Yongwon Seo, and Huen Lee

Transcription

1 Article 4 Hydrate hase Equilibria of the ernary CH 4 NaCl + Water and CH 2 + CO Subscriber access provided by KOREA ADV INS OF SCI & ECH 2 + NaCl + Water, CO + Water Mixtures in Silica Gel ores Yongon Seo, and Huen Lee J. hys. Chem. B, 2003, 107 (3), DOI: /jp026776z ublication Date (Web): 21 December 2002 Donloaded from on May 7, More About his Article Additional resources and features associated ith this article are available ithin the HML version: Supporting Information Access to high resolution figures Links to articles and content related to this article Copyright permission to reproduce figures and/or text from this article he Journal of hysical Chemistry B is published by the American Chemical Society Sixteenth Street N.W., Washington, DC 20036

2 J. hys. Chem. B 2003, 107, Hydrate hase Equilibria of the ernary CH 4 + NaCl + Water, CO 2 + NaCl + Water and CH 4 + CO 2 + Water Mixtures in Silica Gel ores Yongon Seo and Huen Lee* Department of Chemical and Biomolecular Engineering, Korea AdVanced Institute of Science and echnology, Guseong-dong Yuseong-gu, Daejeon , Korea ReceiVed: August 16, 2002; In Final Form: NoVember 25, 2002 Hydrate phase equilibria for the ternary CH 4 + NaCl + ater and CO 2 + NaCl + ater mixtures in 15.0 nm silica gel pores and for the ternary CH 4 + CO 2 + ater mixtures of various CO 2 vapor compositions (20, 40, 60 and 80 mol %) in silica gel pores of nominal diameters 6.0, 15.0, and 30.0 nm ere experimentally measured and compared ith the calculated results based on van der Waals and latteeu model. At a specified temperature, three phase H-L W -V equilibrium curves of pore hydrates ere shifted to a higher pressure region depending on NaCl concentrations and pore sizes. A itzer model for electrolytes solutions and a correction term for capillary effect ere adopted to estimate the activity of ater in the aqueous electrolyte solutions ithin silica gel pores. he cage dependent 13 C NMR chemical shifts of the enclathrated CH 4 molecules in 15.0 nm silica gel pores ere confirmed to be identical ith those of bulk CH 4 hydrates (si) and consistent through different NaCl concentrations and CO 2 compositions. Introduction Gas hydrates are nonstoichiometric crystalline compounds formed hen guest molecules of suitable size and shape are incorporated in the ell-defined cages in the host lattice made up of hydrogen-bonded ater molecules. hese compounds exist in three distinct structures I (si), structure II (sii), and structure H (sh), hich contain differently sized and shaped cages. he si and sii hydrates consist of to types of cages, hereas the sh hydrate consists of three types of cages. 1 Gas hydrates are of particular interest in the petroleum industry as ell as in energy and environmental field. Large masses of natural gas hydrates exist in the permafrost region or beneath deep oceans, here they ere commonly found in sediment pores. 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 CH 4 are regarded as future energy resources. 1 he recent investigations have suggested the possibility of sequestering industrially produced CO 2 as crystalline gas hydrates in the deep ocean to prevent further release into the atmosphere as a greenhouse gas. 2 It has been also investigated that the injection of CO 2 into CH 4 hydrate reserves could result in simultaneous process merits of both CO 2 sequestration and CH 4 exploitation. 3 Because these natural phenomena of hydrate formation/substitution occur in deep ocean sediments, it becomes essential to consider the complicated effects of both porous media and electrolytes on the formation of simple and mixed hydrates. Hoever, any research ork on simple and mixed hydrates containing electrolytes in porous media has not yet appeared in the literature, even though numerous investigations covering separately either porous medium or electrolyte effect have been found from various sources. 1,4-9 he cage substitution mechanism beteen CH 4 and CO 2 molecules might be thought to be easily tractable, but for its complete understanding, both * o hom correspondence should be addressed. hone: Fax: hlee@mail.kaist.ac.kr. equilibrium and nonequilibrium approaches are required in the bulk and porous medium surroundings. Moreover, the highly complex phase behavior of mixed hydrate systems containing multiguest components must be explored as a priori to examine the feasibility of natural gas exploitation in connection ith CO 2 sequestration. In this connection, the present ork as nely attempted to provide fundamental key information of electrolyte effects on hydrate phase equilibrium behavior, particularly, in porous media. First, the hydrate phase equilibria of to ternary CH 4 + NaCl + ater and CO 2 + NaCl + ater mixtures ere measured in 15.0 nm silica gel pores at three different NaCl concentrations of 3, 5, and 10 t % to secure fundamental electrolyte role on simple hydrate formation occurring in pores. Second, the hydrate phase equilibria of the CH 4 + CO 2 + ater mixture in 15.0 nm silica gel pores ere also carefully determined at CO 2 compositions of 20, 40, 60, and 80 mol % in order to meet changeable surroundings of sea floor and sediments. hird, three different silica gels of nominal diameters 6.0, 15.0, and 30.0 nm ere used to check pore-size effects on hydrate equilibrium. All of these measured data ere compared ith calculated values based on the van der Waals and latteeu model incorporated ith to additional terms considering electrolytes and pores. Furthermore, the 13 C NMR spectra ere examined to identify and confirm the hydrate structure of the CH 4 + NaCl + ater and CH 4 + CO 2 + ater mixtures formed in silica gel pores. Experimental Section Materials. CO 2 gas of 99.9 mol % purity as supplied by World Gas (Korea), and CH 4 gas ith a minimum purity of mol % as supplied by Linde Gas UK Ltd (UK). he CH 4 + CO 2 gas mixtures (20, 40, 60, and 80 mol % CO 2 ) ere supplied by World Gas (Korea), and their compositions ere checked again. he ater ith ultrahigh purity as supplied by Merck (Germany). Silica gels of nominal pore diameter 6.0 nm (6.0 nm SG) and 15.0 nm (15.0 nm SG) ere purchased /jp026776z CCC: $ American Chemical Society ublished on Web 12/21/2002

3 890 J. hys. Chem. B, Vol. 107, No. 3, 2003 Seo and Lee from Aldrich (USA), and 30.0 nm silica gel (30.0 nm SG) as purchased from Silicycle (Canada). All materials ere used ithout further treatment. he properties of silica gels having three different pore diameters ere measured by ASA 2000 (Micromeritics, USA). he details of the physical properties and pore-size distributions ere given in the previous paper. 9 Apparatus and rocedure. he used silica gels ere first dried at 373 K for 24 h before ater sorption. hen, the pore saturated silica gels ere prepared by placing these dried silica gels in a desiccator containing degassed and distilled ater, evacuating the desiccator, and alloing more than 5 days in order to establish the solid-vapor equilibrium. he total amount of sorbed ater in the silica gel pores as confirmed by measuring the mass of silica gels before and after saturation and found to be almost identical ith the pore volume of each silica gel. For preparing silica gels containing NaCl solution, e folloed the same method suggested by Uchida et al. 5 he amount of electrolyte solution equivalent to total pore volume of dried silica gels as added to the sample contained in the bottle. After being mixed, the mixture as sealed off ith a cap to prevent ater evaporation. o facilitate ater filling into the pores, the bottle ith the mixture as vibrated and armed for 24 h ith an ultrasonic ave. he validity of this method as verified by comparing the experimental results obtained from to different methods. A schematic diagram and detailed description of the experimental apparatus for hydrate phase equilibria as given in the previous papers. 10,11 he apparatus as specially constructed to measure accurately the hydrate dissociation pressures and temperatures. he equilibrium cell as made of 316 stainless steel and had an internal volume of about 50 cm 3. he experiment for hydrate-phase equilibrium measurements began by charging the equilibrium cell ith about 25 cm 3 of silica gels containing pore ater. After the equilibrium cell as pressurized to a desired pressure ith gas, the hole main system as sloly cooled to about 10 K belo the expected hydrate-formation temperature. When pressure depression due to hydrate formation reached a steady-state condition, the cell temperature as increased at a rate of about 0.1 K/h. he nucleation and dissociation steps ere repeated at least to times in order to reduce hysteresis phenomenon. he equilibrium pressure and temperature of three phases (hydrate (H)-aterrich liquid (L W )-vapor (V)) ere determined by tracing the - profiles from hydrate formation to dissociation. Unlike the bulk hydrate, in case of hydrates in silica gel pores, a gradual change of slope around the final hydrate dissociation point as observed because of the pore-size distribution. As a consequence, it becomes, of course, very difficult to determine the unique equilibrium dissociation point in the - profile measured for the silica gel pores. o overcome these inherent difficulties, the dissociation equilibrium point in silica gel pores as chosen in the present study as the cross point beteen the maximum inclination line and complete dissociation line. As indicated by Uchida et al., 5 this unique point corresponds to the dissociation one in the pores of the mean diameter of used silica gels. o identify the hydrate structure of the CH 4 + NaCl + ater and CH 4 + CO 2 + ater mixtures in silica gel pores, a Bruker 400 MHz solid-state NMR spectrometer as used in this study. he NMR spectra ere recorded at 200 K by placing the hydrate samples ithin a 4 mm o.d. Zr-rotor that as loaded into the variable temperature (V) probe. All 13 C NMR spectra ere recorded at a Larmor frequency of MHz ith magic angle spinning (MAS) at about 2-4 khz. he pulse length of 2 µs and pulse repetition delay of 20 s under proton decoupling ere employed hen the radio frequency field strengths of 50 khz corresponding to 5 µs 90 pulses ere used. he donfield carbon resonance peak of adamantane, assigned a chemical shift of 38.3 ppm at 300 K, as used as an external chemical shift reference. hermodynamic Model. he equilibrium criteria of the hydrate-forming mixture are based on the equality of fugacities of the specified component i in all phases hich coexist simultaneously here H stands for the hydrate phase, L for the ater-rich liquid phase, V for the vapor phase and I for the ice phase. It can be reasonably assumed that electrolytes are completely excluded from hydrate lattice and remain only in the liquid phase. he chemical potential difference beteen the empty hydrate and filled hydrate phases, µ M-H ()µ M - µ H ), is generally derived from statistical mechanics in the van der Waals and latteeu model 12 here ν m is the number of cavities of type m per ater molecule in the hydrate phase and θ mj is the fraction of cavities of type m occupied by the molecules of component j. Holder et al. 13 suggested the method to simplify the chemical potential difference beteen empty hydrate and reference state as follos: µ M-L 0 here 0 is K, the normal melting point of ater, µ is the chemical potential difference beteen empty hydrate and ater at 0 and zero absolute pressure, h M-I and υ M-I are the molar differences in enthalpy and volume beteen empty hydrate and ice, respectively, and h fus and υ fus are the molar differences in enthalpy and volume beteen ice and liquid ater, respectively. a denotes the activity of ater calculated from an equation of state and is equivalent to the product of activity coefficient of ater and salt-free mole fraction of ater, x. he fugacity of ater in the filled hydrate lattice, fˆ H,is calculated by either of the folloing to expressions depending on the equilibrium temperature. If the equilibrium temperature is belo the ice point and above the ice point fˆ ih ) fˆ il ) fˆiv () f I ) (1) µ M-H ) µ M - µ H )- m µ M-I ) µ 0 M-I - h 0 d ) µ 0 - h M-I fus + h 0 d + 2 fˆ H I ) f ν m ln(1 - j υ M-I θ mj ) (2) d (3) υ M-I fus + υ 0 d - ln a (4) exp( µ M-I fˆ H ) f L exp( µ M-L - µ M-H ) (5) - µ M-H ) (6)

4 Hydrate hase Equilibria of the ernary Mixtures J. hys. Chem. B, Vol. 107, No. 3, M-I here µ ) µ M I - µ and µ M-L ) µ M - µ L, respectively. he fugacity coefficient of ater, φ, in the aqueous electrolyte liquid phase is given by the model of Aasberg- etersen et al. 14 ln φ ) ln φ EOS + ln γ EL (7) he first term for normal contribution can be calculated from SRK-EOS, and the second term for electrolyte contribution can be calculated from the itzer model 15 γ EL ) a EL /x (8) ln a EL )- M νm 1000 φ (9) here a EL stands for activity of ater in electrolytes solution, M stands for the molecular eight of ater, m stands for the molality of the electrolyte, ν stands for the number of ions the electrolytes dissociates into, and φ stands for the osmotic coefficient. he osmotic coefficient for single electrolyte solution is as follos: φ - 1 ) z + z - f φ + m( 2ν + ν - ν )B ( φ + m 2[ 2(ν + ν - )3/2 ν ]C ( φ (10) f φ I )-A φ I (11) Figure 1. Hydrate phase equilibria of the ternary CH 4 + NaCl + ater mixtures in 15.0 nm silica gel pores. here A φ is the Debye-Hückel constant for the osmotic coefficient, I is the ionic strength, ν i is the number of ion i in the electrolyte, and z i is the charge on ion i. he binary and ternary ion interaction parameters, B φ ( and C φ (, respectively, are obtained from the complicated empirical best-fit curves. 16 he decrease of ater activity in silica gel pores due to capillary effect occurring by the presence of geometrical constraints can be expressed as ln a ) ln a EL - V L 2 cos θσ HW r (12) here V L is the molar volume of pure ater, θ is the etting angle beteen hydrate and liquid ater phases, σ HW is the interfacial tension beteen hydrate and liquid ater phases, and r is the pore radius. More details of the model description ere given in our previous papers. 9,21-23 Results and Discussion hree-phase H-L W -V equilibria for the ternary CH 4 + NaCl + ater and CO 2 + NaCl + ater mixtures in 15.0 nm silica gel pores ere measured at the NaCl concentration ranges of 3-10 t % and presented along ith model calculations in Figures 1 and 2 and able 1. As expected, the presence of either geometrical constraints or electrolytes caused the H-L W -V curves to be shifted more to the inhibition region represented by the loer temperature and higher pressure condition hen compared ith the ones in the either bulk or pure state. Hoever, in the present ork, the combined effects of porous media and electrolytes that closely simulate real marine sediments ere examined through checking the shift of the experimentally measured H-L W -V curve. Although the experimental determinations of the binary CO 2 + NaCl + ater Figure 2. Hydrate phase equilibria of the ternary CO 2 + NaCl + ater mixtures in 15.0 nm silica gel pores. mixtures in silica gel pores ere restricted to the H-L W -V phase boundary, the model calculation could be extended to to different three-phase boundaries of hydrate (H)-ice (I)- vapor (V) and hydrate (H)-ater-rich liquid (L W )-carbon dioxide-rich liquid (L CO2 ). he upper quadruple point (Q 2 ) here to H-L W -V and H-L W -L CO2 phase boundaries intersect and thus four phases (H, L W,L CO2, and V) coexist as found at the location very close to the corresponding saturation vapor pressure of CO 2. Of course, the melting point of ice is affected by the presence of geometrical constraints and electrolytes. he loer quadruple point (Q 1 ) here four phases (H, I, L W, and V) coexist appears normally adjacent to the corresponding melting point of ice. herefore, Q 1 is knon to be a function of pore radius and electrolyte concentration. In the present study, the values of Q 1

5 892 J. hys. Chem. B, Vol. 107, No. 3, 2003 Seo and Lee ABLE 1: Hydrate hase Equilibrium Data for CH 4 + NaCl + Water and CO 2 + NaCl + Water Mixtures in 15.0 nm Silica Gel ores NaCl 3 t % NaCl 5 t % NaCl 10 t % CH 4 + NaCl + Water Mixtures CO 2 + NaCl + Water Mixtures ABLE 2: Calculated Loer (Q 1 ) and Upper (Q 2 ) Quadruple oints system NaCl (t %) Q 1 Q 2 CH 4 + NaCl + ater, bulk CH 4 + NaCl + ater, nm CO 2 + NaCl + ater, bulk CO 2 + NaCl + ater, nm ere not experimentally measured but calculated by the proposed model. he loer quadruple temperatures ( Q1 )ofch 4 (or CO 2 ) + NaCl + ater mixtures in 15.0 nm silica gel pores decreased from that of CH 4 (or CO 2 ) + ater mixtures in 15.0 nm pores as the NaCl concentration increased. In the present study, Q1 as determined as the intersection point of to calculated H-L W -V and H-I-V phase boundaries. he calculated quadruple points of the ternary CH 4 + NaCl + ater and CO 2 + NaCl + ater mixtures in bulk state and silica gel pores ere listed in able 2. hree-phase H-L W -V equilibria for the ternary CH 4 + CO 2 + ater mixtures of various CO 2 vapor compositions (20, 40, 60, and 80 mol %) in 15.0 nm silica gel pores ere also measured and presented along ith model calculations in Figure 3 and able 3. As generally expected, the H-L W -V lines of the ternary CH 4 + CO 2 + ater mixtures existing beteen those of the binary CH 4 + ater and CO 2 + ater mixtures shoed the pore inhibition. In particular, three-phase H-L W -V equilibria for the ternary CH 4 + CO 2 + ater mixtures of 40 mol %CO 2 in silica gel pores of nominal diameters 6.0, 15.0, and 30.0 nm ere represented along ith model calculations in Figure 4 and listed in able 4. he decrease of pore diameter made the H-L W -V equilibrium line more shifted toard higher pressure region at a specified temperature. In porous media, ater activity is depressed by partial ordering and bonding of ater molecules ith hydrophilic pore surfaces. 18 he decrease of ater activity leads the hydrate formation condition either to much higher pressure at a specified temperature or to much loer temperature at a specified Figure 3. Hydrate phase equilibria of the ternary CH 4 + CO 2 + ater mixtures of various CO 2 compositions (20, 40, 60, and 80 mol %) in 15.0 nm silica gel pores. Figure 4. Hydrate phase equilibria of the ternary CH 4 + CO 2 + ater mixtures of 40 mol % CO 2 in silica gel pores (6.0, 15.0, and 30.0 nm). ABLE 3: Hydrate hase Equilibrium Data for CH 4 + CO 2 + Water Mixtures in 15.0 nm Silica Gel ores 20 mol % CO 2 40 mol % CO 2 60 mol % CO 2 80 mol % CO pressure. his phenomenon is also observed in the mixtures containing inhibitors such as electrolytes and alcohols hich cause a depression in the freezing point of ater thereby

6 Hydrate hase Equilibria of the ernary Mixtures J. hys. Chem. B, Vol. 107, No. 3, ABLE 4: Hydrate hase Equilibrium Data for CH 4 + CO 2 + Water Mixtures of 40 Mol % CO 2 in Silica Gel ores 6.0 nm SG 15.0 nm SG 30.0 nm SG reducing its activity. herefore, the pore effect of geometrical constraints on ater activity can be considered to be equivalent to a change in activity as caused by the inhibitors. 4 A significant proportion of ater in the all of confined spaces has been often found to exist as bound ater ithout undergoing complete freezing transition. 28 his bound ater ill not also participate in hydrate formation under the same pressure-temperature conditions as the pore ater. In the present experiments, the pores of silica gels ere first completely saturated ith ater, and after reaching the H-L W -V equilibrium, they are filled only ith hydrate and liquid ater. It is assumed that the etting angle (θ) is0. Even though the operative interface of hydrate and liquid ater phases plays a key role in understanding the pore effect on hydrate formation, no reliable data of the interfacial tension beteen hydrate and liquid ater phases (σ HW ) have been reported in the literature. According to previous orks, the interfacial tension beteen hydrate and liquid ater phases as assumed to be equivalent to that beteen ice and liquid ater phases (σ HW ) σ IW ) J/m 2 ), 8,18-20 hich resulted in large discrepancies beteen the experimental and calculated values. Recently, Uchida et al. 6 presented the values of σ HW from fitting their experimental values by the Gibbs-homson equation: J/m 2 for CH 4 hydrate and J/m 2 for CO 2 hydrate. By using the values suggested by Uchida et al., 6 it as found that the predicted H-L W -V values of pure CH 4 and CO 2 hydrates in silica gel pores ere in much better agreement ith our experimental ones. 9 o establish the proper interpretation of mixed hydrates in porous media, the values of interfacial tension beteen hydrate and liquid ater phase (σ HW ) for CH 4 + CO 2 mixed hydrates must be obtained from either theoretical or possibly experimental methods but, unfortunately, up to no, have not yet been reported. Accordingly, in this ork, the mole additivity of CH 4 and CO 2 compositions as adopted to determine the folloing values of interfacial tension: J/m 2 for 20 mol %, J/m 2 for 40 mol %, J/m 2 for 60 mol %, and J/m 2 for 80 mol % (CO 2 basis). By applying this method, the calculated values agreed ell ith the experimental ones, and the least %AAD as observed for the overall CH 4 + CO 2 + ater mixtures. For the prediction of the H-I-V equilibrium lines, the interfacial tension beteen ice and hydrate phases (σ IH ) as assumed to be zero for all of the mixtures. At the present time, the exact nature of σ IH still remains unsolved, and to clarify this point, a more sensitive and accurate experiment ill be required for various pore sizes. Hoever, some previous researchers also assumed the value of σ IH to be zero for calculation of the H-I-V equilibria and indirectly confirmed the validity of this assumption by finding that the H-I-V equilibria in porous media as the same as those in the bulk phase. 6,8,19,29 hough the present pore hydrate model as proven to be quite reliable in both qualitative and quantitative manners, the percent average absolute deviations (%AADs) beteen experimental and calculated H-L W -V values ere listed in ABLE 5: ercent AAD beteen the Experimental and Calculated Values of H-L W -V Equilibria system NaCl (t %) %AAD CH 4 + NaCl + ater, 15.0 nm CO 2 + NaCl + ater, 15.0 nm system CO 2 (mol %) %AAD CH 4 + CO 2 + ater, 15.0 nm system pore diameter (nm) %AAD CH 4 + CO 2 + ater, CO 2 40 mol % able 5 for reference. he calculated results agreed ell ith the experimental data, but a little larger deviations ere observed at higher concentration of NaCl, higher composition of CO 2, and smaller pore size. hese deviations might be attributed to a much larger proportion of bound ater existing in the smaller pores, hich may cause more experimental errors in the smaller pore sizes, intrinsic limitation of the itzer model at higher NaCl concentration, and a large solubility of carbon dioxide in aqueous solutions. 21,28,30 More importantly, the more accurate values of σ HW must be anyho provided for better improvement. he objective of the NMR measurement in this study is to identify and confirm the structure of the CH 4 + NaCl + ater and CH 4 + CO 2 + ater mixtures in porous media. A cage dependent 13 C NMR chemical shift of the enclathrated CH 4 molecules can be used to determine structure types of the formed hydrates. 31 From the preliminary experiments, the structure and hydration number of CH 4 hydrates in silica gel pores (6.0, 15.0 and 30.0 nm) ere found to be identical ith those of bulk CH 4 hydrate. 9 For the CH 4 + NaCl + ater and CH 4 + CO 2 + ater mixtures in 15.0 nm silica gel pores, the positions of to peaks from CH 4 molecules trapped in large and small cages of hydrate lattice ere also confirmed to be identical ith those of bulk CH 4 hydrates (si) and consistent through different NaCl concentrations and CO 2 compositions. he cage occupancy behavior occurring in the mixed hydrates is expected to be highly complex. Even though this part is very fundamental on hydrate area, the detailed and organized research has not yet been done so far. herefore, the macro and micro approaches for investigating hydration number, cage occupancy, and ratio of peak areas in the mixed hydrates need to be attempted in the future. he present NMR orks in the porous and electrolyte state is the first one and might be extended to various types of mixed hydrates in order to explore their physicochemical aspects. Conclusion hree-phase H-L W -V equilibria for the ternary CH 4 + NaCl + ater and CO 2 + NaCl + ater mixtures in 15.0 nm silica gel pores and for the ternary CH 4 + CO 2 + ater mixtures of various CO 2 compositions in silica gel pores ith nominal diameters of 6.0, 15.0, and 30.0 nm ere nely measured and compared ith model calculations. he presence of geometrical constraints and electrolytes made H-L W -V equilibrium lines

7 894 J. hys. Chem. B, Vol. 107, No. 3, 2003 Seo and Lee shifted to higher pressure region at a specified temperature. A itzer model for electrolytes solutions and a correction term for capillary effect ere adopted to estimate the activity of ater in the aqueous electrolyte solutions ithin silica gel pores. he hydrate structures of the CH 4 + NaCl + ater and CH 4 + CO 2 + ater mixtures in 15.0 nm silica gel pores ere confirmed to be identical ith that of the CH 4 + ater mixture in bulk state through 13 C NMR spectroscopy. he overall phase behavior considering the combined effects of pore and electrolyte could provide key information for exploiting natural gas hydrates from marine sediments, substituting carbon dioxide molecules into gas hydrate reservoirs, and sequestering carbon dioxide into sea floor as solid hydrates. Acknoledgment. his research as performed for the Greenhouse Gas Research Center, one of the Critical echnology-21 rograms, funded by the Ministry of Science and echnology of Korea and also partially supported by the Brain Korea 21 roject. References and Notes (1) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd edition, revised and expanded; Dekker: Ne York, (2) eng, H.; Yamasaki, A.; Chun, M. K.; Lee, H. Energy 1997, 22, (3) Ohgaki, K.; akano, K.; Sangaa, H.; Matsubara,.; Nakano, S. J. Chem. Eng. Jpn. 1996, 29, 478. (4) Handa, Y..; Stupin, D. J. hys. Chem. 1992, 96, (5) Uchida,.; Ebinuma,.; Ishizaki,. J. hys. Chem. B 1999, 103, (6) Uchida,.; Ebinuma,.; akeya, S.; Nagao, J.; Narita, H. J. hys. Chem. B 2002, 106, 820. (7) Seshadri, K.; Wilder, J. W.; Smith, D. H. J. hys. Chem. B 2001, 105, (8) Smith, D. H.; Wilder, J. W.; Seshadri, K. AIChE J. 2002, 48, 393. (9) Seo, Y.; Lee, H.; Uchida,. Langmuir 2002, 18, (10) Seo, Y.-.; Lee, H. J. hys. Chem. B 2001, 105, (11) Seo, Y.; Lee, H. EnViron. Sci. echnol. 2001, 35, (12) van der Waals, J. H.; latteeu, J. C. AdV. Chem. hys. 1959, 2, 1. (13) Holder, G. D.; Corbin, G.; apadopoulos, K. D. Ind. Eng. Chem. Fundam. 1980, 19, 282. (14) Aasberg-etersen, K.; Stenby, E.; Fredenslund, A. Ind. Eng. Chem. Res. 1991, 30, (15) itzer, K. S. J. hys. Chem. 1973, 77, 268. (16) itzer, K. S.; Mayorga, G. J. hys. Chem. 1973, 77, (17) Clarke, M. A.; ooladi-darvish, M.; Bishnoi,. R. Ind. Eng. Chem. Res. 1999, 38, (18) Henry,.; homas, M.; Clennell, M. B. J. Geophys. Res. 1999, 104, (19) Wilder, J. W.; Seshadri, K.; Smith, D. H. Langmuir 2001, 17, (20) Klauda, J. B.; Sandler, S. I. Ind. Eng. Chem. Res. 2001, 40, (21) Kang, S..; Chun, M. K.; Lee, H. Fluid hase Equilibr. 1998, 147, 229. (22) Chun, M. K.; Lee, H. J. Chem. Eng. Data 2000, 45, (23) Yoon, J. H.; Chun, M. K.; Lee, H. AIChE J. 2002, 48, (24) Adisasmito, S.; Frank, R. J.; Sloan, E. D. J. Chem. Eng. Data 1991, 36, 68. (25) Dholabhai,. D.; Englezos,.; Kalogerakis, N.; Bishnoi,. R. Can. J. Chem. Eng. 1991, 69, 800. (26) Kobayashi, R.; Withro, H. J.; Williams, G. B.; Katz, D. L. roc. NGAA 1951, 1951, 27. (27) Dholabhai,. D.; Kalogerakis, N.; Bishnoi,. R. J. Chem. Eng. Data 1993, 38, 650. (28) Handa, Y..; Zakrzeski, M.; Fairbridge, C. J. hys. Chem. 1992, 96, (29) Zhang, W.; Wilder, J. W.; Smith, D. H. roc. 4th Int Conf. Gas Hydrates 2002, 1, 321. (30) rausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular hermodynamics of Fluid-hase Equilibria, 3rd edition; rentice Hall: Ne York, (31) Ripmeester, J. A.; Ratcliffe, C. I. J. hys. Chem. 1988, 92, 337.