10084
J. Phys. Chem. B 2001, 105, 10084-10090
Multiple-Phase Hydrate Equilibria of the Ternary Carbon Dioxide, Methane, and Water Mixtures Yu-Taek Seo and Huen Lee* Department of Chemical Engineering, Korea AdVanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, South Korea ReceiVed: March 22, 2001; In Final Form: July 6, 2001
Three-phase equilibria consisting of vapor, water-rich liquid, and solid hydrate were measured for the aqueous solutions containing two guest molecules of carbon dioxide and methane in the temperature range of 272284 K and at pressures of 15, 20, 26, 35, and 50 bar. At the specified isobaric condition the three-phase equilibrium temperatures become higher as the relative concentrations of carbon dioxide to methane increase. The upper quadruple points at which the four phases of vapor, water-rich liquid, CO2-rich liquid, and solid hydrate coexist were also measured to examine the phase boundary of the hydrate stability region. At five different temperatures the concentrations of vapor, water-rich liquid, and carbon dioxide-rich liquid were measured and examined through five triangular diagrams. For the prediction of hydrate phase equilibria, the vapor and liquid phases were treated with the Soave-Redlich-Kwong equation of state (SRK-EOS) incorporated with the second-order modified Huron-Vidal (MHV2) mixing rule and the hydrate phase with the van der Waals-Platteeuw model.
1. Introduction Clathrate compounds are crystalline materials formed by a physical interaction between host molecules and relatively light guest molecules. There are various cavities capable of entrapping guest molecules in an open network of host molecules composing a crystalline framework. Depending on the chemical properties of the host molecules, clathrate compounds can be divided into two categories: aqueous and nonaqueous. Clathrate compounds in which the host molecules are water or deuterium oxide belong the aqueous clathrates. This kind of inclusion compound is specifically called a clathrate hydrate or simply gas hydrate. Gas-phase guest molecules generally form nonaqueous clathrates with phenolic compounds such as hydroquinone, phenol, and simple substituted phenols. The huge deposits of natural gas hydrates were founded in porous sediments and sedimentary rocks developed in deep oceans. In 1997, Makogon estimated the potential resource of methane in hydrate state as 10 000 Gt.1 One of the potential applications of gas hydrate is to sequester carbon dioxide in the deep ocean. The replacement of methane with carbon dioxide in gas hydrates may draw an innovative procedure for natural gas production. By injecting carbon dioxide to methane hydrate fields, methane dissociation from hydrate sediments can be facilitated while the formation rate of carbon dioxide hydrates can be largely increased, and therefore the physical fixation of carbon dioxide molecules to hydrate cavities can be easily achieved. To analyze this complex thermodynamic phenomenon, the complete phase behavior of the carbon dioxide and methane mixture in aqueous solutions must be first investigated to understand the overall reformation mechanism occurring in the deep sea floor. In this connection, several related studies have appeared for examining the hydrate equilibrium conditions of the carbon * Corresponding author.
dioxide and methane mixture. Unruh and Katz reported the first phase equilibrium data for this system and determined vapor phase concentrations indirectly.2 Berecz and Balla-Achs showed that hydrates of a carbon dioxide and methane mixture exhibited instability at a carbon dioxide mole fraction of 50% and higher.3 Adisasmito et al. confirmed and extended the data of Unruh and Katz and showed that the result of Berecz and Balla-Achs was very unusual.4 Dholabhai et al. in 1994 measured the threephase (aqueous solution, hydrate, and vapor) equilibrium conditions of pure water and electrolyte solutions containing NaCl, KCl, and CaCl2. The inhibition effect of electrolytes could be seen clearly.5 In 1995, Ohgaki et al. measured the isothermal three-phase equilibria by varying pressure, gas phase composition, and hydrate composition and briefly discussed the possibility of natural gas exploitation and carbon dioxide isolation.6 In 1999, Servio et al. measured the incipient equilibrium hydrate formation conditions for two different compositions of 80/20% and 50/50% methane-carbon dioxide mixtures in the presence of neohexane.7 It was found that the 80/20 gas mixture forms the structure H hydrate. The results from the 50/50 mixture indicate that, above approximately 277.5 K, the structure I hydrate is formed below that temperature and a transition state occurs, resulting in structure H or a mixture of structure H and structure I hydrates. However, the equilibrium conditions in isobaric conditions were not yet investigated precisely. In the present work, the isobaric equilibrium conditions of the carbon dioxide and methane mixture were measured to identify the hydrate-forming stable region. The measured isobaric hydrate equilibrium data were correlated by the SoaveRedlich-Kwong equation of state (SRK-EOS) incorporated with second-order modified Huron-Vidal (MHV) mixing rule and the modified UNIFAC. 2. Thermodynamic Model The equilibrium criteria of the hydrate-forming mixture are based on the equality of fugacities of the specified component
10.1021/jp011095+ CCC: $20.00 © 2001 American Chemical Society Published on Web 09/20/2001
Multiple-Phase Hydrate Equilibria
J. Phys. Chem. B, Vol. 105, No. 41, 2001 10085 chemical potential difference between empty hydrate and water at T0 and zero absolute pressure, and ∆hw and ∆Vw are, respectively, the molar difference in enthalpy and volume difference between empty hydrate and ice. Holder et al. reported the well-organized reference parameter values in eq 3 for simple and mixed hydrate systems.11 The fugacity of water in the filled hydrate lattice, ˆfwH, is calculated by one of the following two expressions, depending on the equilibrium temperature. If the equilibrium temperature is below the ice point,
TABLE 1: Isobaric Three-Phase Equilibrium Conditions (H-Lw-V) for Carbon Dioxide and Methane Mixtures P/bar
T/K
Vapor Phase Composition (CO2 mol %)
15
272.66 273.56 274.36 274.76 273.56 274.36 275.86 276.56 277.16 273.16 275.36 276.76 277.96 278.26 279.16 276.16 278.06 279.26 280.16 280.76 281.46 279.60 281.46 282.56 283.26 283.56
40.67 61.69 90.41 100.00 26.34 33.75 56.48 79.54 100.00 0.00 18.54 39.72 61.95 78.43 100.00 0.00 20.09 42.65 60.87 76.17 100.00 0.00 19.71 40.89 59.89 80.52
20
26
35
50
ˆf wH ) fwI exp
ˆf w ) fw H
∆µw
∆µwH ∆µw0 ) RT RT0
) RT ∆h
υmln(1 + ∑Cmjˆf j ) ∑ m j
∫TT RTw2 dT + ∫0P 0
∆υw dP - lnγwxw RT
L
)
∆µwMT-L ∆µwMT-H exp RT RT
[
fwI ) Psatφwsat exp
(1)
v
(
(4)
(5)
From the phase equilibrium thermodynamics, the fugacity of ice can be represented and directly computed by
where H stands for the hydrate phase such as structure I or II, L for the liquid phase such as the water-rich or guest-rich liquid phases, V for the vapor phase, and I for the ice phase. For the hydrate phase equilibrium analysis the fugacity of water in the hydrate phase, ˆfwH, has been generally calculated from the van der Waals and Platteeuw model,8 relating the chemical potential of water in the hydrate phase to that in the hypothetical empty hydrate lattice. This approach used the classical adsorption theory, Langmuir isotherm, to obtain the chemical potential difference between the empty hydrate and filled hydrate phases and considered the interaction between host water and encaged guest molecules in the hydrate cavities. The Kihara potential with spherical core was 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.9 The values of the Kihara hard-core parameter, a, are given in the literature,10 but the values of the Kihara energy and size parameters, and σ, are determined by regressing the experimental equilibrium data with the following expressions representing the chemical potential difference of water MT-H
)
or
i in all phases that coexist simultaneously
ˆfiH ) ˆfiL ) ˆfiV( ) fwI)
(
∆µwMT-I ∆µwMT-H RT RT
(2)
(3)
where υm is the number of cavities of type m per water molecule in the hydrate phase, Cmj the Langmuir constant of component j on cavity type m, and ˆfjV the fugacity of component j in the vapor phase with which the hydrate phase is in equilibrium. ∆µwMT-H () µwMT - µwH) is the chemical potential difference between the empty hydrate and the filled hydrate phase. T0 is 273.15 K, the normal melting point of water, ∆µw0 is the
]
υwI(P - Psat) RT
(6)
In the complete phase diagram expressed with hydrate equilibrium temperature and pressure, the lower quadruple point at which four phases of H-I-Lw-V coexist in equilibrium must be located exactly at an intersection of two three-phase H-Lw-V and H-I-V curves. When eq 6 is used for the fugacity of ice, the continuity of the fugacity of water in the filled hydrate phase at the lower quadruple point cannot be guaranteed because the fugacity calculated with eq 4 is different from that with eq 5. Therefore, a new approach for calculating the fugacity of ice became essential to overcome this inherent limitation of eq 6 and was attempted in this work. At the lower quadruple point, the following expressions must hold for the fugacity of ice and pure liquid water12
ln fw ) lnPvp I
sat,I
+
∫0
P
υIw dP RT
(7)
and
ln fwL ) lnPvpsat,L +
υL
∫0P RTw dP
(8)
Using the Clausius-Clapeyron equation, the fugacity of ice is related to that of pure liquid water by the following:
(
fwI ) fwL exp -
∫T
T 0
∆hfus w RT2
dT +
∫0
P
)
∆υfus w dP RT
(9)
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 4, the resulting expression for the fugacity of water in the filled hydrate phase is exactly equal to eq 5. 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 the parameter values in eq 9 were obtained from the literature.11 The fugacities of components in the vapor and liquid phases can be routinely calculated from the SRK equation of state incorporated with the modified Huron-Vidal second order
10086 J. Phys. Chem. B, Vol. 105, No. 41, 2001
Seo and Lee
Figure 1. Schematic diagram of the experimental apparatus used in this work: 1. equilibrium cell; 2. water bath; 3. pressure gauge; 4. thermocouple; 5. magnetic stirrer; 6. CO2 cylinder; 7. CH4 cylinder; 8, 9. syringe pumps; 10. multicontroller; 11. check valve; 12. rupture disc; 13. line filter; 14. high-pressure pump; 15. sampling valve; 16. helium gas; 17. gas chromatograph; 18. external heat exchanger; 19. high-pressure pump; 20. sampling port.
mixing rule.13 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.14 3. Experiments Materials. Methane was supplied by the Scientific Gas Products Co. and had a purity of 99.99 mol %. Carbon dioxide with a minimum purity of 99.9 mol % was supplied by World Gas Co. Water was supplied from Sigma-Aldrich Chemical Co. with a purity of 99.1 mol %. Apparatus. A schematic diagram of the experimental apparatus used in this work is shown in Figure 1. The equilibrium cell is made of 316 stainless steel, and its internal volume is about 50 cm3 and equipped with two thermally reinforced sight glasses. The cell contents were agitated by a magnetic spin bar that was coupled with an immersion magnet placed under the cell in the bath. The bath contained about 30 L of a liquid mixture of ethylene glycol and water, the temperature of which was controlled by an externally circulating refrigerator/heater. The actual operating temperature in the cell was maintained with the PID temperature controller (Jeio Tech, MC-31) with (0.1 K accuracy and was measured by a K-type thermocouple probe with a digital thermometer (Cole-Parmer, 8535-26), of which the resolution is (0.1 K (Every Ready Thermometer Co. Inc.). A Heise Bourdon tube pressure gauge (CMM 104957, 0-200 bar range) having the maximum error of (0.1 bar in the full-scale range was used to measure the cell pressure in the system. For the measurement of vapor compositions at a given equilibrium condition, a sampling valve (Rheodyne, 7413) having a sampling loop of about 0.5 µL was installed and connected to a gas chromatograph (Hewlett-Packard, 5890A) on-line through a high-pressure metering pump (Milton Roy,
2396-31). To analyze the compositions of water-rich and carbon dioxide-rich liquid phases, two sampling valves (Rheodyne, 7410) having a sampling loop of 1 µL were also connected to a gas chromatograph on-line. However, to guarantee the equilibrium state, each liquid phase was recirculated more than 10 h after attaining equilibrium through the closed system consisting of an equilibrium cell, a metering pump having dual ports, and a sampling valve. The gas chromatograph used a thermal conductivity (TCD) and a PORAPAK-Q packed column. A vapor-sampling valve was used to perform the GC calibration for two guest molecules of methane and carbon dioxide. The carbon dioxide and methane gas mixture having a predetermined ratio was made using two syringe pumps (ISCO Co. D Series) that have a function of constant flow operation. The charged gas mixture compositions in the equilibrium cell were again checked by a gas chromatograph. Procedure. An amount of approximately 25 mL of liquid water was initially charged into the equilibrium cell using a metering valve. The equilibrium cell was then charged with a mixture of carbon dioxide and methane. When the cell was pressurized to a desired pressure with a gas mixture, the system was cooled to about 5 K below the anticipated hydrate-forming equilibrium temperature. Hydrate nucleation and growth was then induced in the aqueous solution, and the system pressure was continuously decreased due to the mixed hydrate formation. The consumed amount of gas mixture was immediately supplemented by using the high-pressure pump in order to maintain the isobaric condition of the system. When the system pressure reached a steady state, the cell temperature was then very slowly elevated to dissociate the formed hydrates. The external heater was used to increase the system temperature at a rate of 1 to 2 K per h. A little increment of the cell temperature made the solid hydrate particles to be dissociated and caused the corresponding increase of system pressure. To maintain the system
Multiple-Phase Hydrate Equilibria
J. Phys. Chem. B, Vol. 105, No. 41, 2001 10087
TABLE 2: Upper Quadruple Point (H-Lw-LCO2-V) for Carbon Dioxide and Methane Mixtures P/bar
T/K
Vapor Phase Composition (CO2 mol %)
44.12 49.30 55.00 62.20 72.51
283.32 283.86 284.39 285.03 285.76
100.00 94.04 89.13 83.56 79.74
pressure constant, a control valve directly connected to the cell was used and the dissociated gas was vented through the valve. When a minute amount of crystals remained and system pressure was kept constant at least for 8 to 10 h after the system temperature was stabilized, the resulting temperature and pressure were considered as the three-phase H-Lw-V equilibrium conditions. An upper quadruple point at which the four phases of hydrate, water-rich liquid, carbon dioxide-rich liquid, and vapor (H-Lw-LCO2-V) coexist was also determined to establish the upper pressure limit of the H-Lw-V line. When the system pressure and temperature were in equilibrium, each phase was analyzed several times by gas chromatograph to eliminate any fault that could have occurred during the sampling procedure and to confirm the data reproducibility. Each sample was analyzed at least five times, and the average composition was adopted as the equilibrium one at the specified condition. The experimental composition deviations of vapor, water-rich, and carbon dioxide-rich liquids were found to be within (0.1%, (0.2%, and (0.2%, respectively. 4. Results and Discussion The three-phase equilibrium, H-Lw-V, line of the binary carbon dioxide and the water system intersects with two quadruple points. The upper quadruple point at which the four phases, H-Lw-LCO2-V, coexist is located at the intersection between the H-Lw-V equilibrium line and another three-phase equilibrium line involving carbon dioxide-rich liquid, waterrich liquid, and vapor phases. On the other hand, the lower quadruple point comprises the four phases of hydrate, ice, waterrich liquid, and vapor (H-I-Lw-V). These two quadruple points bound the H-Lw-V equilibrium line, and the simple hydrate of carbon dioxide is thermodynamically stable at lower temperature and higher pressure than the H-Lw-V equilibrium line. However, the upper quadruple point for the binary methane and water system cannot exist because the critical point temperature (191 K) of pure methane is far below the lower quadruple point temperature (272.9 K). Such a low critical temperature prevents the vapor pressure line from intersecting the H-Lw-V equilibrium line above 273 K and makes it impossible to produce an upper quadruple point. Accordingly, the lower quadruple point becomes the lowest along the H-Lw-V equilibrium line. The H-Lw-V equilibria for the ternary carbon dioxide, methane, and water system were measured at several isobaric conditions, as shown in Figure 2, and found to agree well with those of Adisasmito et al.4 The addition of methane to carbon dioxide in the vapor phase raised, to a large extent, the hydrateforming/dissociating pressure at the specified temperature. The upper quadruple points were also determined at several different gas-phase compositions. For this ternary system, the upper quadruple point evolves into a line.15 The lower point of this line is regarded as the upper quadruple point intersecting the H-Lw-V curve. The H-Lw-V lines of mixed hydrates were located between those of simple carbon dioxide and methane hydrates. At low carbon dioxide vapor compositions, the
Figure 2. Hydrate dissociation curves of the ternary water, carbon dioxide, and methane mixture. Numbers indicate the mole percent of carbon dioxide in the vapor phase (water-free basis).
H-Lw-V lines were similar to that of simple methane hydrate and intersected only with the lower quadruple points. However, the H-Lw-V lines for high carbon dioxide vapor compositions closely approached that of simple carbon dioxide hydrate and were bounded between the upper and lower quadruple points. This phenomenon can be understood by comparing the sizes and cage occupancy of guest molecules. Methane molecules form structure I hydrate and enter both small and large cavities because of their small size. Although carbon dioxide molecules also form structure I hydrate, they can only occupy the large cavities. When structure I is formed with a mixed gas of carbon dioxide and methane, these two species compete with each other for better occupancy. Experimental results showed that the H-Lw-V lines below 40 mol % carbon dioxide had the same trend with that of simple methane hydrate because methane molecules occupied all small cavities and a great portion of large cavities. Above 60 mol % carbon dioxide, carbon dioxide molecules are encaged in most of the large cavities and methane molecules are encaged in a small portion of small cavities. There are three times as many large cavities as small ones in structure I. The better occupancy of carbon dioxide into the large cavities resulted to closely approaching the H-Lw-V lines of mixed hydrates to that of simple carbon dioxide hydrate. Above 79 mol % carbon dioxide concentration, the H-Lw-V equilibrium lines were observed to intersect the corresponding upper quadruple points. The lower quadruple point can also exist at the intersection of the H-Lw-V line with the H-I-V line where the four phases of hydrate, ice, liquid water, and vapor coexist. Instead of by experimental determination, the lower quadruple locus was estimated from two three-phase equilibrium lines. The full understanding of this phase behavior indicates that hydrates can form only at a temperature and pressure region to the left of the H-Lw-V and H-I-V lines, while to the right no hydrate formation is possible. Figure 3 shows the temperature versus composition diagram based on the three-phase equilibrium composition measurements at several isobars. The equilibrium temperature decreases as the carbon dioxide concentration in the vapor phase decreases. As previously mentioned, the three-phase equilibrium lines termi-
10088 J. Phys. Chem. B, Vol. 105, No. 41, 2001
Figure 3. Hydrate phase equilibria of the ternary water, carbon dioxide, and methane mixture at five different pressures.
nate at their corresponding quadruple points. The upper quadruple locus starts from the upper quadruple point temperature and pressure of the binary carbon dioxide-water mixture (283.32 K, 45.3 bar) and moves to higher temperature and pressure as the carbon dioxide concentration in the vapor phase decreases. It finally terminates at a certain mixture composition of carbon dioxide and methane. To the right of the upper quadruple locus, the hydrate phase cannot exist and the system will contain only fluid phases. Below the lower quadruple pressure (25 bar) of pure methane, the isobaric H-Lw-V lines terminate at their lower quadruple points having the different
Seo and Lee vapor phase compositions. In the region below the lower quadruple locus, the ice phase of course appears. While the slope of the lower quadruple locus is nearly flat, that of the upper quadruple locus is quite steep. These phase behaviors might provide valuable information for developing several types of the hydrate-based chemical technologies. Two three-phase curves of the H-Lw-V and H-I-V are calculated from the model discussed in the previous section and depicted in Figures 2 and 3. As can be seen in Figure 2, the calculated results agree well with the experimental data at the low concentration of carbon dioxide in the vapor phase, but at high concentration deviate a little, particularly in the high-pressure region. These results might be due to the intrinsic uncertainty of the modified UNIFAC model. Despite this limitation, the modified UNIFAC was used in this study because of its great simplicity and adaptability. All of the reference properties of carbon dioxide and methane hydrates are obtained from the literature.15 By using the P-T and T-yCO2 diagrams depicted in Figures 2 and 3, the H-Lw-V surface in the P-T-yCO2 space was constructed in Figure 4, which was truncated by the upper quadruple locus existing only at high carbon dioxide vapor compositions. With decreasing carbon dioxide composition in the vapor phase, the corresponding pressure at the upper quadruple point increases at a large extent. At 75 mol % carbon dioxide in the vapor phase, the corresponding H-Lw-V curve was observed to ascend continuously without occurring any abrupt change of slope to 120 bar and higher. However, at the slightly higher carbon dioxide concentration, 79 mol %, the H-Lw-V curve was terminated at the quadruple point of 285.76 K and 72.2 bar. These experimental measurements confirm that the terminal point of quadruple locus exists in the carbon dioxide composition range of 75-79 mol %. Considering the 50 bar isobaric plate, the H-Lw-V curve and upper quadruple point
Figure 4. P-T-yCO2 space of the ternary water, carbon dioxide, and methane mixture.
Multiple-Phase Hydrate Equilibria
J. Phys. Chem. B, Vol. 105, No. 41, 2001 10089
Figure 5. Isobaric (50 bar) three-phase H-Lw-V equilibria of the ternary water, carbon dioxide, and methane mixture at 281.36, 282.56, 283.36, and 283.56 K and a four-phase H-Lw-LCO2-V equilibrium at 283.86 K.
can be represented by the T-yCO2 trajectory and a unique point, respectively. At five different temperatures, the concentrations of vapor, water-rich liquid, and carbon dioxide-rich liquid were measured and the overall experimental results were demonstrated in Figure 5 through five triangular diagrams (a-e). The vapor, waterrich liquid, and hydrate phase compositions are represented by the vertices of the specified triangle. Because of the weak solubility of gas components in water, the vapor and waterrich liquid phase compositions are located at the vertex and side of a triangular diagram, respectively. While the structure I hydrate stoichiometrically comprises 85 mol % of water, the composition ratio of carbon dioxide to methane in the hydrate phase increases with raising temperature, indicating that carbon dioxide molecules are more preferably encaged than methane
molecules in the cavities. Vapor and water-rich liquid phase composition was measured by direct analysis using gas chromatography, but hydrate-phase composition was calculated from previously mentioned thermodynamic model. It should be noted before discussing further that, at the specified temperature and pressure, the number of equilibrium phases reduces from three to two when changing vapor phase composition is determined from three-phase equilibria. More specifically, when carbon dioxide composition in the vapor phase exceeds that of the H-Lw-V equilibria, only two phases of hydrate and vapor exist. But, at lower carbon dioxide compositions, the other two phases of vapor and water-rich liquid are formed in the equilibrium state. As temperature increases, the two vertices that represent vapor and hydrate compositions move upward, which leads to the
10090 J. Phys. Chem. B, Vol. 105, No. 41, 2001 enhancement of carbon dioxide composition. As a consequence, the H-Lw-V triangle becomes almost straight at 283.56 K, just below the upper quadruple temperature, 283.86 K. At this quadruple temperature, the amount of carbon dioxide in vapor phase is large enough to liquefy and therefore the single vapor phase separates to vapor and carbon dioxide-rich liquid phases. Due to the negligible solubility of methane and water in carbon dioxide-rich phase, the LCO2 composition appears just near the vertex of the triangular diagram. These five triangular diagrams provide several thermodynamic insights for understanding hydrate stability. When the isobaric plate slices the H-Lw-V equilibrium surface, the decrease of temperature gradually expands a hydrate stability region. In order for hydrate to coexist with water-rich liquid and vapor phases, the initial mixture compositions must lie inside the small domain of the triangle. This three-phase triangular domain becomes smaller and finally the new fourphase tetragonal domain appears at the upper quadruple point. With the basis of general phase behavior of the mixed hydrates having two guest components, a potential hydrate-based gas separation/recovery technology can be possibly developed after checking other key design variables, such as thermal and transport properties.16 5. Conclusion The isobaric three-phase (H-Lw-V) equilibria were measured for the mixtures having two guest components of carbon dioxide and methane and one host component of water at several different composition ratios. The quadruple locus where the four phases (H-Lw-LCO2-V) coexist was found to end at 79 mol % of carbon dioxide. At 50 bar, the H-Lw-V curve and upper quadruple point were represented by the T-yCO2 trajectory and a unique point, respectively. At five different temperatures, the concentrations of vapor, water-rich liquid, and carbon dioxiderich liquid were measured and examined through five triangular diagrams. Three-phase triangular domains became smaller as the equilibrium temperature increased, and finally the new four-
Seo and Lee phase tetragonal domain appeared at the upper quadruple point. Hydrate phase equilibria (H-Lw-V and H-Lw-LCO2-V) were successfully predicted by the RKS-EOS with MHV mixing rule incorporated with the modified UNIFAC method. Two Kihara energy and size parameters, and σ, were obtained by fitting all experimental data in the hydrate-forming region. The proposed model can be effectively used to predict hydrateforming characteristics of highly complex systems. 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. References and Notes (1) Makogon, Y. F. Hydrates of Hydrocarbons; PennWell Books: Tulsa, OK, 1997; Introduction. (2) Unruh, C. H.; Katz, D. L. Pet. Trans. AIME 1949, 83. (3) Berecz, E.; Balla-Achs, M. Gas Hydrates; Elsevier: Amsterdam, 1983; Chapter 5. (4) Adisasmito, S.; Frank, R. J., III; Sloan, E. D., Jr. J. Chem. Eng. Data 1991, 36, 68. (5) Dholabhai, P. D.; Bishnoi, P. R. J. Chem. Eng. Data 1994, 39, 191. (6) Ohgaki, K.; Takano, K.; Sangawa, H.; Matsubara, T.; Nakano, S. J. Chem. Eng. Jpn. 1996, 29, 478. (7) Servio, P.; Lagers, F.; Peters, C.; Englezos, P. Fluid Phase Equilib. 1999, 158-160, 795. (8) van der Waals, J. H.; Platteeuw, J. C. AdV. Chem. Phys. 1959, 2, 1. (9) Mckoy, V.; Sinanoglu, O. J. Chem. Phys. 1963, 38, 2946. (10) Parrish, W. R.; Prausnitz, J. M. AIChE J. 1972, 11, 26. (11) Holder, G. D.; Zeets, S. P.; Pradhan, N. ReV. Chem. Eng. 1998, 5, 2. (12) de Swaan Arons, J.; Diepen, G. A. M. Rec. TraV. Chim. 1963, 82, 249. (13) Huron, M. J.; Vidal, J. Fluid Phase Equilib. 1979, 3, 255. (14) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1988. (15) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: New York, 1998; Chapter 4, 5. (16) Kang, S.-P.; Lee, H. EnViron. Sci. Technol. 2000, 34, 4397.
