Effects of Polyvinyl Alcohol on the Adhesion Force ... - ACS Publications

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Effects of Polyvinyl Alcohol on the Adhesion Force of Tetrahydrofuran Hydrate Particles Juan Du, Yanhong Wang, Xuemei Lang, and Shuanshi Fan* Key Laboratory of Enhanced Heat Transfer and Energy Conversation, Ministry of Education, South China University of Technology, Guangzhou 510640, Guangdong, People’s Republic of China ABSTRACT: Effects of polyvinyl alcohol (PVA) on the adhesion force of tetrahydrofuran (THF) hydrate particles were investigated with the microscopic manipulating technique. The adhesion forces of THF hydrate particles with PVA concentration ranging from 0.1 to 1.0 wt % were measured at atmospheric pressure and
3 °C. The time-influence adhesion force of the 0.1 wt % PVA
THF hydrate particle was measured in 180 min. While the adhesion forces were measured, morphologies of the particles without PVA and with 0.1, 0.5, and 1.0 wt % PVA were observed. The surface property of the particles was investigated using droplets made from 19 wt % THF aqueous solution to contact THF hydrate particles containing 0.1, 0.5, and 1.0 wt % PVA. The adhesion forces of PVA
THF hydrate particles decreased by more than 50% compared to pure THF hydrate particles, which indicates an anti-agglomerating effect of PVA at low concentrations. The adhesion force of the 0.1 wt % PVA
THF hydrate particle was kept small with increasing time, revealing the effects of PVA on stabilizing the particle
particle interaction and maintaining the low adhesion force. Morphologies show roughness on the surface of PVA
THF hydrate particles. The roughness leads to the decrease of the actual contact area between contacting particles, thus lowering the agglomeration tendency between hydrate particles. The reason for the morphological change and the occurrence of roughness is attributed to the hydrogen bonding between PVA molecules and water molecules. PVA was also found to change the surface property of THF hydrate particles by increasing the contact angle and weakening the wettability, which represents a decrease of the particle/medium liquid interfacial energy. Such an effect may alter the capillary bridge forming between the contacting particles. All results suggest that PVA may be a potential antiagglomerant in lowering the hydrate plugging risk.

’ INTRODUCTION Gas hydrates are ice-like clathrate solids that are formed from water and small gas molecules under relatively high pressure and low temperature.1 Although Hammerschmidt discovered that natural gas hydrates were responsible for blocking gas pipelines in 1934,2 the undesirable formation of gas hydrates in natural gas pipelines is still an important industrial problem that has attracted considerable interests of scientists. In the oil and gas industry, the operation environment is favorable for the formation of hydrates in the presence of both water and hydrocarbon. These hydrates can agglomerate into large hydrate masses, which will lead to an increase in the slurry viscosity and eventually form a plug.3 The plug often leads to production shutdown, causing undesirable loss and environmental impacts. In this process, the adhesion force among dispersed hydrate particles plays an important role in the aggregation of the particles.4 If the adhesion force is small enough or disappears, the small hydrate particles will not agglomerate into large masses to block the pipelines. Therefore, reducing the adhesion force between hydrate particles may control or prevent the hydrate agglomeration. The adhesion force of hydrate particles is influenced by the media properties, surface tension, particle morphology, physical and chemical properties of the contact surface, etc. Yang et al.4 and Taylor et al.5 developed a micromechanical technique to measure the adhesion force of hydrate particles based on which some particles of ice, tetrahydrofuran (THF) hydrate, ethylene oxide (EtO) hydrate, and cyclopentane (CyC5) hydrate were tested.4
7 In these studies, the capillary bridge theory was r 2011 American Chemical Society

proposed as an appropriate model to describe the adhesion of hydrate particles. In the theory, particles are held together by capillary forces, which are formed by a liquid bridge.8 The capillary force of hydrate particles is proportional to the interfacial tension between the bridging liquid and the medium phase. Accordingly, hydrate particles in different surrounding media were tested, such as n-decane, toluene, and crude oil. The results showed that the hydrate particle adhesion force increased with an increasing surface tension and revealed that the interfacial energy of the surrounding media substantially affected the adhesion force of hydrate particles.5,9 Anti-agglomerants (AAs) are used to prevent hydrate blockages in pipelines, which can reduce the adhesion force between hydrate particles. A typical structure of the AAs generally contains both a hydrophilic head and hydrophobic tails. The hydrophilic head can interact with the water lattice, making the AAs adsorb on the surface of hydrate crystals. The hydrophobic tails enable the hydrate to disperse easily in the fluid as small particles.10
13 Researchers have explored some AAs to prevent hydrate particles accumulating, such as PVCap, Span20, Span80, etc. PVCap and Span20 were reported to reduce the adhesion force of THF hydrate particles by more than 70%. They were added in n-decane, which lowered the n-decane/water interfacial energy and, thus, reduced the Received: January 22, 2011 Revised: June 20, 2011 Published: June 21, 2011 3204

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Figure 1. Schematic structure of the PVA molecule. It consists of a hydroxyl group at every other carbon in the chain.

Figure 3. Schematic illustration of the micromechanical apparatus experimental technique. (A) Particles are brought into contact at a given preload force. (B) Particles are slowly pulled apart. (C) Particles are pulled apart. The displacement (δ) is measured to determine the adhesion force.

’ EXPERIMENTAL SECTION

Figure 2. Low-temperature hydration cell and micromanipulators.

strength of the capillary bridge. They were also hypothesized to create steric repulsion between the particles.5 Span205 and Span807 were provided to induce morphological change to the surface of the hydrate particle, which might alter the capillary bridge between the particles and, thus, affect the adhesion force. Some natural surface-active components existing in crude oil, such as acid and asphaltene contents, were reported to reduce the water/crude oil interfacial energy and, thus, reduce the adhesion force of CyC5 hydrate particles.9 These chemicals perform well on weakening the adhesion of hydrate particles and can be used as good AAs. However, most developed AAs are not environmentally friendly. Their long-term use will cause a huge burden on the environment. Therefore, AA development has recently been more concentrated on the characteristics including biodegradability, lower toxicity, etc.14 Greener AAs with competitive performance and novel structures are in demand. Polyvinyl alcohol (PVA) is a water-soluble polymer with hydroxyl groups. The molecule in water assumes a multiple-stranded, helical structure.15 The structure of the PVA molecule is schematically shown in Figure 1. PVA is nontoxic16,17 and has susceptible biodegradability,18
20 which satisfies the demands of many industrial applications. The surface activity and weak hydrophobic nature of PVA make it widely used as the steric stabilizer in dispersing and emulsifying applications.21
23 Previous studies reported that PVA in low concentrations was an effective ice inhibitor, which can limit the size24 of ice grains, inhibit the growth25,26 and recrystallization27 of ice crystals, and also prevent the agglomeration28 of ice slurry. Therefore, the effects of PVA on ice control are similar to the effects of AAs on hydrate anti-agglomeration. However, ice and hydrate are different in structure and property. To investigate whether PVA can be used as a hydrate anti-agglomerant, the adhesion force of THF hydrate particles containing PVA was measured in this work. The effects of PVA on the particle
particle adhesion were investigated.

Materials. THF (Sinopharm Chemical Reagent Co., China), PVA (AH-26, Sinopharm Chemical Reagent Co., China; degree of alcoholysis of 0.98), and n-decane (Shanghai Jingchun Chemical Co., China) were used in subsequent experiments. Deionized water was used to prepare all solutions. The solution concentration in this study is given as weight-byweight percentage. Adhesion Force Measurement and Morphology Observation. Experiments were carried out using a microscopic manipulating apparatus shown in Figure 2. This technique was also described by Taylor et al.5 and Yang et al.4 The experimental apparatus consists of (1) an inverted light microscope (Carl Zeiss Axio Observer A1), (2) a lowtemperature cell (Φ 50  30 mm, made of stainless steel), which allows for cantilevers to be loaded in for micromanipulation, (3) two micromanipulators, which are fixed with the cantilevers, and (4) a digital recording system. Adhesion Force Measurement. The experimental procedure of the adhesion force measurement is schematically shown in Figure 3. The low-temperature cell was filled with n-decane and placed under the microscope prior to the experiment. The temperature of n-decane was stabilized at
3 °C and monitored by a thermocouple. Hydrate particles were attached to a glass fiber by the quenching method described in details below. The glass fiber cantilever was held by the micromanipulator (3D hydraulic coarse/fine micromanipulator MWO-202D) and kept stationary during the experiment. A second particle holding by the other micromanipulator (Eppendorf Transfer Man NK2 micromanipulator) was brought into contact with the first, with a preload of 0.5 μN, held stationary for 5 s (Figure 3A), and then slowly pulled away (Figure 3B). At a critical displacement, the particles were pulled apart (Figure 3C). The video of this process was recorded using a digital camera (Imaging MicroPublisher 5.0RTV). The critical displacement (δ) of the particles was identified using image-processing software SimplePIC. The adhesion force F is calculated from Hooke’s law. F ¼ kδ

ð1Þ

The spring constant of the glass fiber k can be determined from the fiber dimension by the relation k¼

3πEd4 64L3

ð2Þ

where E is the elastic modulus of the glass and is 70 GPa in this study and d and L are the diameter and length of the fiber and were determined from microscopic measurements. 3205

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Figure 4. Schematic illustration of surface property estimation. (A) A liquid droplet and a hydrate particle are immersed in cold medium. (B) The liquid droplet is brought into contact with the particle. (C) The droplet wetting on the particle and hydrate growth are initiated. Figure 6. Time-dependence adhesion force of THF hydrate particles with 0.1 wt % PVA. Each data point represents the average value of 30 pull-off movements, and vertical error bars represent the standard deviation. The average standard deviation of the three groups was 0.003 N/m.

Figure 5. Adhesion force of THF hydrate particles with PVA in different concentrations. The forces were measured at 10
15 min after the particles were immersed in n-decane. Vertical error bars represent the standard deviation in 30 pull-off movements for each data point. The average standard deviation of the force measurements was 0.005 N/m. The dashed horizontal line corresponds to the adhesion force for the THF hydrate particles without PVA. To compare the pull-off force for different particle pairs, all force measurements were normalized by the harmonic mean radius (R*) of the particle pair   1 1 1 1 ¼ ð3Þ þ R 2 R1 R2 where R1 and R2 are the radius of the two particles. In this work, each operation consisted of 30 pull-off measurements. The measured adhesion forces are reported in the form of the average value for the 30 pull-off movements, and the standard deviation is represented as a corresponding error bar. Hydrate Particle Preparation. To prepare the hydrate particle, a liquid droplet was placed on the end of a glass fiber. The droplet was then solidified by quenching in liquid nitrogen and rapidly submerged in ndecane. In the present work, the droplets were made from 19 wt % THF in water and additional contents of PVA between 0.1 and 1.0 wt %. Two different experiments were performed in the adhesion force measurements. One was determining the influence of the PVA

concentration on the adhesion force. The particles were made from the solutions with PVA in different concentrations: 0, 0.1, 0.3, 0.5, 0.75, and 1.0 wt %. The other was detecting the time-influenced adhesion force in the presence of 0.1 wt % PVA in 180 min. In this experiment, a pair of particles were submerged in n-decane for 180 min, during which the pulloff operations were performed about every 40
50 min. Morphology Observation. Typical morphologies of the hydrate particles without PVA and with 0.1, 0.5, and 1.0 wt % PVA were observed while measuring the adhesion force. Surface Property Estimation. The surface property of the hydrate particle was detected by observing the wettability of liquid on the particle. The experimental procedure is schematically shown in Figure 4. Prior to the experiment, n-decane, which was filled in the low-temperature cell, was stabilized at
2 °C. The cantilever with a droplet made from 19 wt % THF solution was immersed in n-decane. After 10 min, a hydrate particle on the other cantilever was introduced in and slowly touched to the droplet. Then, the wetting process of the droplet on the hydrate particle can be recorded. The hydrate particles were made from THF aqueous solution without PVA and with 0.1, 0.5, and 1.0 wt % PVA, respectively. Thus, the surface property of the particles can be estimated by a varied wetting area and different droplet
particle contact angle in the recorded images.

’ RESULTS AND DISCUSSION Adhesion Force. Figure 5 shows the adhesion forces of THF hydrate particles with PVA in various concentrations. Each data point was obtained through 30 pull-off movements. The dashed horizontal line represents the average adhesion force of THF hydrate particles without additive, which is 0.024 N/m with a standard deviation of 0.008 N/m. The adhesion forces of the THF hydrate particles at different conditions were obtained and match the results by Taylor et al.5 As seen from Figure 5, the adhesion forces decreased when PVA was added to the particles with the concentration at 0.1, 0.3, 0.5, 0.75, and 1.0 wt %, respectively. The standard deviations increase at 0.5 and 1.0 wt %, but the average values are all falling below the horizontal line. Although there is a rise at 0.5 wt %, the adhesion forces at each concentration remain relatively consistent and decrease by more 3206

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Figure 7. Morphologies of THF hydrate particles. The pictures were focused on the edge of the particles (a
d) and on the central spherical surface (d
g).

than 50%. This indicates that PVA at extreme low concentrations (even as low as 0.1 wt %) exhibits an anti-agglomeration effect on the hydrate particles. The property of the particle surface may change with the immersion time, which alters the interparticle adhesion force. Figure 6 shows that the adhesion forces of 0.1 wt % PVA
THF hydrate particles change with the immersion time. Three pairs of particles were tested, and the longest immersion time was 180 min. Although the standard deviations are different for each data point, it displayed similar regularity that the average adhesion forces remain at a low level and are relatively constant with the increasing time. The result shows no time-dependence adhesion force. Because some possible factors, such as surface diffusion, lattice diffusion, grain boundary diffusion, etc., which functionally associate with the time,29 may play a role in the particle interaction, the result reveals a stable particle interaction with the increasing time. On the basis of these results, it is reasonable to suggest that the addition of PVA in the THF hydrate particles weakens the particle
particle adhesion, stabilizes the particle
particle interaction, and maintains the low adhesion force. PVA as a waterdissolvable polymer in fluid can play a role in lowering the agglomeration tendency. Morphology of THF Hydrate Particles. Figure 7 shows the morphologies of the THF hydrate particles captured during the measurement of the adhesion force. The particles were prepared without additive and with 0.1, 0.5, and 1.0 wt % PVA. The firstline pictures focused on the particle edge (panels a
d of Figure 7), and the second-line pictures focused on the central spherical surface (panels e
h of Figure 7). In the case of THF hydrate without PVA, the profiles of the particles are clear and smooth without any rudeness (panels a and e of Figure 7). When PVA was added, it was apparent that the particle surfaces changed from smooth to rough. For the 0.1 wt % PVA samples, the particle surface is covered with fine hair (Figure 7b) and is partially distributed with small concave pits (Figure 7f). With the PVA concentration increasing, the surfaces become rougher, profiles of the particles change more indistinctly, and the central parts become gloomy because of more and longer fine hair. These results suggest that surface roughness occurred on the particles in the presence of PVA.

PVA was reported to affect the nucleation, growth, and morphology of ice by adsorbing onto the ice crystals and to exhibit an antifreeze effect in the same manner as antifreeze proteins.25
28,30 The widely accepted reason is that PVA molecules bind to the ice surface or undefined ice crystallization sites, preventing water molecules from being incorporated into the ice surface at the adsorption sites. In this process, the hydrogen bonding between PVA molecules and water molecules plays a significant role.27,28,31 For THF hydrate, water molecules form a cavity structure through hydrogen bonding, which hosts the THF molecules.11,32 With PVA presenting in THF solution, the order of water molecules might be rearranged because the hydroxyl groups of PVA molecules can easily interact with the water molecules via hydrogen bonding in the solution.16,31,33 Alternatively, during the formation of hydrates, PVA molecules adsorb onto the hydrate crystals via hydrogen bonding. These molecular interactions will interfere with the crystal cages and lead the cages to develop in undefined irregular manners, thus inducing morphological changes to the hydrate surface. It was provided that inhibitor molecules bound to the water molecules of hydrate cages via hydrogen bonding, which affected the growth of hydrate crystals and resulted in the change of morphologies.34
36 Similarly, in other systems, adsorbed molecules or interacting molecules were known to affect the nucleation or growth habit of various crystals, including ice, amino acids, calcium carbonate, acetaminophen, etc.31,37
39 Additional evidence was obtained in our previous molecular dynamics simulation,40 in which it was found that there were hydrogen bonds between PVA molecules and water molecules of hydrate cages. The simulation showed that the hydroxyl groups of PVA molecules bound to the water molecules of the hydrate cages through hydrogen bonding and perturbed and even destroyed the cage structure. Additionally, the changes of particle morphologies shown in Figure 7 support a molecular dislocation of the crystal bulk. As such, it is reasonable to suggest that the PVA effect on the morphological changes of THF hydrate particles is due to the hydrogen-bonding interaction. The morphological changes on the surfaces of THF hydrate particles induced by PVA are responsible for affecting the adhesion force between the particles. Aman et al.7 reported that the additives that induced morphological changes to the hydrate 3207

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Figure 8. Surface contact geometry of particle
particle adhesion and magnified liquid bridge.

Figure 9. Images of the wetting process of liquid droplets on the hydrate particles. The liquid droplets were made from THF aqueous solution without additives. The hydrate particles were made from THF aqueous solution without additives (first row) and with 0.1 wt % PVA (second row), 0.5 wt % PVA (third row), and 1.0 wt % PVA (fourth row). The time for each picture corresponds to the wetting period. Each row represents the whole process from the beginning of contacting to wetting completion.

surface may cause non-uniform hydrate growth and were more effective in preventing hydrate adhesion. Taylor et al.5 observed the morphological changes of THF hydrate particles induced by Span20 addition. Also, Yang et al.4 proposed that surface roughness was a responsible factor for altering the particle adhesion. Furthermore, surface roughness has been widely reported to be an important factor to particle adhesion.41
43 In solid
solid adhesion, roughness associates with the size and geometry of the particles.41 A different rough pattern will result in an opposite effect on the adhesion force. One pattern can increase the adhesion force. For example, the contact of a particle to a surface with comparable asperities size to the particle might has an increased adhesion because of the increase in the actual contact area. This phenomenon was provided by the Rumpf model44 and studied by Beach et al.41 The other pattern like the present work proposes a roughness phenomenon (Figure 8), which might decrease the adhesion force. The roughness causes the actual area of contact to vary significantly from ideal spherical particles.45,46 As schematically shown in Figure 8, the contact between two particles only occurs on the roughness points, which reduces the actual contact area. According to the capillary bridge model, the liquid bridges will only form at the junction of the tallest

roughness points.4 Thus, the rough particles will inevitably have less surface area in contact and lower adhesion force. Above all, the addition of PVA in THF aqueous solution can form hydrate particles with morphological changes through the hydrogen-bonding interaction between PVA molecules and water molecules. It also induces roughness on the particle surfaces, thus reducing the particle
particle adhesion force. Surface Property. The interfacial property and the wettability of the hydrate particle will affect the particle
particle adhesion force.47,48 In the present work, PVA contributed to the formation of the particles with rough surfaces. It also performed as the surfactant,15 which might affect the surface property of THF hydrate particles. Figure 9 shows the process of liquid droplets contacting hydrate particles. The liquid droplets were made from 19 wt % THF solution without additives. The hydrate particles were made from THF solution without additives and with 0.1, 0.5, and 1.0 wt % PVA. Thus, the surface property of THF hydrate particles with and without PVA can be distinguished. During the process, the droplets wetted the hydrate particles at first (pictures at 0.181 or 0.187 s in Figure 9) and the particles were totally or partially covered by the liquid droplets (pictures at 0.375 or 0.369 s in 3208

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Figure 9). Then, hydrate growth was initiated on the droplet/ particle interface (pictures at 0.375 or 0.369 s in Figure 9), and feather-shape crystals grew from the interface into the liquid droplets (pictures at 3.712 s in Figure 9). Finally, the droplets and particles were sintered together (complete pictures in Figure 9). The process from contacting, wetting, to total or partial covering was very fast, especially the wetting process, which was so rapid that ghost images appeared in the pictures at 0.18 s. The droplets totally or partially covering the particles show different surface properties of the particles. The decrease of the wetting area shows an anti-wetted effect and indicates that PVA can affect the wettability of the THF hydrate particles by enhancing the anti-wetted property. It is believed that the different wetting areas can show the wettability of various particles and is independent of the hydrate growth and sintering. The limited wetting because of PVA addition thus reveals weakened hydrophilicity of the particle surface. After sintering, for the THF hydrate particle without PVA, it is difficult to distinguish the initial hydrate particle and the latter one. The secondary-growing THF hydrate in the droplet merges well with the particle because of the same component (see the complete picture of the first row in Figure 9). However, for the PVA
THF particles, there are obvious morphological differences between the first particles and secondary-growing parts. With the PVA concentration increasing, the diversities of them increase. This indicates that PVA can change the morphology of THF hydrates, which supports the morphological changes of the THF hydrate particles, resulting from the PVA presence. The wetting of a solid surface by a liquid is determined by the contact angle, θ.3 The droplet makes θ with the particle surface at the n-decane/hydrate particle/liquid droplet three-phase contact point (see pictures at 0.369 s in Figure 9). Young’s equation cos θ ¼

γso
γsl γlo

ð4Þ

can be used to show the dependence of the contact angle upon the property of the liquid and solid, including the interfacial tension of the liquid phase, γlo, the free energy of the solid hydrate particle with the liquid droplet, γsl, and with the medium n-decane, γso, etc. γlo, γsl, and γso are marked in Figure 9. As shown in Figure 9, the particle without PVA is completely wetted and covered by the droplet. The contact angle is expected to be near 0°. In the case of 0.1, 0.5, and 1.0 wt % PVA, the contact angle increases and the particles are partially wetted by the droplets. The increment of θ indicates that the solid is less likely to be water-wet, which represents the enhancement of hydrophobicity. On the basis of these results, it is reasonable to suggest that PVA can change the wettability of the THF hydrate particle by inducing hydrophilic restriction. The increase in the contact angle and decrease in the wetting area correspond to the decrease in interfacial energy, which may alter the capillary bridge forming between the two particles and result in the drop of the adhesion force. Additionally, it is important to note that surface roughness plays a significant role in wetting and spreading processes. Both hydrophilicity and hydrophobicity are affected by the surface roughness. Wenzel’s model49 indicates that the surface roughness will enhance the wettability of the hydrophilic surface or weaken the wettability of the hydrophobic surface.50
52 For THF and PVA
THF hydrate particles, their surfaces were hydrophilic.4 Accordingly, the hydrophilicity of the particles

should be enhanced by the surface roughness. However, it was found that the actual hydrophobicity of the PVA
THF hydrate particles was enhanced, which illustrates that the anti-wetted ability of PVA
THF hydrate particles should be stronger than what was observed in Figure 9. Thus far, instead of changing the surface tension of bulk fluid, PVA changed the surface properties of THF hydrate particles. Zerpa et al.3 reviewed the importance of defining the wettability of hydrate particles in hydrate plug studies. Aspenes et al.47,53 studied the influence of surface wettability on the pipeline surfaces and measured the adhesion forces between cyclopentane hydrate particles and different surface materials. Dieker et al.9 studied the adhesion forces of cyclopentane hydrate particles in different oil phases. Their studies associated oil-wet surfaces with low hydrate plugging tendency. Additional evidence was provided by Høiland et al.,48 who studied the wettability of Freon hydrate. It was demonstrated that oil-wet hydrate particles were correlated to low plugging risk. These studies imply that a hydrophobic transition on the hydrate surface will reduce the particle adhesion. Further, Anklam et al.43 reviewed that increasing the contact angle was one of the abilities of an effective anti-agglomerant. Therefore, the anti-wetted effect induced by PVA will contribute to the weakening of the hydrophilicity of hydrate particles and, thus, lower the hydrate plugging risk.

’ CONCLUSION The effects of PVA on the adhesion force of THF hydrate particles were investigated using the microscopic manipulating technique. The results showed that the adhesion force of THF hydrate particles decreased by more than 50%, when the concentration of PVA was changed from 0.1 to 1.00 wt %. The adhesion forces of PVA
THF hydrate particles were not timedependent. Hydrogen bonding between PVA molecules and water molecules is the key factor that affects the adhesion force by inducing morphological changes on the surface of the hydrate particles and making surface roughness. The roughness will reduce the actual particle
particle contact area and leads to the decrease of the adhesion force. PVA also increases the contact angle and enhances the anti-wetted ability of the THF hydrate particles, which corresponds to a decrease of interfacial energy between the particles and the bulk fluid. These effects thus alter the capillary bridge forming between two particles and result in the decrease of adhesion forces. ’ AUTHOR INFORMATION Corresponding Author

*Telephone: +86-20-22236581. Fax: +86-20-22236581. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors are grateful for the financial support from the National High Technology Research and Development Program (“863” Program) of China (2007AA03Z229), the National Basic Program of China (G200900), and the Fundamental Research Funds for the Central Universities (2009ZM0185). ’ REFERENCES (1) Sloan, E. D., Jr. Clathrate Hydrate of Natural Gases; Marcel Dekker: New York, 1998. 3209

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