Kinetics of Methane Hydrate Formation from SDS Solution - Industrial

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Ind. Eng. Chem. Res. 2007, 46, 6353-6359

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Kinetics of Methane Hydrate Formation from SDS Solution J. S. Zhang,† Sangyong Lee,‡ and Jae W. Lee*,† Department of Chemical Engineering, The City College of New York, New York, New York 10031, and Department of Chemical and Natural Gas Engineering, Texas A&M UniVersitysKingsVille, KingsVille, Texas 78363

The role of sodium dodecyl sulfate (SDS) in methane hydrate formation is investigated in a nonstirred batch reactor. Addition of SDS reduces the induction time, but no systematic trend is observed between induction times and SDS concentrations. The hydrate growth is analyzed by using a diffusion-reaction kinetics model with an assumption that crystallization occurs only in the liquid film at the gas-liquid interface. At the start of hydrate growth, the apparent rate constant increases linearly with increasing aqueous SDS concentrations. The apparent rate constant during hydrate growth increases as more available gas-liquid interface is generated. SDS not only increases hydrate nucleation rate by reducing the interfacial tension between hydrate and liquid but also accelerates hydrate growth rate by increasing the total surface area of hydrate particles and the gas-liquid interfacial area. 1. Introduction Gas hydrates are crystalline compounds in which small molecules such as methane, ethane, CO2, etc. stabilize the cavities formed by hydrogen-bonded water molecules.1 One volume of methane hydrates store ∼170 volumes (standard temperature and pressure, STP) of methane, which corresponds to ∼25% of the volumetric capacity of liquefied methane and is slightly less than the volumetric capacity of compressed gas at a pressure of 20 MPa (200 m3 (STP)/m3).2 Storage of natural gas in the form of gas hydrates is attracting a lot of interest because of its safe and economical features.3 The challenges in the practical application of hydrate storage are slow formation rate, separation/package of hydrate particles, and conversion of entrapped water.4,5 The hydrate formation rate is affected by many operating parameters, such as the level of supercooling, the speed of agitation, the presence of additives, etc.6 Several studies have indicated that certain surfactants can promote hydrate nucleation and accelerate hydrate growth.5,7-10 Among the surfactants investigated, sodium dodecyl sulfate (SDS) was found to be one of the effective additives for maximizing methane storage density as well as accelerating the growth rate of methane hydrates.9,11,12 Zhong and Rogers5 reported that, at a SDS concentration of 284 ppm, ethane hydrates grow at a rate that is 700 times higher than that in a pure water system because of SDS micelle formation. Gayet et al.13 suggested that dissolved SDS prevents hydrate particles from agglomerating; they then grow along the reactor wall as a porous structure, which absorbs the liquid from the bulk to the crystallization front where the gas-liquid interface is renewed and hydrates grow at a high rate without any mechanical agitation. Watanabe et al.14 observed that HFC32 hydrates grow along the reactor wall as porous layers in the presence of SDS, and they proposed a capillary mechanism to interpret the high growth rate in a nonstirred reactor. However, these two recent observations were made visually, and no specific experimental data or theoretical analyses are available for the fundamental understanding of the role of SDS * To whom correspondence should be addressed. Tel.: (212) 6506688. Fax: (212) 650-6660. E-mail: [email protected]. † The City College of New York. ‡ Texas A&M UniversitysKingsville.

in promoting hydrate formation. The objective of this paper is to clearly understand the role of SDS in methane hydrate formation under static conditions. The hydrate nucleation is interpreted according to the gas hydrate nucleation theory, and the hydrate growth is analyzed by using a diffusion-reaction kinetics model. 2. Experimental Section 2.1. Materials. SDS with a certified purity of >99% was purchased from Sigma-Aldrich. Methane was supplied by T. W. Smith with a purity of 99.97%. All chemicals were used as received without further purification. Deionized water was produced in our lab with a resistivity of 17 mΩ cm-1. 2.2. Apparatus. Figure 1 shows the schematic diagram of the experimental setup to analyze nucleation and growth of methane hydrates in the presence of SDS. We used a 450 mL high-pressure reactor that is customized by Parr Instruments with two view windows. However, the actual reactor volume including void space of fitting is 474 mL. The temperature of the reactor was controlled by circulating the coolant from an Isotemp 3006P thermostat (Fisher Scientific) with a stability of (0.01 K inside the jacket around the cell. The temperature of the reactor was monitored with two type-T thermocouples (Omega Engineering), where one was immersed in the liquid and the other was placed in the headspace. The precision of the temperature measurement is (0.5 K. The pressure of the reactor is measured by using a 9001PDM pressure transducer (Ashcroft, 0-34.47 MPa) with an accuracy of (0.03 MPa. The temperatures of the liquid and gas phases as well as the pressure were sampled every 20 s by the Labview interface. 2.3. Procedures. We charged 150 mL of SDS solution to the reactor, purged the reactor with methane twice, and then introduced methane up to 7.5 MPa. The temperature of the reactor was set to 282 K, and the system was kept at this temperature for 2 h. Then, the reactor was cooled down to the desired temperature of 271 or 274 K. The induction time is defined as the period that the temperature remained at the desired value before the onset of a significant temperature change in the system. The amount of methane consumed during hydrate growth was calculated by the Peng-Robinson equation of state (EOS)15 using the gas-phase temperature and pressure. The

10.1021/ie070627r CCC: $37.00 © 2007 American Chemical Society Published on Web 08/18/2007

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r)-

dnG dC ) -DAg-l |y)0 ) dt dy Dkπµ2Cw Ag-l coth(δxkπµ2H/DCw)(fg - feq) (4) H

x

where Ag-l is the gas-liquid interfacial area and nG is the mol of methane in the gas phase. The apparent rate constant, kapp, is defined as

kapp ) Ag-l

x

Dkπµ2Cw coth(δxkπµ2H/DCw) H

(5)

Equation 4 can be rewritten as

r ) kapp(fg - feq) 4. Induction Time for Methane Hydrate Nucleation

Figure 1. Schematic diagram of the experimental setup.

fraction of water converted to methane hydrates is ∼60% at the end of all runs. 3. Kinetic Model of Hydrate Growth For a quiescent system, gas hydrates predominantly start to crystallize at the gas-liquid interface but not in the bulk phase of the SDS solution.13,14 Thus, we will assume that hydrate nucleation and growth occur only in the liquid film at the gasliquid interface. On the basis of the kinetic model for hydrate growth proposed by Englezos et al.,16 the global rate of reaction for all particles can be expressed as

dn ) kπµ2(f - feq) dt

(1)

1 1 1 ) + k kr kd

(2)

where n is the mol of methane consumed; k is the overall rate constant; kd is the mass transfer coefficient; kr is the intrinsic rate constant; µ2 is the second moment of particle-size distribution, which refers to the total surface area of hydrate particles; f is the fugacity of methane in the gas phase; and feq is the equilibrium fugacity of methane. The mass balance on the dissolved methane in a slice of thickness dy and a unit cross section in the liquid film is written by modifying the previous model,16

D

Cw d2f d2C ) D ) kπµ2(f - feq) H dy2 dy2

(6)

(3)

where D is the diffusivity of dissolved methane in water; C is the aqueous methane concentration; Cw is the water concentration; and H is the Henry constant. The boundary conditions are

f ) fg at y ) 0 f ) feq at y ) δ where δ is the thickness of the crystallization zone. The rate of gas consumed during hydrate growth can be derived as follows, starting from the original model16 (refer to the detailed derivation in the Appendix),

In this work, the nominal SDS concentration refers to the aqueous SDS concentration initially charged to the reactor at room temperature. The methane hydrate induction times with respect to different nominal SDS concentrations at 271 and 274 K with 7 MPa are summarized in Table 1. At the nominal concentrations of 260-10000 ppm, the induction time is less than 14 h. For a pure water + methane system, no hydrates were observed for more than 3 days under the same experimental conditions. The induction time versus the nominal SDS concentration is plotted in Figure 2. There is no systematic trend between induction times and nominal SDS concentrations at 274 K, even though the induction time seems to decrease with increasing nominal SDS concentrations at 271 K. The following analysis will show that this trend still lies within the uncertainty of the measurements. At the two nominal SDS concentrations of 2500 and 10000 ppm in Figure 2, the induction time is, respectively, between 0 and 5.9 h (2.8 ( 3.1 h) with 95% confidence at 271 K and between 0 and 10.8 h (4.8 ( 6.0 h) with 95% confidence at 274 K. The difference between the average induction times at 260 and 10 000 ppm at 271 K is 5.7 h, which is within experimental error. These results indicate that the induction time under static conditions is not changed by the different amounts of SDS. Zhong and Rogers5 found that the induction time for ethane hydrate nucleation in a quiescent system levels off at a SDS concentration of 242 ppm, which is similar to our results for methane hydrates. The mechanism of SDS promoting hydrate nucleation under static conditions is still poorly understood. The induction time is a measure of the nucleation period in which water and gas molecules in the metastable region interact to form nuclei of a critical size, from which the gas hydrate growth can proceed.6 The induction time for hydrate nucleation in a quiescent system is influenced by supersaturation, the presence of additives and foreign particles, interfacial tension of hydrate-liquid, etc.17 Several researchers13,18,19 found using experiments and theoretical studies that SDS and other surfactants have no significant effect on the methane hydrate equilibrium. Thus, methane supersaturation exists, but the degree of supersaturation (S ) ln(f/feq)) at a specific temperature is not changed much by the presence of SDS. The presence of SDS may also affect hydrate nucleation because the increased SDS electrolyte concentration decreases water activity and then inhibits initial hydrate nucleation. However, SDS promotes methane hydrate nucleation for the given experimental conditions. Kashchieva and Firoozabadib17 proposed that the induction time decreases with decreasing interfacial tension of hydrate-liquid. One plausible expla-

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Figure 2. Induction for hydrate nucleation at different nominal SDS concentrations at two initial temperatures.

Figure 3. Change in the temperature of gas phase and pressure during hydrate formation with an initial SDS concentration of 1150 ppm.

Table 1. Effect of SDS on the Induction Time (tind/h) for Hydrate Nucleation nominal SDS concentrati ona (ppm) 271 Ka 274 Ka a

first second first second

260

770

1150

2500

10000

8.77 5.41

3.61 3.16 1.18 3.04

5.71 3.37 0.75 1.66

1.31 7.07 2.07 3.67

2.17 0.57 0.41 13.03

Initial conditions.

nation for the effect of SDS on the induction time is that the interfacial tension of hydrate-liquid may decrease to a constant value at SDS concentrations above 260 ppm. Zhong and Rogers5 proposed that SDS micelles containing solubilized ethane are present at SDS concentrations above 242 ppm and act as nucleation sites at 277 K. If SDS micelles are present under our experimental conditions and act as hydrate nucleation sites at aqueous SDS concentrations above 260 ppm, then the induction time should be strongly dependent on the aqueous SDS concentration because the micelle concentration increases proportionally to the aqueous SDS concentration. However, no systematic trend between the induction time and the aqueous SDS concentration is observed for the range of SDS concentrations between 260 ppm and its solubility. Here, the SDS solubility limit can be in the range of 2000-2300 ppm as reported in the previous literature.20 Thus, SDS micelles, if they are present in the aqueous phase, have little influence on the hydrate nucleation. On the other hand, the presence of SDS precipitants at a nominal SDS concentration above the SDS solubility (2000-2300 ppm20) has little effect on the induction time, as shown in Table 1 and Figure 2. 5. Hydrate Formation around the Ice Melting Point Figure 3 shows a typical plot of the gas-phase temperature and pressure versus reaction time during hydrate formation at an initial temperature of 274 K. Here, “initial” means the end of the induction period. As the hydrate growth proceeds, the temperature increases rapidly to a maximum and then it decreases slowly to the initial temperature, whereas the pressure monotonically decreases toward the equilibrium pressure of 3.1 MPa at 274 K, as predicted by the computer program CSMHYD.6 The rapid temperature increase in the initial stage of hydrate growth agrees with the findings of Zhong and Rogers;5 they reported that the gas temperature spikes when the hydrates

Figure 4. Change in the temperature of gas phase and pressure during methane hydrate formation with two initial SDS concentrations at an initial temperature of 271 K.

start to grow in a quiescent system with SDS. The temperature spike is due to the fact that the latent heat of hydrate formation is released faster than the heat transfers through the reactor wall. The change in the gas-phase temperature and pressure during hydrate formation at an initial temperature of 271 K with two SDS concentrations is given in Figure 4. At a nominal SDS concentration of 260 ppm, two temperature spikes are observed: the first one corresponds to the formation of ice because the gas pressure in the reactor increases; the second one is related to hydrate formation due to the reduction of methane pressure. At a nominal SDS concentration of 770 ppm, methane hydrates form first, immediately followed by ice formation at ∼272 K. The same behavior was also observed for hydrate formation with nominal SDS concentrations above 770 ppm. The findings indicate that the order of ice and hydrate formation at temperatures below the ice melting point is dependent on SDS concentrations. The results presented here suggest that methane hydrates may promote ice formation since ice readily forms at a supercooling of ∼1 K in the presence of methane hydrates; however, ice may not be an efficient nucleator for methane hydrates because there is a time delay of ∼1.5 h for methane hydrate growth at a supercooling of ∼12 K after ice forms, as shown in Figure 4.

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Figure 5. Methane consumed during hydrate formation at an initial temperature of 274 K and pressure of 7 MPa with an initial SDS concentration of 1150 ppm.

Figure 6. Relationship between the apparent rate constant at the start of hydrate growth and the aqueous SDS concentration at two temperatures.

6. Hydrate Growth Rate Constant Figure 5 is an example plot of methane consumed versus reaction time during hydrate formation. In all runs, the kinetic curve reveals a linear development initially and then flattens in the later growth stage as the pressure approaches the equilibrium boundary. The instantaneous growth rate is given by

r(ti) ) -

dnG ∆nG nG,i-1 - nG,i+1 |ti ) |ti ) dt ∆t ti+1 - tt-1

(7)

where nG,i-1 is the mol of methane in the gas phase at ti-1 and nG,i+1 is the mol of methane in the gas phase at ti+1. The apparent rate constant kapp at a specific time ti is calculated from the following equation:

kapp )

(

)

nG,i -1 - nG,i+1 /(fg - fe)ti ti+1 - ti-1

(8)

In this paper, we assume that the temperature in the crystallization zone is equal to the temperature of the liquid phase. The equilibrium pressure of methane hydrates is calculated by using the computer program CSMHYD,6 and the fugacity coefficient of methane is calculated from the generalized viral-coefficient correlation.21

Figure 7. Apparent rate constant as a function of time during hydrate growth with three initially nominal SDS concentrations at an initial temperature of 271 K and a pressure of 7 MPa.

Figure 8. Apparent rate constant as a function of time during hydrate growth with three initially nominal SDS concentrations at an initial temperature of 274 K and a pressure of 7 MPa.

6.1. Apparent Rate Constant at the Start of Hydrate Growth. The aqueous SDS concentration will change as hydrate growth proceeds, because not only does the amount of liquid decrease but also SDS may adsorb on methane hydrates. Thus, it is impossible to determine the instantaneous SDS concentration in the aqueous phase during hydrate growth. However, at the start of hydrate growth, the aqueous SDS concentration is nearly equal to the initial concentration, so the starting growth rate provides useful information about the accelerating effect of SDS on hydrate growth. In this paper, the starting growth rate is defined as the methane consumption rate at a time when the amount of methane consumed is ∼4% of the total methane consumed at the end of the run. If the hydrate number is set to be 6,22 then water conversion at this time is ∼2%, suggesting that the aqueous SDS concentration is very close to the initial concentration. As discussed in the previous section, ice forms before methane hydrates at 260 ppm of SDS below the ice melting point and the aqueous SDS concentration at the start of hydrate growth is significantly different from the initial concentration. Thus, we only analyze the growth rate with an initial SDS concentration between 770 ppm and its solubility at the two initial temperatures of 271 and 274 K. The apparent rate constants (kapp) at the start of hydrate growth at different aqueous SDS concentrations are given in Figure 6. The two temperatures of 272.4 and 275.2 K are a little higher than the initial 271 and

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Figure 9. Possible mechanism for methane hydrate formation under SDS.

274 K because hydrate formation already reached 2% of water conversion. At these two temperatures, the kapp increases linearly with increasing aqueous SDS concentration. At the start of hydrate growth (or at end of the induction period), there is a very small amount of hydrate crystals at the gas-liquid interface; thus, the gas-liquid interfacial area, Ag-l, equals the cross-sectional area of the reactor regardless of SDS concentrations. Caskey and Barlage23 reported that SDS has a small effect on the diffusivity of carbon dioxide in water, and Hanright et al.24 proposed that dissolved surfactants have little effect on the interfacial mass transfer. Therefore, we assume that the diffusivity of methane in the crystallization zone and the mass transfer coefficient around the hydrate particles are independent of aqueous SDS concentration. Thus, the diffusion-related terms (D, k, and δ) in eqs 1-5 are independent of aqueous SDS concentration. So is the Henry constant (H), because the presence of SDS does not affect gas hydrate equilibrium.13,19 Therefore, at the beginning of hydrate growth, the increased kapp in Figure 6 indicates that µ2 (which is related to the total surface area of hydrate particles) increases with increasing SDS concentration, according to eq 5. The increase in µ2 with increasing SDS concentration is due to more hydrate particles in the crystallization zone. The increased number of hydrate particles is not coming from the increased nucleation rate, because the induction time is not significantly affected by the SDS concentration, as shown in Figure 2. This means that SDS prevents the agglomeration of hydrate particles, which can contribute to increasing the number of particles over time for a given nucleation rate. 6.2. Apparent Rate Constant during Hydrate Growth. The kapp’s at the two initial temperatures with the three nominal SDS concentrations are illustrated in Figures 7 and 8, respectively. When f/feq < 1.05, large errors may be involved in calculating the pressure-driving force; thus, only kapp’s at f/fe > 1.05 are plotted in these two figures. The kapp at an initial temperature of 271 K increases and then eventually approaches a plateau as hydrate growth proceeds, whereas the kapp at an initial temperature of 274 K increases to a maximum and then decreases as more water converts to methane hydrates. At the plateau and maximum point of the kapp in Figures 7 and 8, the aqueous SDS concentration increment is 4 times their initial values in Figures 7 and 8. As mentioned in the previous section, the increase of kapp’s at the start of hydrate growth is due to the increased number of hydrate particles (µ2 in eq 5). However, during hydrate growth, the increase in µ2 can be partially offset by the decrease in the nucleation rate to some extent because the driving force for hydrate nucleation decreases because of the temperature increase. Thus, the fourfold increase in the kapp’s is coming from the increased gas-liquid interfacial area, Ag-l, as water converts to hydrates. It should be noted that the D, k, and H in eq 5 slightly depend on the temperature in the crystal-growth zone;25,26 thus, they do not change much during hydrate growth, since the increase in the temperature is never >8 K in all runs. Therefore, the kapp is predominantly determined by the gas-liquid interfacial area, Ag-l This increase in the kapp can also be qualitatively explained by the growth behavior of gas hydrates in the previous works13,14 and our experiment. Gayet et al.13 reported that hydrate growth in the saturated hydrate layer is sustained by the transport of SDS solution from the bulk phase to the porous hydrate layer on the reactor wall by a capillary force. We also observed that methane hydrates grow along the reactor wall, and then they transform to dense snowlike particles in the later stage. As the saturated hydrate layer grows along the reactor wall, more gasliquid interface area is produced during hydrate growth. Once all of the SDS solution transports to the hydrate layer on the reactor wall, Ag-l will not change. There seems to be an increase in the kapp in the later stage of hydrate growth in Figure 7, but the rate term in the numerator of eq 8 keeps decreasing over time. This increased kapp can be due to the small difference of (fg - feq) in the denominator of eq 8 as the temperature and pressure approach the equilibrium boundary. The decrease in the kapp in Figure 8 may come from the low nucleation rate,

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which can result in a decrease in the number of hydrate particles in the crystallization zone. Figure 9 illustrates a possible mechanism of methane hydrate nucleation and hydrate growth in the presence of SDS. If it is assumed that SDS does not form micelles under hydrate-forming conditions, as reported by previous works,14,20,27,28 SDS monomer molecules can align in the gas-liquid interface, as shown in Step 1 of Figure 9. Then, the hydrate nucleation may begin from the reactor wall of the gas-liquid interface where the temperature is the lowest due to the coolant circulation as in Step 2. Finally, gas hydrates grow upward on the wall by transferring the SDS liquid solution to the porous hydrates by capillary force.13

F ) 0 at y ) δ Solving this second-order differential equation with the boundary conditions gives

{ (x ) ( x ( x )} exp -

Appendix Derivation of the Kinetic Equation for Gas Hydrate Growth in Liquid Film. We can rewrite eq 3 with the boundary conditions as

D

Cw d2f d2C ) D ) Kπµ2(f - feq) H dy2 dy2

(A1)

f ) fg at y ) 0 f ) feq at y ) δ If we let F ) f - feq, then the equation will be

D

Cw d2F ) Kπµ2F H dy2

F ) fg - feq at y ) 0

(A2)

Kπµ2H y DCw

Then, we obtain eq A4:

7. Conclusions We have first carried out a quantitative analysis of the SDS effect on methane hydrate formation kinetics. SDS dramatically reduces the induction time for methane hydrates; however, no systematic trend is observed between the induction time and the SDS concentrations ranging from 260 to 10000 ppm. Thus, SDS micelles or SDS precipitants, if any, have little effect on hydrate nucleation. Using the gas hydrate nucleation theory, we understand that rapid gas hydrate nucleation comes from the decreased interfacial tension between hydrate surface and SDS solution. At an initial SDS concentration of 770 ppm and at an initial temperature of 271 K, methane hydrates form immediately followed by ice growth at a supercooling of ∼1 K, whereas at an initial SDS concentration of 260 ppm, methane hydrates form 1.5 h after ice forms even with the 12 K supercooling. Thus, the order of ice and hydrate formation at temperatures below the ice melting point is affected by the SDS concentration. The growth rate of methane hydrates was analyzed by using a diffusion-reaction kinetic model, assuming that crystallization only occurs in the liquid film at the gas-liquid interface. At the start of hydrate growth, the increased apparent rate constant with respect to SDS concentrations is due to the increase in the second momentum (the number of hydrate particles). During the hydrate growth period, the apparent rate constant increases as the gas-liquid interfacial area increases by transporting more SDS solution to the porous hydrate layer on the reactor wall.

Kπµ2H y - exp 2 DCw

F ) exp

r)-

(

)

Kπµ2H δ × DCw fg - feq

(x

1 - exp 2

Kπµ2H δ DCw

)

)

(A3)

dnG Cw dF dC ) -DAg-l |y)0 ) -DAg-l | dt dy H dy y)0

) Ag-l

x

DKπµ2Cw coth(δxKπµ2H/DCw)(fg - feq) H

(A4)

Literature Cited (1) Sloan, E. D. Fundamental principles and application of natural gas hydrates. Nature 2003, 426, 353. (2) Thoms, S.; Dawe, R. A. Review of ways to transport natural gas energy from countries which do not need the gas for domestic use. Energy 2003, 28, 1461. (3) Gudmundsson, J. S.; Borrehaug, A. A Frozen hydrate for transport of natural gas. In 2nd International Conference on Natural Gas Hydrate; 1996; p 415. (4) Mori, Y. H. Recent advances in hydrate-based technologies for natural gas storagesA review. J. Chem. Ind. Eng. (China) 2003, 54 (Suppl), 1. (5) Zhong, Y.; Rogers, R. E. Surfactants effects on gas hydrate formation. Chem. Eng. Sci. 2000, 55, 4175. (6) Sloan, E. D. Clathrate Hydrates of Natural Gas, 2nd ed.; Dekker: New York, 1998. (7) Kutergin, O. B.; Mel’nikov, V. P.; Nesterov, A. N. Influence of surfactants on the mechanism and kinetics of the formation of gas hydrates. Dokl. Akad. Nauk SSSR (Russian) 1992, 323, 549. (8) Karaaslan, U.; Parlktuna, M. Surfactants as hydrate promoters? Energy Fuels 2000, 14, 1103. (9) Ganji, H.; Manteghian, M.; Sadaghiani Zadeh, K.; Omidkhah, M. R.; Rahimi Mofrad, H. Effect of different surfactants on methane hydrate formation rate, stability and storage capacity. Fuel 2007, 86, 434. (10) Daimaru, T.; Yamasaki, A.; Yanagisawa, Y. Effect of surfactant carbon chain length on hydrate formation kinetics. J. Petrol. Sci. Eng. 2002, 56, 89-96. (11) Link, D. D.; Ladner, E. P.; Elsen, H. A.; Taylor, C. E. Formation and dissociation studies for optimizing the uptake of methane by methane hydrates. Fluid Phase Equilib. 2003, 211, 1. (12) Di Profio, P.; Arca, S.; Germani, R.; Savelli, G. Novel nanostructured media for gas storage and transport: clathrate hydrates of methane and hydrogen. J. Fuel Cell Sci. Technol. 2007, 4, 49. (13) Gayet, P.; Dicharry, C.; Marion, G.; Graciaa, A.; Lachaise, J.; Nesteroy, A. Experimental determination of methane hydrate dissociation curve up to 55 MPa by using a small amount of surfactants as hydrate promoter. Chem. Eng. Sci. 2005, 60, 5751. (14) Watanabe, K.; Imai, S.; Mori, Y. H. Surfactant effects on hydrate formation in an unstirred gas/liquid system: An experimental study using HFC-32 and sodium dodecyl sulfate. Chem. Eng. Sci. 2005, 60, 4846. (15) Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59. (16) Englezos, P.; Dholabhai, P.; Kapgeralos, N.; Bishnoi, P. R. Kinetics of formation of methane and ethane gas hydrates. Chem. Eng. Sci. 1987, 42, 2647. (17) Kashchieva, D.; Firoozabadib, A. Induction time in crystallization of gas hydrates. J. Cryst. Growth 2003, 250, 499. (18) Rovetto, L. J.; Strobel, T. A.; Koh, C. A.; Sloan, E. D., Jr. Is gas hydrate formation thermodynamically promoted by hydrotrope molecules? Fluid Phase Equilib. 2006, 247, 84.

Ind. Eng. Chem. Res., Vol. 46, No. 19, 2007 6359 (19) Lee, S.; Zhang, J.; Mehta, R.; Woo, T.; Lee, J. W. Methane hydrate equilibrium and formation kinetics in the presence of an anionic surfactant. J. Phys. Chem. C 2007, 111, 4734. (20) Watanabe, K.; Niwa, S.; Mori, Y. H. Surface tension of aqueous solutions of sodium alkyl sulfates in contact with methane under hydrateforming conditions. J. Chem. Eng. Data 2005, 50, 1672. (21) Smith, J. M.; Van Ness, H. D. Introduction to chemical engineering thermodynamics, 4th ed.; McGraw-Hill: New York, 1987; Chapter 11. (22) Circone, S.; Kirby, S. H.; Stern, L. A. Direct measurement of methane hydrate composition along the hydrate equilibrium boundary. J. Phys. Chem. B 2005, 109, 9568. (23) Caskey, J. A.; Barlage, W. B. A study of the effects of soluble surfactants on gas absorption using liquid laminar jets. J. Colloid Interface Sci. 1972, 41, 52. (24) Hanwright, J.; Zhou, J.; Evans, G. M.; Galvin, K, P. Influence of surfactant on gas bubble stability. Langmuir 2005, 21, 4912.

(25) Afanassiev, I. S.; Bezverkhy, P. P.; Martynets, V. G.; Matizen, E. V. Unsteady-state methane absorption by water before hydrate formation. Dokl. Chem. 2001, 381, 341. (26) Lekyam, K.; Bishnoi, P. R. Dissolution of methane in water at low temperatures and intermediate pressures. Fluid Phase Equilib. 1997, 131, 297. (27) Di Profio, P.; Arca, S.; Germani, R.; Savelli, G. Surfactant promoting effects on clathrate hydrate formation: are micelles really involved? Chem. Eng. Sci. 2005, 60, 4141. (28) Zhang, J.; Lee, S.; Lee, J. W. Does SDS micelle under methane hydrate-forming conditions below the normal Krafft point? J. Colloid Interface Sci. 2007, accepted for publication.

ReceiVed for reView May 3, 2007 ReVised manuscript receiVed June 20, 2007 Accepted July 6, 2007 IE070627R