J. Phys. Chem. B 2009, 113, 5487–5492
5487
Phase Equilibria and Thermodynamic Modeling of Ethane and Propane Hydrates in Porous Silica Gels Yongwon Seo,*,† Seungmin Lee,† Inuk Cha,† Ju Dong Lee,‡ and Huen Lee§ Department of Chemical Engineering, Changwon National UniVersity, 9 Sarim-dong, Changwon, Gyeongnam 641-773, Republic of Korea; AdVanced Energy Resource DeVelopment Team, Korea Institute of Industrial Technology, 1274 Jisa-dong, Gangseo-gu, Busan 618-230, Republic of Korea; and Department of Chemical and Biomolecular Engineering, Korea AdVanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Republic of Korea ReceiVed: NoVember 28, 2008; ReVised Manuscript ReceiVed: February 15, 2009
In the present study, we examined the active role of porous silica gels when used as natural gas storage and transportation media. We adopted the dispersed water in silica gel pores to substantially enhance active surface for contacting and encaging gas molecules. We measured the three-phase hydrate (H)-water-rich liquid (LW)-vapor (V) equilibria of C2H6 and C3H8 hydrates in 6.0, 15.0, 30.0, and 100.0 nm silica gel pores to investigate the effect of geometrical constraints on gas hydrate phase equilibria. At specified temperatures, the hydrate stability region is shifted to a higher pressure region depending on pore size when compared with those of bulk hydrates. Through application of the Gibbs-Thomson relationship to the experimental data, we determined the values for the C2H6 hydrate-water and C3H8 hydrate-water interfacial tensions to be 39 ( 2 and 45 ( 1 mJ/m2, respectively. By using these values, the calculation values were in good agreement with the experimental ones. The overall results given in this study could also be quite useful in various fields, such as exploitation of natural gas hydrate in marine sediments and sequestration of carbon dioxide into the deep ocean. 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, structure 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, while the sH hydrate consists of three types of cages.1 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. Naturally occurring gas hydrates in the earth, which contain mostly CH4, are regarded as future energy resources.1 Recent investigations suggest the possibility of sequestering carbon dioxide produced from fossil fuel-fired power plants and industry as gas hydrates in the deep ocean or in the natural gas hydrate layer to prevent further release into the atmosphere.2,3 Since each volume of gas hydrate can contain as much as 170 volumes of gas at standard temperature and pressure conditions, gas hydrate can also be applied to natural gas storage and transportation.1 Handa and Stupin4 first studied the effect of porous media on equilibrium pressures of CH4 and C3H8 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.5,6 experimentally determined the equilibrium pressures of CH4, C3H8, and CO2 hydrates in porous glasses of different pore sizes. Seshadri et al.,7 Smith et al.,8 and Zhang et * To whom correspondence should be addressed. Tel: 82-55-213-3757. Fax: 82-55-283-6465. E-mail:
[email protected]. † Changwon National University. ‡ Korea Institute of Industrial Technology. § Korea Advanced Institute of Science and Technology.
al.9 reported the pore equilibrium pressure-temperature data of C3H8, CH4, and C2H6 hydrates in silica gels, respectively, by using the same experimental method suggested by Handa and Stupin.4 Anderson et al.10,11 presented experimental results of CH4, CO2, and CH4 + CO2 hydrates in mesoporous silica glass. They determined the dissociation equilibrium point of each hydrate by a step heating technique considering the pore size distribution. Seo et al.12 and Seo and Lee13 studied phase equilibria of CH4, CO2, and CH4 + CO2 hydrates in porous silica gels and also the effects of NaCl on the equilibria of the pore CH4 and CO2 hydrates. When gas hydrates directly form from bulk water or powdered ice, the conversion of water or ice to hydrate is not so high because of the quite limited surface area of the host media. Therefore, we adopted the dispersed water in silica gel pores to substantially enhance active surface for contacting gas molecules when porous silica gels were used as natural gas storage and transportation media. In the present study, the hydrate phase equilibria of binary C2H6 + water and C3H8 + water mixtures were measured in 6.0, 15.0, 30.0, and 100.0 nm TABLE 1: Physical Properties of Silica Gel Samplesa sample
6.0 nm SG
15.0 nm SG
30.0 nm SG
100.0 nm SG
mean particle (33-74) (33-74) (40-75) (40-75) diameter (µm) mean pore 6.8 (6.0) 14.6 (15.0) 30.5 (30.0) 94.5 (100.0) diameter (nm) pore volume 0.84 (0.75) 1.13 (1.15) 0.84 (-) 0.83 (-) (cm3/g) 497 (480) 308 (300) 111 (100) 42.4 (50) surface area (m2/g) a
Values in the parentheses are vendor data.
10.1021/jp810453t CCC: $40.75 2009 American Chemical Society Published on Web 03/31/2009
5488 J. Phys. Chem. B, Vol. 113, No. 16, 2009
Seo et al.
Figure 2. Schematic diagram of the experimental apparatus.
Figure 1. Pore-size distribution of the silica gels used in this study.
silica gel pores to thoroughly examine the effect of geometrical constraints on hydrate phase equilibria. C2H6 and C3H8 are the second and third major components of natural gas, respectively. However, the accurate and systematic approach to the hydrate phase equilibria for the binary C2H6 + water and C3H8 + water mixtures in porous media have rarely been reported by other researchers. In this study, we attempted to examine the more precise nature and unique pattern of pore effects on C2H6 and C3H8 hydrate equilibria in silica gel pores of various diameters (6.0, 15.0, 30.0, and 100.0 nm). A more adequate and refined model with the values of hydrate-water interfacial tensions obtained through application of the Gibbs-Thomson relationship to experimental data was proposed for representing several delicate pore characteristics. Experimental Section Materials. The C2H6 and C3H8 gases used for the present study were supplied by Union Special Gas (Korea) and had a stated purity of 99.9 and 99.7 mol %, respectively. Silica gels of nominal pore diameters 6.0 nm (6.0 nm SG) and 15.0 nm (15.0 nm SG) were purchased from Aldrich (USA). Silica gels of nominal pore diameters 30.0 nm (30.0 nm SG) and 100.0 nm (100.0 SG) were purchased from Silicycle (Canada). All materials were used without further treatment. The properties of silica gels having four different pore diameters were measured by ASAP 2420 and Autopore IV 9520 (Micromeritics, USA) and are listed in Table 1. Their pore-size distributions were also determined and are shown in Figure 1. Apparatus and Procedure. There are two methods to saturate silica gel pores with water. One is to use a desiccator and the other is to use a sonicator. For a desiccator method, the silica gels were first dried at 373 K for 24 h before water sorption. Then, the poresaturated 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 found to be almost identical with the pore volume of each silica gel. For a
Figure 3. P-T trace for determination of H-LW-V equilibrium point of C2H6 hydrate in 15.0 nm SG.
sonicator method, the silica gels were first dried at 393 K for 24 h before water sorption. Some amount of dried silica gel powder was placed in a bottle, and an amount of water identical with the pore volume of silica gel was added to the powder. After mixing, the bottle was sealed off with a cap to prevent water evaporation. Then, the bottle was vibrated with an ultrasonic wave at 293.15 K for 24 h to completely fill the pores with water. The validity of these two methods was verified by comparing the experimental results obtained from two different methods. In the present study, the pore-saturated silica gels were prepared by the desiccator method. A more detailed explanation of the method was given in the previous papers.12,13 The experimental apparatus for hydrate phase equilibria was specially constructed to accurately measure the hydrate dissociation pressures and temperatures, as shown in Figure 2. The equilibrium cell was made of 316 stainless steel and had an internal volume of about 150 cm3. The experiment for hydratephase equilibrium measurements began by charging the equilibrium cell with about 80 cm3 of silica gels containing pore water. After the equilibrium cell was pressurized to the desired pressure with C2H6 or C3H8, the whole main system was slowly cooled to a temperature lower than the expected equilibrium one. When pressure depression due to hydrate formation reached a steady-state condition, the cell temperature was increased in
Ethane and Propane Hydrates in Porous Silica Gels
J. Phys. Chem. B, Vol. 113, No. 16, 2009 5489
TABLE 2: Kihara Potential Parameter for Guest-Water Interaction gas
a (Å)
σ (Å)
ε/k (Å)
C2H6 C3H8
0.4 0.68
3.4383 3.4435
175.0 187.4
∆µwMT-L ∆µw0 ) RT RT
T0
∫
P
0
0.3 K steps, with sufficient time. The equilibrium pressure and temperature of the three phases (hydrate (H)-water-rich liquid (LW)-vapor (V)) were determined by considering the pore-size distribution of the silica gels used. Unlike the bulk hydrate, in the case of hydrates in porous silica gels, it becomes very difficult to determine the unique equilibrium dissociation point in the P-T profile. In the present study, to overcome this inherent difficulty, the dissociation equilibrium point in porous silica gels was chosen as the inflection point of P versus T curve, which corresponds to the extremum point of the dP/dT versus T curve (Figure 3). As indicated by Anderson et al.,10 the inflection point of the heating curve (P versus T) corresponds to the equilibrium dissociation point in the pores of the mean diameter of the silica gels used. A strong resemblance between the heating curve (dP/dT versus T) and pore-size distribution curve guarantees the validity of this method for determining the equilibrium dissociation point in silica gels with broad poresize distributions. Thermodynamic Model. The equilibrium criteria of the hydrate-forming mixture are based on the equality of fugacities of the specified component i in all phases which coexist simultaneously:
ˆf iH ) ˆf iL ) ˆf iV()f wI)
∫
T
∆hwMT-I + ∆hwfus RT2
dT +
∆υwMT-I + ∆υwfus dP - ln aw RT
(4)
where T0 is 273.15 K, the normal melting point of water, ∆µw0 is the chemical potential difference between empty hydrate and water at T0 and zero absolute pressure, ∆hwMT-I and ∆υwMT-I are the molar difference in enthalpy and volume between empty hydrate and ice, respectively, and ∆hwfus and ∆υwfus are the molar difference in enthalpy and volume between ice and liquid water, respectively. aw denotes the activity of water calculated from an equation of state and is equivalent to the product of the activity coefficient of water and the mole fraction of water, xw.
(1)
where H stands for the hydrate phase, L for the water-rich liquid phase, V for the vapor phase, and I for the ice phase. The chemical potential difference between the empty hydrate and filled hydrate phases, ∆µwMT-H ()µwMT - µwH), is generally derived from statistical mechanics in the van der Waals and Platteeuw model:14
∆µwMT-H ) µwMT - µwH ) -RT
∑ νm ln(1 - ∑ θmj) m
Figure 4. Plot of the reciprocal pore diameter (1/d) versus ∆Tm,pore/ Tm,bulk for C2H6 and C3H8 hydrates in silica gel pores.
(2)
j
where µMT w is the chemical potential of water in the hypothetical empty hydrate lattice, νm the number of cavities of type m per water molecule in the hydrate phase, and θmj the fraction of cavities of type m occupied by the molecules of component j. The optimized Kihara potential parameters for C2H6 and C3H8 used in this study are presented in Table 2. Holder et al.15 suggested the method to simplify the chemical potential difference between empty hydrate and reference state as follows:
∆µwMT-I ∆µw0 ) RT RT
∫
T
T0
∆hwMT-I RT2
∫
P
dT +
0
∆υwMT-I dP RT (3)
Figure 5. Hydrate phase equilibria of the binary C2H6 + water mixtures in silica gel pores.
5490 J. Phys. Chem. B, Vol. 113, No. 16, 2009
Seo et al.
TABLE 3: Equilibrium Pressure-Temperature Data for C2H6 Hydrate in Silica Gel Pores 6.0 nm SG
15.0 nm SG
30.0 nm SG
100.0 nm SG
T (K)
P (MPa)
T (K)
P (MPa)
T (K)
P (MPa)
T (K)
P (MPa)
271.97 274.48 275.55 276.99 278.07
0.975 1.42 1.733 2.11 2.529
274.73 277.6 279.99 280.94 282.54
0.976 1.367 1.895 2.244 2.814
277.2 280.1 281.84 283.61 284.4
0.903 1.301 1.663 2.157 2.505
278.69 281.1 283.15 284.13 285.24
1.024 1.414 1.863 2.162 2.556
In the present study, the pores of silica gels were completely saturated with water, and, thus, in 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, which is mainly due to the capillary effect caused by the presence of geometrical constraints, can be expressed as16,17
ln aw ) ln(xwγw) -
FVL cos θ σHW rRT
(5)
where F is the shape factor, a function of the curvature of the hydrate-liquid interface, VL the molar volume of pure water, θ the wetting angle between pure water and hydrate phases, σHW the interfacial tension between hydrate and liquid water phases, and r the pore radius. As noted by Anderson et al.10 and Llamedo et al.,18 in the present study F ) 1 was used for hydrate dissociation in narrow pores. Combining and solving eqs 1, 2, 4, and 5 determines the values of H-LW-V equilibrium pressure and temperature for pores of radius r. A more detailed description of thermodynamic modeling was given in the previous papers.12,13,19 Results and Discussion In the present study, the pores of silica gels were first completely saturated with water, and upon reaching the H-LW-V equilibrium, the pores were filled with only hydrate and liquid water. Therefore, it is assumed that the wetting angle
Figure 6. Hydrate phase equilibria of the binary C3H8 + water mixtures in silica gel pores.
(θ) is 0°. Even though the operative interface of the hydrate and liquid water phases is very important in understanding the pore effect on hydrate formation/dissociation and thermodynamic modeling of pore hydrate equilibrium, no data for the C2H6 hydrate-water and C3H8 hydrate-water interfacial tensions (σHW) have been reported in the literature. To relate the dissociation temperature depression (from bulk conditions) with the pore size of silica gels at a given pressure, the Gibbs-Thomson equation was used in this study. According to this relationship, the temperature depression of hydrate dissociation in a cylindrical pore, ∆Tm,pore, relative to the bulk dissociation temperature, Tm,bulk, is defined as10,20
(
)
(6)
(
)
(7)
∆Tm,pore σHW cos θ )Tm,bulk Fh∆Hh,dr or, in terms of pore diameter
∆Tm,pore 2σHW cos θ )Tm,bulk Fh∆Hh,dd
where ∆Tm,pore is the difference between the pore (Tm,pore) and bulk dissociation temperature, Tm,bulk, at a specified pressure, FH the hydrate density, ∆Hh,d the hydrate dissociation enthalpy, r the pore radius, and d the pore diameter. As shown in Figure 4, the interfacial tension between the hydrate and water can be estimated from the slope of the plot of the reciprocal pore diameter (1/d) versus ∆Tm,pore/Tm,bulk for hydrate dissociation in silica gel pores. Handa21 reported ∆Hh,d values of 71.8 kJ/mol for C2H6 hydrate and 129.2 kJ/mol for C3H8 hydrate through calorimetric studies. For C2H6 hydrate, assuming the hydration number is 7.67 (C2H6 · 7.67H2O), which yields a hydrate density of 969 kg/m3, and hydrate dissociation enthalpy is 71.8 kJ/mol, and applying these values to eq 6 or eq 7, an average value for C2H6 hydrate-water interfacial tension of 39 ( 2 mJ/m2 was obtained from the slope of data in Figure 4. For C3H8 hydrate, assuming the hydration number is 17.0 (C3H8 · 17.0H2O), which gives a hydrate density of 0.898 kg/m3, and hydrate dissociation enthalpy is 129.2 kJ/mol, and applying these values to eq 6 or eq 7, an average value for C3H8 hydrate-water interfacial tension of 45 ( 1 mJ/m2 was obtained from the slope of data in Figure 4. To the best of our knowledge, the value for C2H6 hydrate-water interfacial tension was obtained for the first time in this work. This value is a little larger than those of the ice-water interfacial tension, 32 ( 2 mJ/m2, CH4 hydrate-water interfacial tension, 32 ( 1 mJ/m2, and CO2 hydrate-water interfacial tension, 30 ( 1 mJ/m2.6,11 The value for C3H8 hydrate-water interfacial tension obtained in this work is slightly smaller than that of Uchida et al.,6 50 ( 2 mJ/m2. However, Uchida et al.6 used the mixed gas of 91.2% C3H8, 6.7% CH4, and 2.1% C2H6 to determine the value for C3H8 hydrate-water interfacial tension.
Ethane and Propane Hydrates in Porous Silica Gels
J. Phys. Chem. B, Vol. 113, No. 16, 2009 5491
TABLE 4: Equilibrium Pressure-Temperature Data for C3H8 Hydrate in Silica Gel Pores 6.0 nm SG
15.0 nm SG
30.0 nm SG
100.0 nm SG
T (K)
P (MPa)
T (K)
P (MPa)
T (K)
P (MPa)
T (K)
P (MPa)
263.53 264.22 264.84 264.86
0.233 0.265 0.321 0.309
268.48 269.95 270.47 271.75 272.58
0.187 0.251 0.286 0.349 0.401
271.94 273.12 273.98 274.88 275.74
0.176 0.233 0.286 0.353 0.417
272.83 274.3 275.32 276.44 276.81
0.192 0.259 0.325 0.413 0.449
TABLE 5: Percent AAD between the Experimental and Calculated Values system
pore diameter (nm)
% AAD
C2H6 + water
6.0 15.0 30.0 100.0 6.0 15.0 30.0 100.0
6.4 13.8 2.4 4.0 23.6 15.8 6.5 6.5
C3H8 + water
In the present study, for the prediction of the hydrate (H)-ice (I)-vapor (V) equilibrium line the interfacial tension between TABLE 6: Calculated Lower and Upper Quadruple Points of Hydrates in Silica Gel Pores Q1
Q2
system
pore diameter (nm)
T (K)
P (MPa)
T (K)
P (MPa)
C2H6 + water
6.0 15.0 30.0 100.0 bulk 6.0 15.0 30.0 100.0 bulk
262.0 268.3 270.8 272.2 273.0 260.25 267.7 270.7 272.35 273.13
0.290 0.380 0.422 0.446 0.470 0.089 0.127 0.147 0.159 0.164
279.28 284.1 286.0 287.1 287.65 267.15 273.8 276.43 277.9 278.62
2.764 3.098 3.226 3.310 3.369 0.395 0.485 0.525 0.546 0.559
C3H8 + water
ice and hydrate phases (σIH) was assumed to be zero for C2H6 and C3H8 hydrates. The three-phase H-LW-V equilibria of C2H6 and C3H8 hydrates confined in silica gel pores with nominal diameters of 6.0, 15.0, 30.0, and 100.0 nm were measured between lower and upper quadruple point temperatures. The hydrate equilibrium data of the binary C2H6 + water mixtures are presented along with model calculation in Figure 5 and listed in Table 3. Figure 5 also includes the hydrate equilibrium data obtained by Zhang et al.9 for 6.0 and 15.0 nm pores, which showed a similar trend. At specified temperatures, the H-LW-V lines of C2H6 hydrates in silica gel pores were shifted to a higher pressure region depending on pore size when compared with that of bulk hydrate. In addition, hydrate equilibrium data of the binary C3H8 + water mixtures are presented along with model calculations in Figure 6 and Table 4. For a close comparison, the pore hydrate data reported in the literature are all included in Figure 6: Uchida et al.6 for 10.0, 30.0, and 100.0 nm pores and Seshadri et al.7 for 6.0 and 15.0 nm pores. The present experimental data are in good agreement with those of Uchida et al.,6 but largely deviated from those of Seshadri et al.,7 even though Uchida et al.6 used Vycor porous glass beads and a mixed gas of 91.2% C3H8, 6.7% CH4, and 2.1% C2H6.
Although the experimental determinations of the binary C2H6 (or C3H8) + 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)-water-rich liquid (LW)-C2H6 (or C3H8)-rich liquid (LC2H6(or LC3H8)). The upper quadruple points (Q2), where two H-LW-V and H-LW-LC2H6(or LC3H8) phase boundaries intersect and, thus, four phases (H, LW, LC2H6(or LC3H8), and V) coexist, were located very closely along the saturation vapor pressure curve of C2H6 (or C3H8). The lower quadruple points (Q1), where two H-LW-V and H-I-V phase boundaries intersect and, thus, four phases (H, I, LW, and V) coexist, appear generally adjacent to the corresponding melting point of ice. The calculated quadruple points of the binary C2H6 + water and C3H8 + water mixtures in silica gel pores are listed in Table 5. By use of the values of the hydrate-water interfacial tension suggested by the present work, the predicted H-LW-V values were generally in good agreement with the experimental ones, although a little deviation was found in the results of smaller pores, especially for C3H8 + water mixtures. As indicated by Handa et al.,22 a much larger proportion of bound water, not converted to hydrate, exists in the smaller pores. This might be the reason for only slight deviation at the smaller pores. Although the present thermodynamic model for pore hydrates was proven to be quite reliable in both quantitative and qualitative manners, the percent average absolute deviations (% AADs) between experimental and calculated H-LW-V values are listed in Table 6 for reference. In the present study, we examined the effect of pore size on the hydrate phase equilibria to utilize porous silica gels, which can yield an enhanced surface area for contacting gas molecules, as natural gas storage and transportation media. The optimum pore size for natural gas storage and transportation should be determined by considering both the larger surface area at smaller pore sizes and smaller pressure shift at larger pore sizes. From the experimental results, it was found that silica gels with pore diameter over 30.0 nm gave only very slight pressure shift at a specified temperature and, thus, could be a good candidate for natural gas storage and transportation. Conclusions Three-phase H-LW-V equilibria of C2H6 and C3H8 hydrates confined in silica gel pores with nominal diameters of 6.0, 15.0, 30.0, and 100.0 nm were measured and compared with the calculated results based on the van der Waals and Platteeuw model. Decrease in water activity due to geometrical constraints caused pore hydrates to form at much higher pressure at a specified temperature. Through the Gibbs-Thomson equation fordissociationwithinthecylindricalpores,theC2H6 hydrate-water interfacial tension (σHW) of 39 ( 2 mJ/m2 and the C3H8 hydrate-water interfacial tension (σHW) of 45 ( 1 mJ/m2 were obtained. By use of these values, calculated values of H-LW-V
5492 J. Phys. Chem. B, Vol. 113, No. 16, 2009 were in good agreement with the experimental ones. The values of hydrate-water interfacial tension and thermodynamic results obtained in this study could be used for understanding the fundamental phase behavior and thermodynamic models of gas hydrates in pores, and, thus, could be quite useful in various fields, such as exploitation of natural gas hydrate in marine sediments and sequestration of carbon dioxide into the deep ocean. Acknowledgment. The authors acknowledge funding from the Korea Ministry of Knowledge Economy (MKE) through “Energy Technology Innovation Program”. This research is also financially supported by Changwon National University in 2008 and partially supported by the Brain Korea 21 project. References and Notes (1) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008. (2) Tajima, H.; Yamasaki, A.; Kiyono, F. Energy Fuels 2004, 18, 1451. (3) Park, Y.; Kim, D. Y.; Lee, J.-w.; Huh, D.-G.; Park, K.-P.; Lee, J.; Lee, H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 12690. (4) Handa, Y. P.; Stupin, D. J. Phys. Chem. 1992, 96, 8599. (5) Uchida, T.; Ebinuma, T.; Ishizaki, T. J. Phys. Chem. B 1999, 103, 3659. (6) Uchida, T.; Ebinuma, T.; Takeya, S.; Nagao, J.; Narita, H. J. Phys. Chem. B 2002, 106, 820.
Seo et al. (7) Seshadri, K.; Wilder, J. W.; Smith, D. H. J. Phys. Chem. B 2001, 105, 2627. (8) Smith, D. H.; Wilder, J. W.; Seshadri, K. AIChE J. 2002, 48, 393. (9) Zhang, W.; Wilder, J. W.; Smith, D. H. AIChE J. 2002, 48, 2324. (10) Anderson, R.; Llamedo, M.; Tohidi, B.; Burgass, R. W. J. Phys. Chem. B 2003, 107, 3500. (11) Anderson, R.; Llamedo, M.; Tohidi, B.; Burgass, R. W. J. Phys. Chem. B 2003, 107, 3507. (12) Seo, Y.; Lee, H.; Uchida, T. Langmuir 2002, 18, 9164. (13) Seo, Y.; Lee, H. J. Phys. Chem. B 2003, 107, 889. (14) van der Waals, J. H.; Platteeuw, J. C. AdV. Chem. Phys. 1959, 2, 1. (15) Holder, G. D.; Corbin, G.; Papadopoulos, K. D. Ind. Eng. Chem. Fundam. 1980, 19, 282. (16) Henry, P.; Thomas, M.; Clennell, M. B. J. Geophys. Res. 1999, 104, 23005. (17) Clarke, M. A.; Pooladi-Darvish, M.; Bishnoi, P. R. Ind. Eng. Chem. Res. 1999, 38, 2485. (18) Llamedo, M.; Anderson, R.; Tohidi, B. Am. Mineral. 2004, 89, 1264. (19) Yoon, J. H.; Chun, M. K.; Lee, H. AIChE J. 2002, 48, 1317. (20) Clennell, M. B.; Hovland, M.; Booth, J. S.; Henry, P.; Williams, J. W. J. Geophys. Res. 1999, 104, 22985. (21) Handa, Y. P. J. Chem. Thermodyn. 1986, 18, 915. (22) Handa, Y. P.; Zakrzewski, M.; Fairbridge, C. J. Phys. Chem. 1992, 96, 8594. (23) Deaton, W. M; Frost, E. M., Jr. U.S. Bur. Mines Monogr. 1946, 8, 101.
JP810453T
