Pattern Variety of Tetrahydrofuran Clathrate Hydrates Formed in

Article pubs.acs.org/JPCC

Pattern Variety of Tetrahydrofuran Clathrate Hydrates Formed in Porous Media Michihiro Muraoka and Kazushige Nagashima* Department of Physics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan ABSTRACT: We observed the pattern formation of tetrahydrofuran (THF) clathrate hydrates in a mixture of a THF− 17H2O solution and glass beads (2 and 50 μm diameter). The overall hydrate growth rate, V, was controlled using a directional growth apparatus. We are the first to successfully obtain a variety of hydrate patterns: a disseminated type at higher V values, a nodular type in the middle range of V, and massive and layer types at lower V values. The hydrate images obtained were analyzed by several methods to quantitatively characterize the patterns. Image processing retaining the relatively large hydrate regions (90% of the total hydrate area formed by segregated growth) was suitable for evaluating the number density of the hydrate grains and the average hydrate area, which dominated the total hydrate area. The segregated growth area of the hydrates was one of the most useful indices for quantitatively categorizing the hydrate types. The image analysis results showed that the segregated growth area of the hydrates and the average hydrate area increased and the number density of hydrate grains decreased with decreasing V. These results are qualitatively consistent with the theoretical frost heave model. Clennell et al.12 proposed a conceptual model for hydrate stability and hydrate formation in sediment in a manner analogous to ice in freezing soil. This model predicts that the hydrate equilibrium temperature in fine-grained sediment is reduced by the capillary effect that originates from the coupling of the interfacial energy of the hydrate/water and the surface curvature of the hydrates. In addition, the segregated growth of hydrates in sediment (the formation of pure hydrate regions larger than the pore scale of sediments) was suggested on the basis of the capillary pressure of hydrate. When the inner pressure (phase pressure) of the hydrates, which is elevated by the capillary effect in fine-grained sediment, exceeds the effective confining stress combined with the tensile strength of the sediment, the hydrates push the sediment and form hydrate patterns. Buffett et al.13 experimentally studied the formation of CO2 hydrates in soil from CO2 dissolved in water in the absence of gas bubbles and ice crystals in order to confirm commonly proposed marine hydrate formation models.14,15 Their results showed successfully that gas hydrates can nucleate at a dissolved gas concentration less than the concentration when free gas is present. However, hydrate formation stopped once the dissolved gas was depleted. This was caused by the limited time during an experimental run for the dissolved gas to diffuse into the hydrates. Moreover, Rempel et al.16 produced a model for the formation and accumulation of hydrates using a moving boundary mathematical technique. This model predicts that 2

1. INTRODUCTION Clathrate hydrates are ice-like crystals composed of a network of hydrogen-bonded water molecules containing guest molecules in cavities. Generally, gas hydrates have three crystal structures: structure I, structure II, or structure H, mainly depending upon the size of the guest gas molecules. Globally, large quantities of methane hydrates have been found in sediment under ocean floors. These methane hydrates are of significant interest because of their potential for causing global climate change and as an energy resource.1,2 Sediment cores recovered from ocean floors have been reported to contain a variety of patterns (textures) and sizes of hydrates. These hydrates have been classified into four categories by Malone:3 disseminated (fine hydrates in the pore space of sediments), nodular (hydrates up to 5 cm in diameter), layered (parallel hydrate layers), and massive (as thick as 3−4 m, containing 95% hydrates and less than 5% sediment), as shown in Figure 7.7 of ref 1. Tohidi et al.4 and Katsuki et al.5,6 conducted visual observational studies on the growth of pore-scale hydrates on an etched glass plate to simulate the effect of porous media. These studies highlighted the significance of understanding the nature of pore-scale interactions in gas-hydrate formation in porous media and the role of grain size. It is known that the freezing of water in soil causes frost heave. Growing ice crystals absorb water from the pore space, pushing the soil particles apart and forming a pure ice layer called an ice lens.7−9 The frost heave phenomenon is not unique to water, it has also been reported during the growth of He crystals10 and Ar crystals11 in porous media. © 2012 American Chemical Society

Received: June 25, 2012 Revised: October 24, 2012 Published: October 24, 2012 23342

dx.doi.org/10.1021/jp306224w | J. Phys. Chem. C 2012, 116, 23342−23350

The Journal of Physical Chemistry C

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× 105 years would be required to achieve 1% accumulation of hydrates. These results suggest that hydrate formation from dissolved gases in water might require unrealistically long experimental times because the concentration of dissolved gas (CH4, CO2) in water is much lower than the concentration of gas in the hydrate at typical oceanic conditions. The tetrahydrofuran (THF)−water system is useful as an idealized experimental hydrate model system without the diffusion effect of guest molecules. THF is miscible with water at all molar ratios. A stoichiometric THF−water solution (THF−17H2O) forms a structure-II hydrate17 below 4.4 °C at atmospheric pressure.18 The THF−water system can enlarge the hydrate stability zone compared with the corresponding single gas hydrate system (e.g., hydrogen, oxygen),19,20 and THF−O2 clathrate hydrate shows anomalous magnetic properties.21 These THF hydrates are of interest for applications including functional materials and gas storage. Although the THF hydrates are used as a model for gas hydrates in general, it shows some anomalies such as abnormal heat capacity,22,23 thermal expansivity,24 magnetic properties, and so on.25,26 During the past years, discussions started whether there might be a guest−host binding in THF hydrate that can be an explanation for some of the experimental observations.27−29 In a previous study,30 we performed growth experiments on THF clathrate hydrates in a mixture of glass (silica) beads and a THF−water (THF−17H2O) solution using a directional growth technique31,32 to clarify the relationship between selforganized methane hydrate patterns in recovered cores and the hydrate growth rate in sediment. To clarify the formation mechanism of methane hydrate in oceanic sediment, it is important to understand the effect of the sediment and the diffusion limited effect of guest molecules. However, it is difficult to study both effects simultaneously. Therefore, our previous study was performed using a stoichiometric THF− water solution to clarify the effect of the sediment only, and the diffusion limited effect of guest molecules was eliminated from the model system. However, we thought that this model system could probably be used in a step-by-step approach to clarify the diffusion limited effect of guest molecules by performing experimental runs at different THF concentrations. The results revealed that multilayered pure hydrate patterns were formed in the mixture when 2 μm glass beads were used because hydrate growth pushed the glass beads (inducing segregated growth). Both the thickness of a hydrate layer and the interval between the neighboring layers decreased with increasing growth rate in accordance with the power laws. However, when 50 μm beads were used, a hydrate pattern was not observed and the hydrates grew only in pore spaces of the sediment model (disseminated pore space type). In the study presented here, we investigated pattern formation of hydrates in a mixture of glass beads and a THF−17H2O solution as a function of growth rate using a directional growth apparatus based on the one used in our previous study.30 The objective was to clarify the effect of mixing two sizes of glass beads (2 and 50 μm diameter) on pattern formation. To quantitatively classify the newly formed hydrate patterns, the hydrate images obtained were processed and analyzed using several methods. The results are discussed in relation to the frost heave model.

our previous study.30 The sediment model system sample was a mixture of spherical glass beads and a THF−water solution (THF−17H2O). Dehydrated stabilizer-free tetrahydrofuran (99.5 wt % purity, Kanto Chemical Inc.) and ultrapure water (18.2 MΩ·cm resistivity) were used as the reagents. The mean glass bead diameters were 2 μm (silica microbeads P-600, Catalysts and Chemicals Ind. Co. Ltd.) and 50 μm (Unibead SPL-50, Union Co Ltd.) and both types of beads were composed of silica. The two sizes of beads were mixed at a weight ratio, w2/w50, of 1:1 (where w2 is the weight of the 2 μm beads and w50 is the weight of the 50 μm beads). The gravimetric solution content in the sample was defined as ws/ wg, where ws is the weight of the THF−water solution and wg is the weight of the glass beads. The ws/wg value in this study [ ws/(w2 + w50)] was 1.0, which is the same as that in our previous study (ws/w2 for 2 μm beads or ws/w50 for 50 μm beads),30 although the two bead sizes were mixed in this study. 2.2. Experimental Methods. Figure 1 shows a schematic illustration of the growth cell and directional growth apparatus,

Figure 1. Schematic illustrations of (a) the growth cell (top view) and (b) directional growth apparatus (side view).

which are essentially the same as those used in our previous study30 except that the growth cell used in this study is twice as long as that used in the previous one. The growth cell consists of two glass plates (25 × 150 × 1 mm) and spacers that are inserted between them, as shown in Figure 1a. Chemicalresistant rubber sheets (Kalrez compound 6375, 0.5 mm thick; DuPont) are used as the spacers to enhance sealing performance. Capillaries are connected to both ends of the cell to prevent the volatilization of THF from the sample. The growth cell, filled with the sample, was placed horizontally in two copper blocks, as shown in Figure 1b. One of the blocks was maintained at temperature TL = −1.4 °C (lower than the equilibrium temperature, Teq) and the other was maintained at TH = 7.4 °C (higher than Teq) using thermoelectric modules in order to apply a temperature gradient, G, along the length of the growth cell. The temperature profile in the growth cell between the cold and hot blocks was measured before experimental runs using a thermocouple in the growth cell. As the growth cell was moved from the hot block toward the cold block, the temperature was recorded as a function of the position of the thermocouple tip. The temperature profile was linear and the slope, G, was found to be 1.3 K mm−1. The value of the temperature gradient is the same as that in our previous study.30 The thermocouple was removed during the actual experiment. Next, hydrate crystals were compulsorily nucleated using a chilled wire at the edge of the growth cell in the colder region.

2. EXPERIMENTAL SECTION 2.1. Materials. The reagents, composition of the THF− water solution, and glass beads were the same as those used in 23343



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Noise reduction was applied to the images. The quite small white dots caused by electrically induced noise and the small white dots caused by light transmitted through the 50 μm beads in the binary image were removed. The threshold value for removing the small white dots was 2500 μm2 (50 × 50 μm). The interior holes (black dots) in the hydrate regions were filled with white dots for the hydrate area to be analyzed. Both relatively large hydrate grains, which have a dominant effect on the total area of hydrates, and relatively small hydrate grains are shown in Figure 2b. To quantitatively evaluate the number density and average hydrate area of the relatively large hydrate grains, the relatively small hydrate grains must be removed from the image. Two methods for removing small hydrates were tested. Method I. Hydrates smaller than the average hydrate area in the noise reduction images were removed using a threshold value, Sav, of Shyd/N (where Shyd is the total area of hydrate regions and N is the total number of hydrate grains). Method II. Each hydrate area in the noise reduction image was measured and then the areas were arranged in the descending order: S1, S2, S3, ..., SN (S1 > S2 > S3 > ... > SN). The hydrate areas were then one by one added together in the descending order. When the sum just exceeded Shyd × 0.9 (i.e., 90% of the total area of hydrates), the value of the last area added (the smallest value of the hydrate areas added together) was defined as the threshold value, Sk (i.e., Shyd × 0.9 ≈ S1 + S2 + S3 + ... + Sk). The hydrates that were smaller than Sk (Sk+1, Sk+2, ..., SN) were removed from the image. These methods are called methods I (Sav) and II (S90%) in this manuscript for simplicity and clarity. Note that, although 90% of the total hydrate area was selected as the threshold in this study, it can be varied for different purposes. In this study, we used a threshold of 90% to retain the hydrate grains that had a dominant effect on the total hydrate area. The effect of this threshold value is described in the Results. Images were processed and analyzed using the image processing program Image J 1.44p (National Institutes of Health, U.S.A.).

A pure hydrate layer was initially formed in the sediment model by maintaining constant conditions in the growth cell for 20 min after nucleation. The growth cell was then moved, at a constant velocity, V, toward the cold block. The growth interface was forced to remain between the two blocks because of the applied temperature gradient; therefore, the overall hydrate growth rate could be controlled by controlling the velocity of the growth cell. The total length of the hydrate growth region (i.e., the movement distance of the growth cell) was 25 mm. This study allowed lower growth-rate experiments (i.e., longer duration experiments), with a minimum V of 0.04 μm s−1, than our previous study (in which the minimum was 0.4 μm s−1). This was achieved using an improved pulse motor controller, in which rotational motion was transferred to directional motion using a translational stage with a micrometer caliper. The patterns of the hydrates formed in the sediment model were observed using a digital microscope (VH-5500, KEYENCE Co. Ltd.) and images of the hydrates were recorded as digital image files on a personal computer. 2.3. Image Processing. A hydrate image is shown in Figure 2 as an example. A 256 gray scale image (Figure 2a) was processed to produce binary (black and white) images (Figure 2b), in which the white regions indicate the hydrates formed by pushing the glass beads and the black regions indicate glass bead-rich regions where hydrates formed in the pore space of the sediment model.

3. RESULTS 3.1. Hydrate Patterns Formed at Various V Values. Figure 3 shows entire images of the hydrates formed in the sediment model at two constant V values. The white areas in the images show the hydrates and the black and dark gray areas show the glass bead-rich regions. The vertical white line on the left of the images indicates the initially formed hydrate layer just after compulsory nucleation. The overall growth direction is toward the right of the image and is indicated by an arrow. Therefore, the rightmost side of the image corresponds to the region just before the end of the run. Various patterns (textures) of hydrates were formed using the mixed 2 and 50 μm bead sediment model. Figure 3a shows the entire image of hydrates formed at V = 3.0 μm s−1. After the initial hydrate layer was formed, multiple hydrate grains repeatedly formed until the end of the run. The size of the hydrate grains slightly decreased from the initial stage (grain size of 1−2 mm or less) to the middle stage (0.5 mm or smaller) of the run. However, the grain size and pattern were almost constant from the middle to the end of the run (i.e., there was steady-state growth). The hydrate pattern formed corresponds to the nodular type categorized by Malone.3 The image region for analysis (inside the whitedashed square) was obtained in the steady-state growth region to avoid the initial transient stage of growth.

Figure 2. Images of hydrates formed in the sediment model (2 and 50 μm glass beads): (a) original image (256 gray scale values) and (b) black and white binary image. The original 256 gray scale image was processed to produce the black and white binary image. 23344



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Figure 3. Entire images of hydrates formed in the sediment model at constant V: V = (a) 3.0 and (b) 0.4 μm s−1. The analyzed image region is surrounded by a white dashed square.

Figure 4. Steady state hydrate patterns in the sediment model with V values (μm s−1) of (a) 10.0, (b) 5.0, (c) 3.0, (d) 1.0, (e) 1.0, and (f) 0.4.

Figure 3b shows an image of hydrates formed at V = 0.4 μm s−1. Large hydrate grains (approximately 4−5 mm) were formed after the initial hydrate layer. The size and pattern of these hydrates were almost constant from the middle to the end of the run, and these hydrates were extremely large compared with the hydrates formed at higher V. If the entire image is considered a single hydrate region, this region contained a large amount of pure hydrates and a relatively small amount of glass beads. This texture probably corresponds to the massive type categorized by Malone.3 Note that the hydrates formed in this study (up to 2 mm for the nodular type and 4−5 mm for the massive type) were much smaller than natural gas hydrates found under ocean floors (where nodular hydrates are up to 5 cm and massive type hydrates are as thick as 3−4 m).3 In this study, we categorized the types of hydrate patterns (textures) on the basis of the

pattern and the relative size differences of the hydrates. Quantitative differences between the nodular type and the massive type of THF hydrates are described later. The image region for analysis (inside the white-dashed square) was obtained in the steady-state growth region. Figure 4 shows the steady-state hydrate patterns in the final stage of different runs with different V values. The image obtained at V = 10 μm s−1 (Figure 4a) shows predominantly black and dark gray levels and few pure hydrate regions (segregated growth regions). This corresponds to the disseminated pore space type. The images at V = 15 and 20 μm s−1 were also obtained but not discussed in detail because the results are similar to the image at V = 10 μm s−1 (the disseminated type hydrate formed). At V = 5 (Figure 4b) and 3 μm s−1 (Figure 4c), the nodular type of hydrates were formed. Figure 4d,e shows hydrates formed at the same V (1 μm s−1) in 23345



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Figure 5. Entire images of hydrates formed in the sediment model at the lowest range of V: V = (a) 0.2, (b) 0.08, and (c) 0.04 μm s−1. The analyzed image region is surrounded by a white-dashed square.

Figure 5a shows the entire image obtained at V = 0.2 μm s−1. After the initial hydrate layer was formed, the massive type of hydrate formed until the middle of the run. However, the layer type of hydrates was formed in the final stage of the run. At V = 0.08 μm s−1 (Figure 5b), an extremely large hydrate region formed just before the middle stage of the run. This was found to be a very wide hydrate layer. The width of the hydrate layers suddenly decreased in the final stage of the run, and the final hydrate layer, at the rightmost side of the image, was faint and unclear. At the lowest V of 0.04 μm s−1 (Figure 5c), extremely large hydrate regions formed in the initial and middle stages of the run, then the size of the massive hydrates suddenly decreased and no hydrate region was formed in the final stage of the run. The reasons for the hydrate patterns and sizes changing drastically, even in the same run, at these low V values are discussed in section 4. To obtain quantitative results at the low V values, the massive hydrate image region (surrounded by white-dashed squares) in the middle stage of Figure 5a,c were chosen for analysis. The extremely large hydrate layer in the middle stage of Figure 5b (V = 0.08 μm s−1) was not chosen for analysis because the analysis used in this study focuses on hydrate grains and is not suitable for the analysis of layered hydrates. 3. 3. Image Processing. In the previous section, the hydrate types (massive, nodular, and disseminated) were

different runs. As shown in Figure 4d, relatively large hydrate grains were formed compared with the hydrates formed at higher V, and the hydrates shown in Figure 4e were even larger. Some hydrate patterns in these images are not nodular (small grains) but are similar to the massive type, indicating that the hydrate pattern changed from the nodular type to the massive type at approximately V = 1 μm s−1. In fact, at V = 0.4 μm s−1 (Figure 4f), the massive type pattern was formed. The multiple small circular bright points in and around the hydrate regions are 50 μm beads. In summary, the disseminated type of hydrates formed at higher V values (V ≥ 10 μm s−1), the nodular type formed in the middle range of V (1 μm s−1 ≤ V ≤ 5 μm s−1), and the massive type formed at lower V values (V ≤ 1 μm s−1). The velocity range (0.4 μm s−1 ≤ V ≤ 10 μm s−1) was the same as that used in our previous study in which multilayered hydrates formed in the sediment model of 2 μm beads, but a variety of hydrate patterns were formed depending on V in this study using mixed beads of two diameters. 3.2. Hydrate Patterns Formed at the Lowest Range of V. The hydrate patterns formed at the lowest range of V (0.04 μm s−1 ≤ V ≤ 0.2 μm s−1) changed drastically during a single run, even from the middle stage of the run to the end. Therefore, only entire images are shown in this section. 23346



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qualitatively judged by visual examination of the images. To quantitatively characterize the hydrates formed, we performed image processing and analysis as mentioned in section 2.3. The gray scale images were initially binarized before subsequent image processing was performed. Figure 6 shows the results of processing an image obtained at V = 0.04 μm s−1 (Figure 5c). Note that the outer parts of the

Figure 7. Images for analysis obtained at V = 3.0 μm s−1: (a) original binary image, (b) noise reduction image, (c) processed image obtained using method I (Sav), and (d) processed image obtained using method II (S90%).

will remove half of the grains because the threshold is the average area, Sav, of the grains. Because the noise reduction image (Figure 7b) contains hydrate grains of the same size order, method I over-removed hydrate grains, as shown in Figure 7c. We found that method II retained the most number of hydrate grains of the same size order, all of which almost equally contribute to the total area of the hydrate region. We conclude that the hydrate grains of the same size order retained using noise reduction processing should not be removed to evaluate the number density of hydrate grains and the average area of the hydrate grains, because they dominate the total area of the hydrates. The quantitative differences in each processed image are shown in detail in the following section. 3.4. Analysis of Processed Images of the Hydrate Patterns. The total hydrate area, Shyd, the total area of the image used, Simg, and the total number of hydrate grains, N, were obtained by analyzing the four types of processed images (i.e., the original binary image, the noise reduction image, the method I image (Sav), and the method II image (S90%)) for various V values. Figure 8 shows the ratio of the total hydrate area to the area of the image used, Shyd/Simg, plotted against V. Shyd/Simg was used to evaluate the segregated growth area of the hydrates. We found that Shyd/Simg could be classified into three regions with different orders of magnitude. The three regions are circled in Figure 8 and the types (textures) of hydrates observed depending on V are denoted under each circle. In the lowest V range, 0.04 μm s−1 ≤ V ≤ 0.4 μm s−1, the Shyd/Simg value was the largest ranging from 0.3 to 0.4. Shyd/Simg discontinuously decreased at V = 1 μm s−1. Note that the results of two different runs at V = 1 μm s−1 are shown: lower Shyd/Simg values were obtained from Figure 4d than from Figure 4e. In the middle range of V, 2 μm s−1 ≤ V ≤ 5 μm s−1, Shyd/Simg ranged from

Figure 6. Images for analysis obtained at V = 0.04 μm s−1: (a) original binary image, (b) noise reduction image, (c) processed image obtained using method I (Sav), and (d) processed image obtained using method II (S90%).

image shown in Figure 5c (inside the white-dashed square) were removed and the magnification of the remaining image was increased in order to show the results of processing the image more clearly. Figure 6a shows an original binary image that contains all of the hydrate regions and noise. Figure 6b shows a noise reduction image obtained from the original binary image. The two methods were tested using this noise reduction image for the removal of small hydrate grains in order to retain only relatively large hydrates that dominate the total area of the hydrate regions. Figure 6c shows the processed image obtained using method I (Sav), and Figure 6d shows the processed image obtained using method II (S90%). The number of hydrate grains in the method I image was almost the same as that in the method II image. Both methods effectively removed small hydrate grains and retained the dominant, large hydrates. Figure 7 shows the results of processing an image obtained at V = 3.0 μm s−1 (Figure 4c). The outer parts of the image were removed and the magnification was increased, as mentioned above. Figure 7a,b shows the original binary image and the noise reduction image, respectively. Figure 7c shows the processed image obtained using method I (Sav), and Figure 7d shows the processed image obtained using method II (S90%). There were fewer than half the number of hydrate grains in the method I image than in the method II image. If all hydrate grains are of approximately the same size, method I processing 23347



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Figure 9 shows the number density of hydrate grains, nd (N/ Simg), in units of cm−2, as a function of V. The solid lines

Figure 8. Relationship between Shyd/Simg (the ratio of the total hydrate area, Shyd, to the total area of image used, Simg) and V. Figure 9. Relationship between the number density of hydrate grains, nd, and V.

0.01 to 0.04, which is 1 order of magnitude lower than that in the lowest range of V. In the highest range of V, 10 μm s−1 ≤ V ≤ 20 μm s−1, Shyd/Simg for the original binary image was smaller than 0.001. The Shyd/Simg values for the noise reduction images and the method I and II images for this range of V were 0 (and do not appear in the graph) because all the quite small white dots in the original binary images were smaller than the noise reduction method threshold and were removed. The three velocity range groups from this quantitative analysis correspond to the velocity ranges classified by the visual hydrate pattern characteristics: the massive type in the lowest range of V, the nodular type in the middle range of V, and the disseminated pore space type in the highest range of V. Thus, we found that the segregated growth area of the hydrates was a useful index for quantitatively classifying the hydrate types. Note that all image processing methods showed the same tendency. The suitable image processing method to evaluate the size scales and number density of the relatively large hydrate grains was determined from the number density of hydrate grains as a function of V, because the number density is sensitive to the differences between the methods. In this study, the quite small bright points in the original binary images, which were removed by noise reduction processing, were not considered hydrate regions formed by segregated growth. However, the ratio of the total hydrate area containing noise (the original binary image) to the total hydrate area in the noise reduction image was approximately 1.01 in the lowest range (0.04 μm s−1 ≤ V ≤ 0.4 μm s−1) and up to approximately 1.6 in the middle range (2 μm s−1 ≤ V ≤ 5 μm s−1). Because the effect of noise on the total hydrate area ratio was not significant, the original binary image results are shown in Figure 8 to show the relationship between each processed image and its original binary image. However, the noise level increased significantly with the brightness level of the images. Because the effect of noise is too large to evaluate the number density and average area of the hydrate grains, the original binary image results are not shown in further figures. The noise reduction and methods I and II analysis results are shown for all images except for those taken at V ≥ 10 μm s−1, because at that V value, results of all of these processed images showed a completely black region, as described above.

indicate the best linear fit for the data. The noise reduction images gave a larger number density, nd, than the other two methods for all ranges of V. The difference was particularly large for the lowest range of V because the noise reduction method counts many small hydrates, which have little effect on the total hydrate area, as mentioned in section 3.3 (Figure 6b). For example, at V = 0.04 μm s−1, approximately 90% of the total hydrate area in the image region for analysis consisted of 14 relatively large hydrate grains and approximately 10% of the total hydrate area consisted of 134 relatively small hydrate grains. Method I (Sav) gave a smaller nd than the other two methods for all ranges of V. Note that method I underestimated the value of nd for the higher range of V because it overremoved hydrate grains, as mentioned in section 3.3 (Figure 7c). Finally, the nd from method II (S90%) was almost the same as that from method I for the lower range of V and almost the same as the nd from the noise reduction method for the higher range of V. Therefore, method II (S90%) is suitable for evaluating the relatively large hydrate grains that dominate the total hydrate area and the noise reduction method is suitable for counting all hydrate grains. Figure 10 shows the average area of the hydrate grains, Shyd/ N, as a function of V. The solid lines indicate the best linear fit for the data for two ranges of V. Note that the lower Shyd/N values for V = 1 μm s−1 were not included in the best linear fit because they deviated markedly from the other V = 1 μm s−1 data. The Shyd/N values decreased with increasing V with a discontinuous decrease at V = 1 μm s−1. The Shyd/N values from the noise reduction images in the lower range of V were lower than those from the other two methods because the relatively small hydrate grains were included in the value of N from the noise reduction images (see Figure 9). The Shyd/N values for the method I images in the higher range of V were overestimated because the value of N was underestimated. The method II (S90%) results are the suitable for quantitatively characterizing the relatively large hydrate grains that dominate the total hydrate area. 23348



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block in the apparatus used, experiments using a longer growth distance are needed to clarify this possibility. The theoretical estimation of δs and the transition time will be quite useful to clarify the hydrate growth process (i.e., transport of the THF−water solution in the sediment model). To obtain these, some unknown coefficients (compressibility and permeability of the pore water) for the THF−water solution and glass beads are required. Note that the theoretical model by Takashi et al. assumes that frost heave proceeds in soil at a constant velocity without assessing the criteria for frost heave occurrence. Therefore, the result only indicates the water transport process in soil. Clennell et al.12 suggested criteria for segregated growth of hydrates in sediment. According to this model, the inner pressure (phase pressure) of the hydrates is elevated by the capillary effect in which fine-grained sediment exceeds the effective confining stress combined with the tensile strength of the sediment. Consequently, the hydrates can push the soil particles and form hydrate patterns. Our series of model experiments showed a tendency to correspond with the predictions of the model proposed by Clennel et al. The hydrates grew only in the pore space of the 50 μm bead sediment model, but hydrate patterns formed in the mixture of small and large (2 and 50 μm) beads. Therefore, the finegrained bead had a critical effect on pattern formation of hydrate. However, the reasons why hydrates formed different pattern types (nodular, massive, and layer) has not been elucidated yet. Model experiments using different mixing ratios, w2/w50, of the two diameters of beads might be useful in clarifying the formation mechanism for each hydrate pattern. Such experiments are in progress and will be reported soon.

Figure 10. Relationship between the average hydrate area, Shyd/N, and V.

4. DISCUSSION In this study, we have shown that, as V decreased, the segregated growth area of the hydrates (Figure 8) and the average hydrate area (Figure 10) increased and the number density of the hydrate grains (Figure 9) decreased. The results are now discussed in relation to the frost heave model. Takashi et al. derived a theoretical model for the frost heave of ice in soil.33 In their study, a one-dimensional consolidation equation obtained by Terzaghi,34 which is of the same type as the diffusion equation (concentration was replaced by pore water pressure), was transformed to an equation with a moving frame of reference fixed at the unidirectional freezing front advancing at the freezing velocity V. This theoretically allows obtaining the distribution of pore water pressure in front of the freezing front. It was shown that the length of the dewatered consolidation region, δs, was inversely proportional to V. Based on this result, the hydrates in our study also appear to have absorbed more solution from the sediment model far from the growing hydrates at lower V. As a result, the segregated growth area of the hydrates and the average hydrate area increased with decreasing V. The formation of large hydrates at lower V results in a decrease in the number density of the hydrate grains. In addition, our results showed that at the lowest range of V (0.04 μm s−1 ≤ V ≤ 0.4 μm s−1), as shown in Figure 5, the size scale of the hydrates decreased drastically and no hydrate regions were observed in the final stage of the run. As mentioned above, the length of the dewatered consolidation region, δs, increases with decreasing V. If the dewatered consolidation region of the THF−water solution in our study reached the right edge of the growth cell, solution transport to the growing hydrates would decrease. Thus, one possibility might be that the length of the growth cell affected the results. A longer growth cell needs to be used in further experiments to clarify this possibility. Takashi et al.33 also showed that the transition time to attain steady state is inversely proportional to V2. The growth distance necessary to attain steady state is inversely proportional to V. Thus, the final stage of the run in our study might be the growth transition stage before attaining steady state. Because the overall directional growth distance was limited by the moving distance (25 mm) of the growth cell toward the cold

5. CONCLUSIONS We observed pattern formation of THF clathrate hydrate in a mixture of a THF−17H2O solution and glass beads (2 and 50 μm diameter). The overall growth rate, V, of the hydrates was controlled using a directional growth apparatus. We successfully formed hydrates in a variety of patterns: a disseminated type in the higher range of V ≥ 10 μm s−1, a nodular type in the middle range of 1 ≤ V ≤ 5 μm s−1, and a massive type in the lower range of V ≤ 1 μm s−1 (and a layer type in the lower range of V ≤ 0.2 μm s−1). To quantitatively characterize these hydrate patterns, three types of image processing (a noise reduction method and methods I (Sav) and II (S90%) and analysis were performed on the hydrate images. We found that the segregated growth area of the hydrates in the mixture discontinuously decreased as V increased, indicating three separate velocity ranges (high, middle, and low) that correspond to visual characteristics of the hydrate patterns (disseminated, nodular, and massive). Thus, we found that the segregated growth area of the hydrates was a useful index for quantitatively classifying the hydrate types. Note that all image processing methods showed the same tendency. Method II (S90%) was suitable for evaluating the number density of relatively large hydrate grains. It retained a small number of large hydrates, which are dominant in all hydrate regions in the lower range of V, and retained a large number of small hydrates, which contribute equally to the total hydrate area in the higher range of V. On the other hand, the noise reduction method was suitable for evaluating the number density of all hydrate grains regardless of the size of the hydrate. The image analysis results showed that as V decreased, the segregated growth area of the hydrates and the average hydrate area increased and the number density of the hydrates 23349



Article

(27) Alavi, S.; Susilo, R.; Ripmeester, J. A. J. Chem. Phys. 2009, 130, 174501. (28) Alavi, S.; Udachin, K.; Ripmeester, J. A. Chem.Eur. J. 2010, 16, 1017−1025. (29) Lehmkühler, F.; Sakko, A.; Sternemann, C.; Hakala, M.; Nygård, K.; Sahle, C. J.; Galambosi, S.; Steinke, I.; Tiemeyer, S.; Nyrow, A.; Buslaps, T.; Pontoni, D.; Tolan, M.; Hämäläinen, K. J. Phys. Chem. Lett. 2010, 1, 2832−2836. (30) Nagashima, K.; Suzuki, T.; Nagamoto, M.; Shimizu, T. J. Phys. Chem. B 2008, 112, 9876−9882. (31) Nagashima, K.; Furukawa, Y. J. Cryst. Growth 1997, 171, 577− 585. (32) Nagashima, K.; Furukawa, Y. J. Phys. Chem. B 1997, 101, 6174− 6176. (33) Takashi, T.; Ohrai, T.; Yamamoto, H. J. Jpn. Soc. Snow Ice 1977, 39, 53−64. (34) Terzaghi, K. Erdbaumechanik auf Bodenphysikalischer Grundlage; Franz Deuticke: Vienna, 1925.

decreased. These results are qualitatively consistent with the theoretical model for frost heave. We successfully reproduced various hydrate patterns and established protocols for image processing and analysis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by JSPS KAKENHI Grant Number 21540498.

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REFERENCES

(1) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008. (2) Kvenvolden, K. A. Terra Nova 2002, 14 (5), 302−306. (3) Malone, R. D. Gas Hydrate Topical Report, DOE/METC/SP-218; U.S. Department of Energy: Washington, DC, April 1985. (4) Tohidi, B.; Anderson, R.; Clennell, M. B.; Burgass, R. W.; Biderkab, A. B. Geology 2001, 29, 867−870. (5) Katsuki, D.; Ohmura, R.; Ebinuma, T.; Narita, H. Philos. Mag. 2006, 86 (12), 1753−1761. (6) Katsuki, D.; Ohmura, R.; Ebinuma, T.; Narita, H. Philos. Mag. 2007, 87 (7), 1057−1069. (7) Taber, S. J. Geol. 1929, 37, 428−461. (8) Taber, S. J. Geol. 1930, 38, 303−317. (9) Watanabe, K. J. Cryst. Growth 2002, 237−239, 2194−2198. (10) Hiroi, M.; Mizusaki, T.; Tsuneto, T.; Hirai, A.; Eguchi, K. Phys. Rev. B 1989, 40, 6581−6590. (11) Zhu, D.-M.; Vilches, O. E.; Dash, J. G.; Sing, B.; Wettlaufer, J. S. Phys. Rev. Lett. 2000, 85, 4908−4911. (12) Clennell, M. B.; Hovland, M.; Booth, J. S.; Henry, P; Winters, W. J. J. Geophys. Res. 1999, 104, 22985−23004. (13) Buffett, B. A.; Zatsepina, O. Y. Marine Geol. 2000, 164, 69−77. (14) Hyndman, R. D.; Davis, E. E. J. Geophys. Res. 1992, 97B5, 7025−7041. (15) Soloviev, V.; Ginsburg, G. D. Bull. Geol. Soc. Denmark 1994, 41, 86−94. (16) Rempel, A. W.; Buffett, B. A. J. Geophys. Res. 1997, 102 (B5), 10151−10164. (17) Jeffrey, G. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vol. 1, p 135. (18) Gough, S. R.; Davidson, D. W. Can. J. Chem. 1971, 49, 2691− 2699. (19) Yang, H. J.; Fan, S. S.; Lang, X. M.; Wang, Y. H. J. Chem. Eng. Data 2011, 56 (11), 4152−4156. (20) Lee, H.; Lee, J. W.; Kim, D. Y.; Park, J.; Seo, Y. T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 2005, 434 (7034), 743−746. (21) Park, Y.; Dho, J.; Seol, J.; Yeon, S.-H.; Cha, M.; Jeong, Y. H.; Seo, Y.; Lee, H. J. Am. Chem. Soc. 2009, 131 (16), 5736−5737. (22) Leaist, D. G.; Murray, J. J.; Post, M. L.; Davidson, D. W. J. Phys. Chem. 1982, 86, 4175−4178. (23) Tombari, E.; Presto, S.; Salvetti, G.; Johari, G. P. J. Chem. Phys. 2006, 124, 154507. (24) Park, Y.; Choi, Y. N.; Yeon, S. H.; Lee, H. J. Phys. Chem. B 2008, 112, 6897−6899. (25) Davidson, D. W.; Ripmeester, J. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: London, 1984; Vol. 3, p 69. (26) Gough, S. R.; Hawkins, R. E.; Morris, B.; Davidson, D. W. J. Phys. Chem. 1973, 77, 2969−2976. 23350


Pattern Variety of Tetrahydrofuran Clathrate Hydrates Formed in

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