Morphology Study of Structure I Methane Hydrate Formation and

May 20, 2009 - The effect of kinetic inhibitors on the morphology of methane structure I hydrate was observed using a high pressure sapphire crystalli...
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CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 7 3014–3023

Articles Morphology Study of Structure I Methane Hydrate Formation and Decomposition of Water Droplets in the Presence of Biological and Polymeric Kinetic Inhibitors Hallvard Bruusgaard, Lindsay D. Lessard, and Phillip Servio* Department of Chemical Engineering, McGill UniVersity, Montre´al, Que´bec, Canada H3A 2B2 ReceiVed June 21, 2007; ReVised Manuscript ReceiVed April 17, 2009

ABSTRACT: The effect of kinetic inhibitors on the morphology of methane structure I hydrate was observed using a high pressure sapphire crystallizer. Two kinetic inhibitors were studied, poly(VP/VC), a lactam ring copolymer of polyvinylpyrrolidone (PVP) and polyvinylcaprolactam (PVCap), and type-I antifreeze protein (AFP). The experiments were performed at temperatures ranging from 274.2 to 275.2 K and pressures from 4200 to 7200 kPa. The experiments were conducted on three droplets simultaneously (a pure water droplet, a droplet containing 0.01 mol/m3 poly(VP/VC), and a droplet containing 0.01 mol/m3 AFP). The morphology and translucency were compared and found to vary significantly due to the presence of kinetic inhibitors. Hydrates formed under a higher driving force had dendrite formation on all but the AFP droplet. Low driving force experiments produced noticeably smoother surfaces on all droplets compared to high driving force experiments. Translucency also varied with AFP and poly(VP/VC) having the appearance of thinner films. Hydrate decomposition was also studied. The pure water droplet had the fastest rate of decomposition, followed by the droplet containing the AFP. The poly(VP/VC) droplet has a visible hydrate skin for a substantially longer period of time than the pure water and the AFP droplet. Introduction Gas hydrates, also known as clathrates, are nonstoichiometric crystalline compounds that form when water molecules hydrogen bond in a network to form cavities that are thermodynamically unstable without the presence of a guest molecule such as a gas or volatile liquid. Hydrates have been problematic in the oil and gas industry for several decades because they have been found to block pipelines, causing severe damage to equipment such as pumps and compressors. Therefore, it is of great interest to find environmentally safe inhibitors that can prevent hydrates from forming or growing large enough to block pipelines.1 Crystal morphology studies are important in terms of providing valuable insight into the mechanistic aspects of hydrate nucleation, growth, and decomposition. The first hydrate crystal morphological studies were performed by Makogon.2 Later, by studying water droplets saturated with a fluorocarbon, Sagaya determined that the surface morphology strongly depends on the degree of saturation of the water phase.3 This was followed by other interfacial surface morphology experiments by Ohmura,4-6 Servio,7,8 and Uchida.9,10 Inhibitors used to prevent hydrate formation are classified as either thermodynamic or kinetic inhibitors.11 Thermodynamic * Corresponding author. Tel: (+1) 514-398-1026; fax: (+1) 514-398-1026; e-mail: [email protected].

Figure 1. Chemical structures of poly(VP/VC).

inhibitors alter the equilibrium conditions for hydrate growth, while kinetic inhibitors either increase the time required to form hydrates or reduce the tendency to agglomerate.11,12 The effect of two different kinetic inhibitors was studied on hydrate nucleation, growth, and decomposition. Previous studies on the effect of kinetic inhibitors on hydrate morphology include reports by Sakaguchi et al.13 and Lee & Englezos.14 The current work is the first to compare the morphological differences between pure water, water with a biological inhibitor (AFP), and water with a polymeric inhibitor (poly(VP/VC)). The poly(VP/VC), a lactam rings copolymer, is characterized by an amide group attached to a polymer backbone. The chemical structures of poly(VP/VC) are given in Figure 1.

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Morphology of Structure I Methane Hydrate Formation

Polyvinylpyrrolidone (PVP) consists of five-member lactam rings attached to a carbon backbone. Molecular weights for these polymers typically range from 10 000 g/mol to 350 000 g/mol. A similar kinetic inhibitor, poly(N-vinylcaprolactam), or PVCap, belongs to the same family of lactam ring polymers as PVP and is characterized by a seven-member lactam ring protruding from a polymeric backbone. Poly(VP/VC) is a copolymer of PVP and PVCap and is thus characterized by five-member and seven-member lactam rings. It has been suggested by Lederhos et al. that during hydrate growth lactam rings adsorb onto the hydrate crystal through hydrogen bonding by the amide group, sterically blocking hydrate growth.15 Furthermore, they suggested that a polymer network extends between small stabilized hydrate particles, possibly providing an inhibiting structure to the surrounding water while blocking the most active growth sites of hydrate crystals. Antifreeze proteins (AFPs) and antifreeze glycoproteins (AFGPs) are proteins that bind to the surface of ice nuclei16 and recently have been found to also prevent hydrate growth.17 They are naturally synthesized by adapted species of fish, plants, and insects that live in subfreezing environments. These proteins prevent the water contained within the organism from freezing in a noncolligative manner thereby keeping them alive.18 Several types of AFGPs and AFPs have been discovered. AFPs have been divided into different types based on their host species, primary amino acid sequences, and 3D structures. Many insect and plant AFPs have been discovered all with their own structures and varying levels of ice inhibiting activity,19 but for the purpose of this study we will focus only on type-I AFP. Type-I antifreeze protein is a small alanine-rich, amphipathic R-helix and is produced by flounder and sculpin species of fish. It is the simplest of the fish AFPs and the one that has been most extensively studied. It has been used as a model system to deduce how these proteins bind to ice.19 Recently, fish and insect AFPs were added to a tetrahydrofuran hydrate forming system in separate experiments, and they were shown to be able to delay the nucleation of hydrates. Experiments were also done on propane hydrates where the AFPs were shown to inhibit their formation.17 In a more recent study, fish AFPs were shown to outperform PVP in terms of delaying nucleation.20 The effects of type-I AFP and poly(VP/ VC) on methane hydrate growth has also been investigated showing that both the biological and polymeric inhibitor have similar performance in inhibiting hydrates.21

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Figure 2. Schematic of droplet setup.

Figure 3. Simplified schematic of laboratory setup; C is the chiller; M is the motor; B is the temperature controlled bath; R is the reactor; L is the fiber-optic light-source; D is the data acquisition system; V is the camera; G is the gas cylinder.

Experimental Apparatus and Procedures The main component of the experimental apparatus consisted of a high pressure crystallizer designed to withstand pressures up to 20 000 kPa with an internal volume of approximately 77 cc. The crystallizer is constructed of a sapphire tube by Insaco Inc., which is located between two stainless steel supports that is connected using three stainless steel rods. A stainless steel rod, 0.5 in. in diameter and 1.5 in. in height, is coated with polytetrafluoroethylene tape and placed inside the reactor. Three droplets, each with a volume of 10 µL, were placed on the Teflon-coated bar as shown in Figure 2. The reactor is placed in a water bath which is maintained at a constant temperature by a Thermoelectron RTE-17 refrigeration unit. The refrigeration unit ran a 50-50-volume % water and ethylene glycol mixture through a copper coil immersed in the bath. A motorized impeller is installed in the bath in order to maintain a constant temperature. The temperature of the gas phase in the reactor is monitored with a type T RTD with an uncertainty of ( 0.1 K. The pressure in the crystallizer is measured with a Rosemount Smart pressure transducer (3051CD, Norpac Controls) with operating limits of 0-13 790 kPa. The uncertainty of the transducer is 0.04% the span

Figure 4. Pressure vs time procedure during a reformation experiment. Time t ) 0 h indicates the start of decomposition and time t ) 0.5 h indicates when the reformation process was initiated. which in our experiments is equivalent to ( 5.5 kPa. The pressure transducer and RTD are both connected to a data acquisition system made in Labview to monitor the pressure and temperature in the reactor. The stainless steel bath is equipped with clear polymethylmethacrylate (PMMA) viewing windows. A Schott KL 2500 fiber optic light pipe provided illumination for the high speed camera through a stainless steel tube installed from the top of the reactor. A polycarbonate piece at the end of the light pipe ensured equal lighting for all droplets. Figure 3 shows a simplified schematic of the laboratory setup. In the experiments three droplets, each 10 µL, were placed on a Teflon coated stand with the use of a Hamilton 10 µL syringe. A droplet of distilled deionized water was placed in the center of the stand and

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Figure 5. Experiment 2: Prior to nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 6. Experiment 2: Nucleated droplets. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 7. Experiment 2: 10 min after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right). the droplets containing the inhibitors were placed on each side. The two inhibitors used were a copolymer, poly(VP/CV) and an antifreeze protein (AFP), both at a concentration of 0.01 mol/m3. The reactor was sealed and flushed three times with the experimental gas, ultrahigh purity CH4 (99.99%), at a pressure of 1000 kPa to remove any possible residual gas in the reactor before the reactor was pressurized to the desired operating pressure. In the reformation experiments, the hydrates nucleated and grew for 6 h before they were decomposed by setting the pressure 25% below the equilibrium pressure. Reformation was initiated according to the procedure outlined in Figure 4. The high resolution pictures were obtained using a PCO 2000 camera that has a resolution of 2048 × 2048 pixels (4.2 megapixel) combined Table 1. Experimental conditions

a

experiment

T(K)

P(kPa)

1 2 3a 4 5 6a 7a 8 9 10b 11a,b 12b 13b 14b,c 15b,c

274.2 274.2 274.2 274.2 275.2 275.2 275.2 275.2 275.2 275.2 275.2 275.2 275.2 275.2 275.2

7200 7200 7200 7200 4200 4200 4200 4200 4200 7200 7200 7200 7200 7200 7200

No nucleation for 5 days. Experiment was terminated. on droplets with memory. c Alternative droplet order.

b

Formation

with two high magnification objective lenses. The entire setup was situated on an optical table. Each experimental condition was repeated three times to ensure repeatability in the morphological patterns.

Results and Discussion The morphology of the droplets were observed with the use of a high resolution camera. The experiments were performed at a pressure of 4200 and 7200 kPa and a temperature of 274.2 and 275.2 K as can be seen in Table 1. Experiments were performed with and without the memory effect.8 A substantial amount of time was required for hydrate formation without memory. The difficulties in forming hydrates are likely due to the lack of impurities and disturbances as deionized distilled water was used in small amounts and the setup was located on an optical table. Formation under High Driving Force. High driving force formation experiments were studied in which the three droplets were left to nucleate and grow. Prior to hydrate growth all the droplets appeared identical; see Figure 5. After full surface coverage of the droplets was achieved, morphological patterns between each droplet were observed and found to differ significantly; see Figure 6. The hydrate layer on the water droplet and the poly(VP/VC) droplet appeared rough, while the AFP droplet had a smooth wet surface appearance. The rough surface morphology is due to the formation of dendrites which are hydrates growing radially outward from the center of the droplet. Dendrites are known to

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Figure 8. Experiment 2: 3 h after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 9. Experiment 10: 5 s after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 10. Experiment 10: 29 s after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 11. Experiment 10: 39 s after nucleation. Poly(VP/VC) (left), water (middle) and AFP (right).

form on hydrate droplets exposed to high driving forces.8 Once hydrate formation had occurred, the high resolution camera lens was switched to allow for individual high resolution pictures of the droplets. The high resolution picture captured after hydrate formation, Figure 7, shows the three hydrate covered droplets with large differences in morphology, translucency, and frequency and size of dendrites. This is a clear indication that the inhibitor affects growth patterns and results in large variations in the thickness of the hydrate layer as well as dendrite growth. The water droplet has a thick hydrate surface covered in dendrites, giving the droplet a coarse appearance. In the case of the poly(VP/VC) droplet, only minor dendrite formation can be observed while

no dendrites are present on the AFP droplet. In addition, both droplets containing inhibitors have very characteristic individual surface growth patterns that can be easily observed due to the lack of or limited dendrite formation. Poly(VP/VC) has been suggested to bind to hydrate crystals, preventing growth in the respective plane.22 However, the inhibitor does not necessarily fully cover the surface of the droplet at a uniform concentration or bind to all of the resulting hydrate. The result of such uneven or limited distribution of inhibitor can be seen in the poly(VP/VC) section of Figure 7. The hydrate growth pattern is composed of repeated “rod”-like sections of thicker hydrate growth separated by areas of a thinner

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Figure 12. Experiment 10: 7 min after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 13. Experiment 14: Alternative droplet order. Water (left), poly(VP/VC) (middle), and AFP (right).

Figure 14. Experiment 14: Alternative droplet order. Water (left), poly(VP/VC) (middle), and AFP (right).

hydrate layer. The variation in thickness is likely to be directly related to the local presence of inhibitors and indicates that poly(VP/VC) has large local concentration gradients repeated across the surface. This differs from the pattern observed on the AFP droplet. Although variations in surface thickness are observed and the overall variation in hydrate thickness might exceed that of the poly(VP/VC), the AFP droplet appears to have clear but smaller thickness gradients across the surface compared to the poly(VP/VC), resulting in a much smoother, wet-looking hydrate surface. It can also be seen that the crystal surface patterns extend for hundreds of micrometers in a linear fashion across the AFP droplet which is not present in the other two droplets. Dendrites are not stable over time and gradually disappear. After 3 h dendrites could no longer be observed as seen in Figure 8. Dendrites have been reported to collapse into the hydrate surface with time when exposed to high driving forces.7 The surface on the two droplets containing the kinetic inhibitors remains more or less unchanged except the disappearance of

the minor dendrite growth on the poly(VP/VC) droplet. The pure water droplet undergoes major morphological changes and attains a surface covered in local rodlike structures. Image analyses were performed and the rods were found to have diameters up to 35 µm on the pure water droplet. It is also important to mention that conclusions can be made about the hydrate thickness with respect to the translucency of the droplets. In the absence of hydrates, due to the angle of the camera which is normal or close to normal with respect to the surface on the lower region of the droplet, the bottom half of the droplets appear black; see Figure 5. This is because of translucency and you can see through the droplet and see the dark surroundings behind the droplet. The top half of the droplets appears white as it reflects the Teflon-coated base due to the reflection of light. The formation of hydrate, particularly on the black lower part of the droplet, reduces the transparency of the droplets in that region as the crystal layer on the surface reflects light toward the camera. As a result, the less black viewed at the bottom of the droplets indicates more reflection

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Figure 15. High vs low driving force - Experiment 2: high driving force on the top row. Experiment 10: low driving force on the bottom. Poly(VP/ VC) (left), water (middle), and AFP (right).

Figure 16. Experiment 10: 1 h after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 17. Experiment 10: 18 h after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

of light which can only be achieved due to the presence of a thicker hydrate layer. On the basis of the above rationale, it appears that in every experiment performed in this work, the AFP and poly(VP/VC) droplet is more translucent than the pure water droplet. Formation with Memory. There are no discernible morphological differences, at this magnification, between droplets formed with memory and droplets formed under low driving force conditions, which will be discussed later. This has also

been confirmed by other researchers.7 A progression of the nucleation and growth of hydrate on droplets with memory can be observed in Figures 9-11. Once nucleation commenced, the growth of hydrate proceeded radially away from the point of nucleation until the entire surface of the droplet was covered by a thin hydrate layer. During the reformation the pure water droplet was the last to form. This is a result of the memory effect and not a measure of the effectiveness of the inhibitor. In all experiments conducted with

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Figure 18. Experiment 10: 43 h after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 19. Experiment 13: 3.5 days after nucleation. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 20. Experiment 13: 80 s after pressure reduction. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 21. Experiment 13: 6 min after pressure reduction. Poly(VP/VC) (left), water (middle), and AFP (right).

memory, the AFP droplet was always the first one to nucleate, indicating that the kinetic inhibitor might inhibit hydrate crystals or nuclei decomposition as well as formation. Since this is a reformation experiment, the time for crystals to appear after pressure and temperature conditions have been restored is not an indication of kinetic inhibitor performance. A possible explanation is that the binding of the inhibitors to the hydrate crystals acts as a preserving agent and causes the crystal to decompose at a much slower rate. Hence, not all nuclei have been destroyed in the droplets containing inhibitors before the reformation experiment is initiated. The degree of crystal translucency on the droplet is a better indication of inhibitor effectiveness, and these results are supported by kinetic studies that have demonstrated the effectiveness of these polymeric and biological inhibitors.21 After full surface coverage of the droplets was achieved, the morphological patterns were studied and found to be strongly affected by the inhibitor present as shown in Figure 12.

In the experiments with memory, no traces of dendrites were observed. In the case of the poly(VP/VC), “rod”-like patterns can be observed, while the AFP droplet has the appearance of smaller local hydrate thickness gradients. The hydrate on the pure water droplet has only minor local variations in thickness, but overall appears as a thick smooth surface. Image analysis was performed on the picture of the poly(VP/VC) droplet and the thicknesses of the “rods” were found to have diameters up to 60 µm. The Effect of Droplet Positioning. Droplet positioning was found to have no effect on the resulting hydrate morphology. Figures 13 and 14 show experiment 14 which is a replica of the conditions used in experiments 10-13 but with poly(VP/ VC) rather than the water droplet placed in the middle position. As Figure 14 demonstrates, surface morphology is independent of the droplet order as the surface morphology is identical to that observed in Figure 12.

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Figure 22. Experiment 13: 10 min after pressure reduction. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 23. Experiment 13: 1 h after pressure reduction. Poly(VP/VC) (left), water (middle), and AFP (right).

Figure 24. Experiment 13: 3 h after pressure reduction. Poly(VP/VC) (left), water (middle), and AFP (right).

The Effect of Driving Force. The effect of a high driving force is shown in Figure 15, which demonstrates the difference in surface morphology between the experiments with the memory effect [or low driving force] and without the memory effect [at a high driving force], Figures 7 and 12. The most noticeable difference is the absence of dendrites on the hydrate surface under reformation or low driving force experiments. The result is more predominant on the pure water droplet, where driving force [and dendrites] result in a drastically different surface morphology. While the dendrite formation results in a rough surface structure on the pure water droplet, the lack of

dendrites gives the droplet a relatively smooth surface. The morphology of the water droplet with poly(VP/VC) shows large local thickness gradients on the surface, regardless of driving force, and dendrite formation. Similar to the pure water droplet, the poly(VP/VC) droplet had no dendrite formation during low driving force [or with memory] experiments. Apart from the minor dendrite formation, the poly(VP/VC) droplet looks almost identical, independent of driving force or memory effect. The AFP droplets maintain their wet-looking surface independent of driving force and had no dendrite formation at either high or low driving forces. The AFP does have more defined thickness

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gradients when formed under high driving force experiments compared to when formed under low driving force [or with memory] which can be observed when comparing the lineartype surface morphology formed under high driving force to the more patternless, nonlinear surface morphology in the case of the low driving force experiments. Effect of Aging. Following the initial formation of hydrate, the droplets were left growing for a longer period of time to investigate the development of surface morphology with increasing conversion of water into hydrate. The droplets were monitored for 43 h with constant temperature and pressure maintained throughout the growth shown in Figures 16-18. During the continued growth of hydrate, there are few fundamental changes to the local surface morphology. When considering the changes over 42 h and comparing Figures 16 and 18 there are two noticeable related differences repeated for all the droplets: First, the translucency decreased, indicating a thicker hydrate layer, and second, the droplets imploded due to the conversion of free-water and gas into hydrate. The implosion of pure water droplets forming hydrates has also been observed by other researchers.7 In addition, a more local implosion process can be observed for the pure water droplet after 43 h of growth which is clearly seen in the higher magnification image in Figure 18 and appear as craters on the large imploded area. Overall, the surface morphology of the poly(VP/VC) droplet appears to be the least affected by continuous growth of hydrate as seen when comparing Figures 16 and 18 where the local hydrate “rods” still can be clearly identified on the surface despite the shape deformation of the crystal covered droplet. Decomposition. The hydrate skin on each droplet was decomposed by dropping the pressure to 2900 kPa, approximately 10% below the equilibrium pressure of 3200 kPa at the experimental temperature of 275.2 K.11 Hydrate decomposition can be demonstrated both in terms of the changing translucency and in terms of the minimization of surface area eventually resulting in a normal water droplet shape. The decomposition is shown for the first 6 min in Figures 19-21 after an uninterrupted growth period of 3.5 days. Decomposition of hydrate in the presence of the poly(VP/VC) inhibitor, Figure 21, was noticeably slower than decomposition of hydrate on a pure water droplet and the AFP droplet, despite the thicker appearance of the hydrate skin on the pure water droplet. Although the pure water droplet appeared to have the thickest hydrate layer prior to decomposition, it appeared to have the fastest rate of decomposition. Under high magnification a thin hydrate layer can still be observed on the surface of the droplets, along with gas bubbles, after 10 min of decomposition as seen in Figure 22. While the pure water droplet has very thin scattered hydrate crystals on the surface, the AFP and the poly(VP/VC) droplets are still completely covered in a thin hydrate layer. The poly(VP/VC) droplet still possesses some of the initial surface morphological characteristics with large local thickness gradients. As expected, there is a large amount of gas released during the decomposition of the droplets which floats to the top of the droplet where it remains trapped while it slowly diffuses into the gas phase. After 1 h of decomposition, Figure 23, the poly(VP/VC) droplet is still partially covered by a thin layer of hydrate. This is significant as all traces of hydrate vanished from the pure water and the AFP droplet after approximately 15 min. It is clear that although poly(VP/VC) inhibits hydrate growth it also seems to stabilize the hydrate once formed and as a result inhibits hydrate decomposition.

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After 3 h of decomposition a thin layer of hydrate can still be observed on the poly(VP/VC) droplet in Figure 24. After 3.5 h hydrates could no longer be observed on any of the droplets. Conclusion Morphology studies were performed on droplets in the presence of two different kinetic inhibitors, a lactam ring copolymer and antifreeze protein. The hydrate morphologies on the pure water, water with AFP, and water with poly(VP/ VC) droplets were found to differ significantly. Under high driving forces dendrites would form on the surface of the pure water droplet, but minor to no dendrite formation occurred on the droplets with inhibitors present. The morphologies of the hydrates formed under low driving forces were found to be identical to the hydrates formed on droplets with memory. The order of the droplets was not found to affect the surface morphology. The water droplet was found to have the thickest hydrate layer, based on translucency, while the droplet containing the inhibitors was found to have variations in thickness along the surface. The poly(VP/VC) droplet had larger local thickness gradients than the AFP droplet and formed characteristic local “rod”-like structures. With the exception of minor dendrite formation on the poly(VP/VC), the inhibitors yielded a very consistent morphology regardless of driving force and memory. Surface morphology did not change significantly during the continuous hydrate conversion of the droplets; however, all the droplets did implode and deform over time. During hydrate decomposition, it was observed that the water droplet decomposed first followed by the AFP droplet. The poly(VP/VC) took significantly longer than the water and AFP droplet to completely decompose. Acknowledgment. The financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), and Le fonds que´be´cois de la recherche sur la nature et les technologies (FQRNT) is greatly appreciated. Supporting Information Available: High resolution pictures of the morphology of hydrates formed on water droplet in the presence of kinetic inhibitors were captured. This information is available free of charge via the Internet at http://pubs.acs.org.

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Morphology of Structure I Methane Hydrate Formation (17) Zeng, H.; Wilson, L. D.; Walker, V. K.; Ripmeester, J. A. Can. J. Phys. 2003, 81, 17–24. (18) DeVries, A. L.; Wohlschl, D. E. Science 1969, 163, 1073. (19) Davies, P. L.; Baardsnes, J.; Kuiper, M. J.; Walker, V. K. Philos. Trans. R. Soc. London, Ser. B 2002, 357, 927–933. (20) Zeng, H.; Wilson, L. D.; Walker, V. K.; Ripmeester, J. A. J. Am. Chem. Soc. 2006, 128, 2844–2850.

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