In Situ Studies of the Mass Transfer Mechanism across a Methane

Dec 9, 2009 - Hydrate films typically form at gas−water interfaces where the concentrations of guest and host molecules are the highest. Once formed...
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J. Phys. Chem. C 2010, 114, 1173–1180

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In Situ Studies of the Mass Transfer Mechanism across a Methane Hydrate Film Using High-Resolution Confocal Raman Spectroscopy Simon R. Davies, E. Dendy Sloan, Amadeu K. Sum, and Carolyn A. Koh* Center for Hydrate Research, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401 ReceiVed: September 30, 2009; ReVised Manuscript ReceiVed: NoVember 10, 2009

Hydrate films typically form at gas-water interfaces where the concentrations of guest and host molecules are the highest. Once formed, the films provide a significant mass transfer barrier to further hydrate formation. However, controversy exists about whether it is the transport through the crystal film of the guest or the host (water) molecule that controls further hydrate growth. In this study, methane hydrate films were formed at a gas-water interface, and the gas and water phases were then replaced by isotopic tracers. The concentration profiles of the tracers across the hydrate films were studied over time using confocal Raman spectroscopy in order to determine the relative mobility of guest and host molecules within hydrate film. The films were found to contain gas-filled pores, which provided pathways for gas migration. These pores annealed over time, increasing the mass transfer resistance. The results indicate that the host water molecules are the most mobile species in the hydrate phase, and that hydrate growth is controlled by the movement of water within the hydrate film. Introduction Gas hydrates are crystalline inclusion compounds composed of water cages (host) that trap small guest molecules, such as methane and carbon dioxide.1 Gas hydrates occur naturally worldwide, in sediments beneath the ocean and in arctic regions.2,3 These natural hydrated deposits are estimated to contain over twice the amount of energy of all other fossil fuels available, thereby presenting a potentially plentiful alternative energy resource.1,4 Gas hydrates also form blockages in subsea oil and gas flowlines, which can result in severe economic, safety, and environmental consequences. Other applications of gas hydrates include energy storage in the form of methane or hydrogen, as well as carbon dioxide sequestration.5 An appealing hydrate application is the use of carbon dioxide to recover methane from natural hydrate deposits; methane is produced while carbon dioxide, a greenhouse gas, is sequestered.6 To aid in advancing the technological developments for energy recovery and storage and controlling hydrate formation in flowlines, insight into the hydrate formation process is critical. Due to the availability of the hydrate formers, gas hydrates tend to form first at interfaces between a water-rich phase and a phase rich in the guest molecule, such as methane or CO2. The rate of hydrate formation at such interfaces is rapid and leads to the formation of a film that separates the two phases and retards the hydrate formation rate.1 This effect has been observed for hydrate formation from water-hydrocarbon interfaces,7-11 CO2-water interfaces,8,12-18 water-fluorocarbon interfaces,19-21 on the surface of ice particles,22-24 and on emulsified water droplets.23 Once the hydrate film has formed across the interface, the hydrate film can thicken from the diffusion of guest molecules initially dissolved inside the waterrich phase and host molecules initially dissolved in the guestrich phase. However, at longer time scales when the dissolved hydrate formers become depleted, the hydrate formation rate is * To whom correspondence should be addressed. E-mail: [email protected]. Tel: (+1) 303-273-3237. Fax: (+1) 303-273-3730.

limited by the mass transfer of the hydrate formers or water across the hydrate film. The growth rate of a hydrate film across an interface between a guest-rich phase and a water-rich phase has been studied in detail for both CO2-water systems14,15 and methane-water systems.25 These studies showed that the growth rate was limited by heat or mass transfer between the growing hydrate front and the bulk fluid phases. The various heat transfer models have been summarized by Mochizuki and Mori,26 and a similar mass transfer model is described by Mochizuki and Mori.18 The time scale of the initial growth of a hydrate film is very short: film growth rates from 20 to 1000 µm/s have been reported.14,15,25 The subsequent mass transfer limited growth period is much slower, but controversy still exists about whether the transport of the guest2,12,13,23,27,28 or water molecules29-34 controls the hydrate growth rate. This question has notable importance, as it determines the driving force for hydrate formation and how this driving force transfers between different systems. It is the aim of this study to better understand the mass transfer mechanism across a hydrate film. Since ice Ih is composed of a hydrogen-bonded water lattice, it is often used as an analogue to hydrate. The mass transfer mechanisms of water and gas molecules within ice Ih are comparatively well understood. There is general agreement that the diffusion of gas molecules in ice Ih is dependent on the molecular radii of the gas molecules, with smaller molecules such as helium, neon, and argon diffusing faster than larger molecules such as nitrogen, oxygen, and methane. The measured diffusivities of helium, neon, and argon in ice Ih were determined to be 10-9, 10-10, and 10-11 m2/s, respectively, at temperatures between 258 and 268 K.35 The diffusivities of molecular nitrogen and oxygen in ice Ih were estimated at 10-13 m2/s at 263 K.36 The diffusivity of methane in ice was estimated at 10-13 m2/s at 268 K,37 and similar estimates for the diffusivity of CO2 in ice gave a value of 10-12 m2/s at 268 K.38 Predictions of the diffusion rate of gas molecules in ice Ih using molecular orbital calculations gave similar values; the diffusivity of

10.1021/jp909416y  2010 American Chemical Society Published on Web 12/09/2009

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oxygen, nitrogen, and methane in ice were predicted to be 10-11, 10-12, and 10-14 m2/s, respectively.39 In all cases, the diffusion of gas molecules in ice Ih was found to be much higher than the diffusion of water through ice. The self-diffusion coefficient of ice is known to be highly sensitive to temperature, with values increasing from 10-16 to 10-14 m2/s as the temperature is increased between 233 and 273 K.40 At lower temperatures, the self-diffusion coefficient was found to be even lower, between 10-20 and 10-18 m2/s at temperatures between 140 and 170 K.41-43 On the basis of the findings for ice, one might expect that gas molecules would also diffuse faster than water molecules in hydrate. However, the mechanisms for the diffusion of gas and water molecules in ice are quite different. Molecular dynamics simulations of water and helium diffusion in ice Ih have shown that interstitial water molecules diffuse by distorting the water lattice, whereas helium hops from one site to the next through hexagonal rings.44 In the case of sI hydrate, a molecule diffusing from large cage to large cage through hexagonal rings would be retarded if an adjacent cage were already occupied by a guest molecule. This would result in a slower diffusion rate of gas in hydrate compared to ice since the diffusion rate in solids is proportional to the number of free sites.45 Estimates based on the hydrate formation rate from ice particles place the diffusivity between 10-17 and 10-16 m2/s, although it is unclear whether the hydrate formation was due to the diffusion of water or methane in the hydrate.22,24 A number of research groups have studied the relative mass transfer rates of guest and host molecules in hydrate. It was noted that CO2 hydrate forms faster than methane hydrate under the same fugacity driving force, which might indicate that the diffusion of the guest molecule is responsible for the hydrate growth; the apparent gas-water diffusion coefficient for methane hydrate was found to be approximately 10-16 m2/s and about 1 order of magnitude faster for CO2 hydrate at 10-15 m2/s.22 However, by regression of a number of parameters to experimental data using some constraints, Salamantin et al. suggested that air molecules diffuse through hydrate 10 times slower than water, but that their diffusion is still significant; the value of the diffusion coefficient was estimated at 10-14 m2/s.46 Monte Carlo simulations suggest that the diffusivity of CO2 in hydrate is much higher than water in hydrate: 10-12 m2/s for CO2 at 273 K compared to 10-23 m2/s for water at 200 K.47 In addition, recent kinetic Monte Carlo equilibrium path sampling also suggested that guest molecules diffuse faster than water molecules in sI hydrate; a diffusivity of 10-16 m2/s was obtained for methane in sI hydrate.48 Scanning electron microscope (SEM) images of hydrates reveal mesoporous structures. Mesopores would significantly increase the mass transfer rate across a hydrate film compared to solid surfaces that are modeled in molecular simulations. The pores have been shown to fill over time, making the hydrate denser.49,50 The pores ranged in size from 0.1 to 1 µm, and, despite the water-wet nature of the hydrate,51 the pores can be filled with gas.52 The porous structure likely depends on the hydrate formation conditions. In the case of ice that was formed from brine, the pores tend to be larger for shock-cooled water (up to 300 µm), and smaller for ice formed under controlled conditions (up to 50 µm).53 In this study, Raman spectroscopy was used to study the mass transfer of methane and water across a hydrate film to determine whether the diffusion of water or gas is responsible for the growth of the hydrate film. The hydrate films were formed at a gas-water interface and a tracer was then added to the vapor

Davies et al.

Figure 1. A schematic of the experimental setup for the gas replacement (left) and water replacement experiments (right).

or water phase. The concentration profile of the tracer in the hydrate was then monitored as a function of time using either the peak-area ratio (PAR) in the case of the vapor-based tracer, or the peak position in the case of the water-based tracer from the Raman spectrum of the respective phases. It has been previously demonstrated that the PAR method can be used to determine the concentration of dissolved methane in water under pressurized conditions.54 The PAR method was also shown to give reliable values for the diffusivity of dissolved methane in water under pressurized conditions.55 Experimental Method A confocal Raman spectrometer was used for these experiments to allow the tracer concentration to be measured as a function of time and position in the hydrate film. The confocal Raman spectrometer also allowed images of the hydrate film to be recorded to observe morphological changes as the film annealed over time. The Raman spectrometer, a LabRamHR confocal microspectrometer (Horiba Jobin Yvon), was equipped with a 20× objective lens. A diode laser with a wavelength of 532.08 nm provided the excitation source. Scattered light from the sample was collected at an angle of 180° from the incident source and passed through a 200 µm hole and an entrance slit that was typically set at 100 µm, and was then dispersed by a grating with a density of 1800 grooves/mm. The focal length for the spectrometer was 800 mm. The spectrometer was calibrated using neon emission lines, and the resolution of the spectrometer was less than 1 cm-1. The spectra were analyzed using Grams AI Version 7.02 from Thermo Galactic, Inc. The spatial resolution of the spectrometer was within 100 µm. The experimental setups that were specifically developed for this work are shown in Figure 1 for the vapor and water replacement experiments. For each experiment, the hydrate film was formed inside a cylindrical high pressure cell that was fitted with a sapphire window (Sam O. Colgate, Inc.). Hydrate films were formed along the gas-water interface so that one side of the film was observable through the sapphire window. This allowed for visual observation and for the acquisition of confocal Raman spectra at various locations in the film along the interface of the hydrate and the window. The cell was cooled by an external glycol jacket. The pressure rating of the cell was 35 MPa and the volume was 1 cm3. First, deionized water was loaded into the cell using a glass syringe. The volume of water added to the cell for the vapor replacement experiments was critical: too little water, and the resultant hydrate film would consume most of the water phase and would be difficult to measure; too much water, and hydrate would block the two gasfilled ports located half way up the cell. A water volume of 0.3 cm3 was found to be optimal for these experiments. For the water replacement experiments, the setup was modified as shown

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Figure 2. Confocal microscope images of the hydrate film showing pore filling as the film annealed.

in Figure 1 (right). Avoiding the blockage of the two ports in these experiments was more complicated since the hydrate film would need to be formed above the ports to allow the water phase to be replaced. In addition, pressurizing the cell with gas was a challenge since the line used for gas charging was still filled with gas that was in contact with water. This line would inevitably plug with hydrate when the cell was cooled. To avoid this problem, a small volume of water was displaced into the line before hydrate formation. This was achieved by filling an adjacent section of tubing, 8 cm in length and 0.3175 cm (1/8 in.) diameter with H216O water at the same time as the cell was filled. The gas was charged through the other port, and, subsequently, 1 cm3 of water was displaced from the tubing, through the cell, into the line that had been used for gas charging. The cell was filled with a water volume of approximately 0.7 cm3 for the water replacement experiments. Prior to the water replacement experiments, 3 cm3 of the H218O water had been loaded into another piece of tubing, 8 cm in length and 0.635 cm (1/4 in.) in diameter. The two pieces of tubing were connected in parallel by two three-way valves, which allowed either tube to be used to displace the water in the cell. Once the hydrate film had been formed and annealed, the three-way valves were opened to the H218O, and the water phase in the cell was slowly displaced. The total volume of water replaced was 3 cm3. This ensured the effective replacement of the H216O water beneath the hydrate film with H218O water. When replacing the water or the vapor phase in the cell, it was essential to avoid changes in pressure within the system. Such changes were found to lead to the cracking of the hydrate film. Such pressure changes were avoided using a custom-made Ruska Tandem Pump, which consisted of two gas cylinders, each with a volume of 100 cm3, connected by a piston, which ensured that the total volume, and thus the pressure, of the two cylinders was conserved as the piston was moved. For the vapor replacement experiments, the tracer gas was added to one of the cylinders, and the hydrate-former was added to the other. Once the hydrate had formed, the tandem pump could then be used to displace the vapor phase in the cell with the tracer gas without affecting the pressure. In the case of the water replacement experiments, both of the cylinders were filled with the hydrate-forming gas, and the H218O water was added to the

cell by displacing the water from the 0.635 cm (1/4 in.) diameter tubing into the cell. Temperature in the Raman cell was controlled by a circulating cooler (model 1167P from VWR). Once the gas or water had been replaced, the cell was isolated using two needle valves, and the associated piping was vented. The cell was disconnected using two quick connects, and the cell and cooler assembly were moved to the confocal Raman spectrometer where it was mounted on a manual (x-y-z) stage, which was used to move and control the position of the hydrate film relative to the fixed spectrometer. The protiated methane used for these experiments was acquired from General Air, Inc. (99.97 mol % purity). The isotopic tracers, CHD3 and H218O, were acquired from Cambridge Isotopes, Inc. at purities of 98 mol % and 97 mol %, respectively. For the gas replacement experiments, a single Raman acquisition of 60 s was used. For the water replacement experiments, three Raman acquisitions of 100 s were needed to adequately capture the lattice vibrational modes of the hydrate. Results and Discussion The confocal ability of the Raman spectrometer allowed microscopic images of the hydrate film to be acquired at the interface of the hydrate film and the sapphire window. Figure 2 shows a set of images of one methane hydrate film that was taken at the interface of the vapor and hydrate phases shortly after the hydrate film formed at 277 K and 7 MPa. The gas phase appears as a light color, and the hydrate and water appear as the darker areas in the images. The hydrate films appeared quite uneven, as shown in Figure 2, and varied in apparent thickness from 150 to 1500 µm. This wide variation was attributed to the way the film formed on the meniscus of the water phase against the sapphire window. The thickness and position of the hydrate film proved very difficult to control. The figures clearly indicate the presence of gas-filled pores within the film, and over time the pores filled with hydrate. The intensity of the gas-phase contribution decreased as the spectrometer was moved toward the hydrate-water interface, indicating that the film became less porous or that more of the pores within the film were filled with water further from the overlying vapor phase. The tracer gas selected for these experiments was CHD3. The peak positions and intensities for the gas phase of CHD3, CH3D,

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Figure 3. Example Raman spectra for the gas phase of CHD3 compared to CH4 at 277 K and 7 MPa showing the peak positions assigned by Bermejo et al.56

Figure 4. Example Raman spectra for a mixed gas hydrate of CHD3 and CH4 with some vapor phase contribution at 277 K and 7 MPa.

CH2D2, and CD4 were measured previously at 0.15 MPa.56 CHD3 was found to be the most suitable gas phase tracer for this work since it has an asymmetric (υ3) stretching mode at 2991.5 cm-1,56 which is sufficiently far apart from the symmetric stretching mode of CH4 at 2916.7 cm-1 to allow both peaks to be distinctly resolved, while being close enough to allow both to be viewed with the same grating position. In addition, the relative intensity of the asymmetric stretching mode is quite strong, which means that the tracer could be detected in low concentrations. Typical Raman spectra for the gas phases of CH4 and CHD3 at 277 K and 7 MPa are shown in Figure 3.

Davies et al. The υ3a(a1) asymmetric stretch of CHD3 is separated from the symmetric stretch of CH4 by approximately 75 cm-1, but has only 35% of the intensity. Figure 4 shows a typical Raman spectrum of a binary hydrate of CH4 and CHD3. The relative intensities of CH4 in the large and small cages are quite similar, in contrast to the typical 3:1 sI ratio. This suggests that there is some gas phase contribution to the small cage peak intensity, since the methane small cage frequency almost coincides with methane in the gas phase. The spectrum also shows that the asymmetric stretch of the CHD3 molecule splits into two peaks in the presence of hydrate, which likely results from the different environments of the large cage of sI hydrate and the small cage or vapor phase. The clear separation of the peaks for CHD3 in the gas and hydrate large cage allowed for calibration curves to be constructed to relate the ratio of the CH4 and CHD3 peak areas to the ratio of the mole fractions for the vapor and hydrate phases using known gas compositions. Calibration curves were constructed for both the vapor and hydrate phases using the peaks at 2979 cm-1 and 2990 cm-1 to represent the hydrate phase and vapor phase, respectively (see Supporting Information). The contribution of the small cages was neglected in the construction of these calibration curves due to the difficulty in deconvoluting that peak from the gas phase contribution. It was assumed for these experiments that the hydrate had no preference for the protiated methane (CH4) or the tracer (CHD3). In the literature, a small preference of the hydrate for protiated methane has been reported; however, the difference between the composition of the vapor and hydrate phases was shown to be less than 5 mol % at 274.2 K.57 The calibration curves allowed the molar concentrations of the gas and hydrate phases to be determined from the PARs that were measured in the gas replacement experiments. Figures 5 and 6 show the tracer concentrations that were measured in the vapor and hydrate phases as a function of distance from the top of the hydrate film (the gas-hydrate interface) at different times after the gas phase had been replaced for four different experiments. Each point in the figures represents an average of five measurements at different horizontal positions within the hydrate film; each measurement was made using a 60 s acquisition time. The typical standard deviation for the five measurements was 0.02 in mole fraction. In the first experiment, the hydrate film was formed at 7 MPa and 277 K, and the vapor phase was replaced soon after the

Figure 5. Mole fraction of CHD3 in the vapor (left) and the hydrate (right) as a function of distance from the top of the hydrate film for various times after the gas replacement for a non-annealed hydrate film that was formed at 277 K and 7 MPa.

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Figure 6. Mole fraction of CHD3 in the vapor (left) and the hydrate (right) as a function of distance from the top of the hydrate film for various times after the gas replacement for a hydrate film that was formed at 277 K and 7 MPa and annealed for 24 h before the gas replacement.

film had nucleated. The results from this experiment are shown in Figure 5. The mole fractions of the tracer that were measured indicated that the vapor was highly mobile within the hydrate film, but the concentrations of CHD3 measured in the hydrate phase were much lower than in the vapor phase. Over time, more of the tracer became incorporated into the hydrate phase with the greatest concentration toward the top of the hydrate film. However, from these results alone, it was unclear as to whether the incorporation of the tracer into the hydrate phase was a result of the pore-filling phenomenon observed in Figure 2, or a result of the high mobility of the guest molecules from within the hydrate phase. In order to differentiate these two effects, a second experiment was performed (Figure 6), in which the hydrate film was allowed to anneal for 24 h before the vapor phase was replaced. This annealing step ensured that most of the pore filling had occurred prior to the addition of the tracer. Again, the composition of the tracer in the gas-filled pores rapidly increased to the bulk gas phase composition, indicating the high mobility of the gas phase within the hydrate film. However, in this case, little tracer was incorporated into the hydrate phase even 84 h after the tracer had been added to the gas phase. This result indicated that the increase in CHD3 concentration in the hydrate that was observed in the first experiment was caused by pore filling rather than the high mobility of the guest molecules within the hydrate phase. Toward the end of the second experiment, the concentration of CHD3 in the hydrate at the top of the hydrate film started to increase, indicating either the formation of new hydrate, or occurring as a result of the diffusion of gas molecules through the hydrate lattice. The results obtained in these experiments showed no dependence on the system pressure: the results from hydrate films formed at 7, 10.3, and 14 MPa were qualitatively similar (see Supporting Information). In order to provide complementary evidence for the mass transfer mechanism, experiments were performed where the water phase beneath the hydrate film was replaced by an isotopic tracer. The isotopic tracer chosen for these measurements was H218O. In the literature, it has been shown that H216O and H218O diffuse at the same rate in ice Ih.58 It is therefore assumed that both would behave similarly in a hydrate lattice. In addition, the diffusion rate of helium in ice Ih formed from H216O and H218O was found to be similar.59 One disadvantage of using H218O as a tracer is that hydrate has been shown to concentrate

Figure 7. The effect of the concentration of H218O on the lattice vibration of ice Ih.

the H218O in bulk systems by up to 0.3 mol %.60-62 This effect is considered negligible for the interpretation of these results. An alternative to H218O would have been deuterated water (D2O). The diffusion rate of D2O and H218O in ice Ih are reported to be similar at the temperatures of interest.63 However, D2O has more disadvantages than H218O. First, at temperatures below 200 K, D2O is known to diffuse faster in ice Ih than H216O, and it is therefore unclear how the diffusion rates would compare in a hydrate lattice.64 Second, the diffusion rate of helium in D2O ice was shown to be higher than in H216O ice because of the lower vibrational frequency of the O-D bond, which allows for easier hopping of the gas molecule from site to site.59 Hydrates have also been shown to concentrate D2O by approximately 2 mol %, a greater extent than for H218O.61,62 Finally, the hydrate equilibrium temperature for D2O-methane hydrate is approximately 2.5 K higher than for H2O-methane hydrate.65 The lattice vibrational modes of ice Ih are expected to depend on the concentration of H218O in the lattice. It has previously been predicted that the lattice vibrational frequency of ice would decrease as the concentration of H218O is increased; the shift in frequency is expected to be between 5 and 30 cm-1 for H218O and H216O ice.66 Figure 7 shows the measured Raman spectra of ice Ih for three different H218O concentrations. The difference in the lattice vibrational frequency between H218O and H216O ice, was measured as 12 cm-1. Each spectrum was taken using five acquisitions, each of 60 s. The vibrational mode for the

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Figure 8. The effect of the concentration of H218O on the lattice vibration of sI methane hydrate at 277 K and 7 MPa.

Figure 9. A calibration curve relating the Raman shift of the lattice vibration to the mole fraction of H218O in the hydrate phase at 277 K and 7 MPa.

liquid phase was found to be weak compared to the lattice vibrational mode of the ice phase. The measured lattice vibrational mode for the hydrate film was also found to depend on the concentration of H218O. The spectra shown in Figure 8 are for methane hydrate formed from H216O and H218O at 7 MPa and 277 K. The spectra were taken using three acquisitions, each of 100 s. The lattice vibrational frequencies for sI methane hydrate were also found to shift to lower frequencies as the H218O concentration was increased. The frequency shift between H218O and H216O methane hydrate

Davies et al. was measured at 16 cm-1; however, the peaks were much broader than for ice Ih and were found to have a bimodal distribution. The lattice vibrational frequency was found to decrease linearly with H218O concentration as shown in Figure 9. This finding could be used to determine the H218O concentration in the hydrate film from the measured lattice vibrational frequency. Again, the vibrational mode for the liquid phase was found to be weak compared to the lattice vibrational mode of the hydrate phase and was neglected. Figure 10 shows the results from two water-replacement experiments. The methane hydrate films were formed at 7 MPa and 277 K and allowed to anneal for 24 h before the water phase was replaced. The efficiency by which the water phase had been replaced could be evaluated at the end of each experiment by determining the concentration of H218O in the water phase by freezing the water and measuring the lattice vibrational frequency of the resultant ice phase. This could be related to the isotope concentration as shown in Figure 7. The results from the water replacement experiments suggest that the water molecule is highly mobile within the hydrate film. The first set of measurements was taken 1 h after the water phase had been replaced. The results showed that the H218O concentration increased with the distance from the top of the hydrate film. The top of the hydrate contained very little H218O, whereas the concentration of H218O in the hydrate at the bottom approached that of the bulk water phase. Within 24 h, the concentration of H218O in the hydrate phase approached that of the bulk water. This result indicates that water molecules are more mobile in the hydrate than the guest molecules, and it is predominantly the movement of water through the hydrate film that results in further hydrate formation, leading to the pore filling and film growth that was shown in Figure 2. The apparent mobility of the water molecules within the hydrate films was startlingly high. Previous estimates of the diffusivity of hydrate formers in a nonporous hydrate phase are between 1 × 10-17 and 1 × 10-15 m2/s.22,24 Treating the hydrate film as a flat nonporous plate and applying a one-dimensional Fickian diffusion model that was evaluated using a Fourier series,10 little movement of the hydrate formers through a hydrate film would be expected in the first 24 h based on an effective diffusivity of 1 × 10-16 m2/s. The effective diffusivity would need to be increased to 1 × 10-13 m2/s for a similar trend in the hydrate former mobility in a 24 h period (see

Figure 10. Mole fraction of H218O in the hydrate lattice as a function of distance from the top of the hydrate film for various times after the water replacement for two hydrate films that were formed at 277 K and 7 MPa and annealed for 24 h before the water replacement.

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J. Phys. Chem. C, Vol. 114, No. 2, 2010 1179 REMRSEC [DMR 0820518]. A.K.S. acknowledges the support from DuPont as a DuPont Young Professor. Supporting Information Available: Calibration curves for CH4 in the vapor and hydrate phases, and additional concentration profiles of CHD3 in the hydrate film. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 11. Expected tracer concentration in the film at 24 h for various effective diffusivities.

Figure 11). The unexpectedly high mobility of the water molecules that was observed in these experiments suggests that other factors influenced the measured mobility of water molecules. One possible factor is that the contact of the hydrate film on the sapphire window caused water molecules to be preferentially more mobile along the interface observed with the Raman spectrometer; this would bias the results, as the Raman spectra can only be measured in the portion of the film immediately close to the window. An alternative explanation is that the polycrystalline nature of the hydrate film with numerous visible pores contributed to the relatively high mobility of water and hydrate formers inside the hydrate film. This latter hypothesis is in agreement with the capillary permeation model proposed by Mori and Mochizuki and supports the concept that mass transfer resistance to hydrate film growth is defined by the rate of transport of water molecules across the film.32 Conclusions This study suggests that water molecules are more mobile than methane molecules within methane hydrate. The hydrate films formed in this study initially contained numerous gasfilled pores, which provided pathways for the rapid migration of gas molecules within these pores. However, the gas molecules were slow to be incorporated into the hydrate phase relative to the water molecules, indicating a low mobility within the hydrate phase. Over time, hydrate formed within the gas-filled pores in a water-limited reaction, increasing the mass transfer resistance to further hydrate formation. CHD3 was found to be a good tracer for the gas phase since its composition within the hydrate can be monitored with Raman spectroscopy using the ratio of the symmetric stretch of CH4 to the asymmetric stretch of CHD3, as both are observable with the same grating position in the spectrometer. H218O was found to be a good tracer for the water phase since its composition within the hydrate can be monitored with Raman spectroscopy using the lattice vibrational mode. Acknowledgment. We are grateful to Professor Walter Chapman and Professor Emeritus Riki Kobayashi at Rice University for loaning us the Ruska Tandem pump. The authors acknowledge Drs. P. R. S. Prasad, T. Sugahara, H. Ohno, and T. Strobel for their advice and assistance with the Raman spectroscopy measurements. This work was supported by the CSM Hydrate Consortium. The authors acknowledge the additional financial support from the United States Department of Energy under Contract DE-FG02-05ER46242, and from NSF-

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