77 (15.0 nm SG), 3.55 (30.0 nm SG), and 3.70 (bulk), and the resulting hydration numbers were 6.23 (6.0 nm SG), 6.19 (15.0 nm SG), 6.12 (30.0 nm SG), and 6.17 (bulk). These values were in agreement with other literature ones of bulk hydrate (5.8 - 6.3)27-29 and also with that of pore CH4 hydrate in 15.0 nm SG (5.94)3. From the present 13C NMR results, it can be concluded that the structure of CH4 (27) Handa, Y. P. J. Chem. Thermodyn. 1986, 18, 915. (28) Uchida, T.; Hirano, T.; Ebinuma, T.; Narita, H.; Gohara, K.; Mae, S.; Matsumoto, R. AIChE J. 1999, 45, 2644. (29) Ripmeester, J. A.; Ratcliffe, C. I. J. Phys. Chem. 1988, 92, 337. (30) Ripmeester, J. A.; Ratcliffe, C. I. J. Struct. Chem. 1999, 40, 654. (31) Davidson, D. W.; Handa, Y. P.; Ripmeester, J. A. J. Phys. Chem. 1986, 90, 6549.

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Langmuir, Vol. 18, No. 24, 2002

Seo et al.

importantly the hydration numbers of the pore CH4 hydrates did not depend on the pore diameters of silica gels and were identical with that of bulk CH4 hydrate within experimental error range. Conclusions Three-phase H-LW-V equilibria of CH4 and CO2 hydrates confined in silica gel pores with nominal diameters of 6.0, 15.0, and 30.0 nm were measured and compared with the pore hydrate model calculations. At a specified temperature, the H-LW-V equilibrium lines of pore hydrates were shifted to higher pressure region depending on pore sizes when compared with that of bulk hydrate. Decrease in water activity because of the presence of geometrical constraints caused hydrate to form at higher pressure at a specified temperature as usually observed in mixtures containing inhibitors. By using the values of interfacial tension between hydrate and liquid water phases which were recently presented by Uchida et al.,5 the resulting accuracies and overall H-LW-V trend particularly approaching the H-I-V line obtained from the present pore hydrate model were greatly improved both quantitatively and qualitatively. The structure of CH4 hydrates formed in silica gel pores (6.0, 15.0, and 30.0 nm) was confirmed to be identical with those of bulk CH4 hydrate through NMR spectroscopy. Furthermore, the pore hydration number was found to be almost constant for all pore sizes. The overall thermodynamic and spectroscopic results drawn from the present study can be used for understanding the fundamental phase behavior and structure details of pore hydrates and, thus, could be applied as a valuable key information to developing the natural gas hydrate in marine sediments and sequestering carbon dioxide into the deep ocean. Figure 6. 13C NMR spectra of CH4 hydrates in silica gel pores and bulk state at 200 K.

hydrates formed in porous silica gels (6.0, 15.0, and 30.0 nm SG) was the same as that of the bulk CH4 hydrate (structure I) without structure transition and more

Acknowledgment. This research was performed for the Greenhouse Gas Research Center, one of the Critical Technology-21 Programs, funded by the Ministry of Science and Technology of Korea and also partially supported by the Brain Korea 21 Project. LA0257844