Cohesion Force Measurement of Methane Hydrate and Numerical

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Cohesion Force Measurement of Methane Hydrate and Numerical Simulation of Rising Bubbles Covered with a Hydrate Membrane within a Contracting Pipe Junichi Sato,† Taiki Iida,† Fumio Kiyono,‡ and Toru Sato*,† †

Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8563, Japan Environmental Fluid Engineering Research Group, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8569, Japan

‡

ABSTRACT: Depressurization is considered to be one of the realistic production methods of methane gas from methane hydrate (MH). However, there is a concern about this method: flow blockage takes place inside the pipe, as MH forms on the surface of methane bubbles rising within a riser pipe. The objective of this study is to develop a numerical simulation method that can analyze the behavior of rising bubbles covered with MH in the water within a riser pipe. For this purpose, we measured the cohesion force of MH, considering that the bubbles come into contact with each other. The results, however, suggested that there is little force between 2 MH samples for them to detach in the water. We then numerically simulated the behaviors of rising methane bubbles in the water within a contracting pipe and found that the bubbles may clog the neck of the contraction, depending upon the contact angle at the pipe wall in the water.

1. INTRODUCTION Flow assurance in a gas pipeline generally involves the blockage of gas flow produced by the formation of methane hydrate (MH). At the moment, the Japanese government is planning a demonstrative field experiment of gas production via depressurization from sub-seabed MH reservoirs off Japan’s coasts, with future business for industry in mind. Although there must be no flow assurance problems when the system works properly, we may have clogs in the reservoir or in the riser pipes if the system stops accidentally and, consequently, the pressure recovers toward the original value. Therefore, it is important to investigate the mechanisms of the MH formation in sedimentary sand layers or in the riser pipes. The objective of this study is to develop a numerical simulation method that can analyze the behaviors of rising bubbles covered with MH within a riser pipe. For this purpose, it is necessary to know the cohesion force between MH membranes when the bubbles come into contact with each other in the water. There has been some research on the cohesion force between gas hydrate surfaces. Yang et al.1 measured the cohesion force of tetrahydrofuran (THFH) set at the top of a cantilever. They concluded that the force between two THFH balls is smaller than that of two ice pieces and increases as the condition approaches equilibrium. Joseph et al.2 measured the cohesion force of synchro-pentane hydrate (SPH) and the adhesion force between SPH and carbon steel and showed that both forces are remarkably weak near the equilibrium condition. Dieker et al.3 measured the cohesion of SPH, THFH, ethylene oxide hydrate (EtOH), and ice. From those results, it can be concluded that the cohesion force of ice is the largest and that of SPH is the smallest. Aspenes et al.4 measured the cohesion force of SPH and found that it becomes 10 times larger when water droplets exist on the SPH surface. Du et al.5 conducted measurements of the cohesion force of THFH in the © XXXX American Chemical Society

poly(vinyl alcohol) solution and concluded that there is no temporal dependency if the contact time is less than 180 min and that the cohesion may be due to the capillary effect. Aman et al.6,7 measured the cohesion force of SPH under various conditions and attributed the force to the capillarity of the thin water layer existing between the two hydrate balls, because the force becomes almost zero when measured in the water. They also discussed that, as the condition approaches equilibrium, the water layer becomes thicker and, consequently, the capillary force increases. Although the cohesion forces of the other gas hydrates were studied, these previous studies did not measure the forces of MH per contact area. Therefore, in this study, we developed an experimental apparatus that can measure the cohesion force per unit surface area of MH. According to the present experimental results, which, in fact, imply that there is no cohesion of bubbles covered with MH in the water, we developed a numerical method to simulate the behaviors of rising bubbles covered with MH in the water. The present method is based on the two-phase lattice Boltzmann method (LBM) of Inamuro et al.,8 and we modified it to treat bubbles that cannot coalesce when they come into contact with each other. We then conducted numerical case studies of rising bubbles with MH surfaces in the water flow within a contracting pipe, to see how the bubbles clog the pipe.

2. MEASUREMENT OF COHESION FORCE OF MH 2.1. Experimental Methods. The cohesion force of MH is measured with an experimental device shown in Figure 1. Note that the originality of this experiment lies in the fact that the contact area between two MH samples is constant and known: 78.5 mm2. To Received: June 2, 2016 Revised: August 18, 2016

A

DOI: 10.1021/acs.energyfuels.6b01341 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 2. Temporal change of force measured by a load cell during the experiment. 2.2. Experimental Results. Figure 3 shows the cohesion forces of ice versus subcooling, depending upon the contact times. Measure-

Figure 1. Experimental apparatus to measure cohesion forces of MH. ensure the contact area, MH powder was molded in a sample holder, which was set in a pressure vessel. The inside of the vessel was filled with methane dry gas or water, and the temperature and pressure were adjusted using a cooling pool and a syringe pump, respectively. While the pressure was always kept constant, temperature, contact force, and contact time varied, depending upon the experimental conditions shown in Table 1. The temperature was always kept within the range

Figure 3. Measured cohesion forces of ice versus subcooling, depending upon the contact time. The contact force was set to be 6.4 kPa.

Table 1. Experimental Conditionsa case

material

surrounding material

subcooling (°C)

contact force (kPa)

contact time (s)

0 1 2 3 4 5 6 7

ice MH MH MH MH MH MH MH

air CH4 gas CH4 gas CH4 gas CH4 gas CH4 gas CH4 gas water

0.9 and 4.2 0.2 0.4 0.2 0.2 0.2 0.2 0.0−0.6

1.9−6.4 2.5 2.5 5.1 7.6 5.1 5.1 2.5−10.2

10−50 10 10 10 10 50 120 10−1200

ments were repeated 3 times under each experimental condition. The contact force was set to be 6.4 kPa in all of the cases in Figure 3. It is seen that the cohesion force for the subcooling of 0.9 °C is larger than that for 4.2 °C. However, the effect of the contact time is not very clear in the case that the contact time is 50 s or less. Figure 4 shows the cohesion forces of ice versus contact forces. In these measurements, the subcooling and contact time were set to be 4.2 °C and 50 s, respectively. It may be indicated that, if the contact force is 4.6 kPa and less, the larger the contact force, the larger the cohesion force.

“Sub-cooling” means how much lower than equilibrium is the experimental temperature.

a

in which MH is stable under the given pressure. The cohesion force of ice in the air was also measured as comparative experiments. “Subcooling” in the table represents how the experimental temperature is lower than equilibrium: the freezing point for ice and the threephase equilibrium temperature for MH. Figure 2 shows the temporal change of the force measured by a load cell during a specific experimental case. When the upper MH sample descends and starts contacting the lower MH sample, the force starts increasing gradually. When the upper sample reaches a set contact force (0.6 N at about 20 s in Figure 2), it stops descending and, then, maintains its height for a set contact time (for 10 s in Figure 2). After a set contact time (at about 30 s in Figure 2) passes, the sample starts ascending at a constant speed and the detachment force is measured. Here, we define the absolute value of the negative lowest peak during the detachment (at about 30.5 s in Figure 2) as the cohesion force of MH samples.

Figure 4. Measured cohesion forces of ice versus contact force. The subcooling and contact time were set to be 4.2 °C and 50 s, respectively. B


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Energy & Fuels Figure 5 shows the cohesion forces of MH measured in the ambient methane gas versus subcooling, corresponding to cases 1 and 2. All of

Figure 8. Measured cohesion forces of MH measured in the water versus contact time in case 7. hydrate in the literature: e.g., Yang et al.1 for THFH and Dieker et al.3 for SPH, THFH, and EtOH. Figure 6 shows the cohesion forces of MH measured in the methane gas versus the contact forces, corresponding to cases 1, 3, and 4. Error bars are, again, the 95% confidence intervals of the 10 measurements. As seen in Figure 6, the cohesion force for the contact force of 7.6 kPa is the largest among those for the three contact forces and the second largest among the three was obtained when the contact force is 5.1 kPa. Figure 7 shows the cohesion forces of MH measured in the methane gas versus the contact time, corresponding to cases 3, 5, and 6. For the contact times of 50 and 120 s, it is seen that the corresponding cohesion forces were almost the same, and for the contact time of 10 s, it is a little smaller than them. Next, the cohesion forces of MH in the water (case 7) are shown in Figure 8. All of the resultant values are smaller than 0.01 kPa, which is the lower limit of the present measurement apparatus. 2.3. Discussion. There is a peephole made of sapphire glass on the pressure vessel, so that the inside can be observed during the experiments. In the methane gas, between the surfaces of the upper and lower MH samples, thin layers of the water were observed at all times through the peephole in cases 1−6. An example photograph of the water film is shown in Figure 9. From these observations, it is thought that the measured cohesion force is caused by the surface tension of the water film existing between the two MH surfaces in the gas.

Figure 5. Measured cohesion forces of MH measured in the methane gas versus subcooling in cases 1 and 2 (contact force, 2.5 kPa; contact time, 10 s). The 95% confidence intervals of the average values of 10 measurements are also shown as error bars. the measurements using MH in this study were repeated 10 times for each case, and their average is plotted in Figures 5−8. Error bars

Figure 6. Measured cohesion forces of MH measured in the methane gas versus contact force in cases 1, 3, and 4 (subcooling, 0.2 °C; contact time, 10 s). The 95% confidence intervals of the average values of 10 measurements are also shown as error bars.

Figure 9. Example photograph of the observed water film through the peephole. If the surface tension of the water film is the main mechanism of the cohesion of MH in the gas phase, the undetectably small (less than 0.01 kPa) contact forces in case 7 can be neglected. The results of the present experiment are also reasonable: that the cohesion force of MH in the gas becomes larger as the temperature comes closer to the threephase equilibrium, that the cohesion force increases asymptotically as either the contact force or the contact time increases, and that the cohesion force is far smaller than that of ice. This mechanism of cohesion was suggested by Aspenes et al.4 for SPH and Du et al.5 for THFH. Specifically, Aman et al.6,7 strongly proposed that the cohesion force in the water should be caused by the capillarity of the thin water layer existing between the two hydrate balls. Obviously, the results of the present experiments support their findings.

Figure 7. Measured cohesion forces of MH measured in the methane gas versus contact time in cases 3, 5, and 6 (subcooling, 0.2 °C; contact force, 5.1 kPa). The 95% confidence intervals of the average values of 10 measurements are also shown as error bars. indicate the 95% confidence intervals of the average of the 10 measurements. First of all, it is observed that the values are one digit smaller than those of ice. As seen in Figure 5, the cohesion force for the subcooling of 0.2 °C is larger than that of 0.4 °C. These results for MH do not conflict with the previous measurements for the other gas C


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3. NUMERICAL SIMULATION OF RISING BUBBLES COVERED WITH MH 3.1. Simulation Methods. We adopted the LBM for twophase flows of Inamuro et al.8 and Yan et al.9 as the base scheme for analyzing the bubble behaviors. There are various models for discretising velocity, and in this study, we adopted the three-dimensional 15 velocity (D3Q15) model of Qian.10 Nash et al.11 confirmed the stability of this model in complex flow domains. The governing equations of the present LBM are

where cs is the pseudo-speed of sound and defined as cs = c/ √3. Inamuro et al.8 developed a LBM for two-phase flow with incorporation of a Poisson equation of pressure to ensure the incompressibility. They also added the viscous term explicitly in eq 2 and erased the implicit viscous effect with adding the fifth term on the right-hand side of eq 5. These treatments can release the viscosity from the constraint of eq 9, and τg and cs can be set free to maintain the stability of computation. Following Inamuro et al.8 and Yan et al.,9 we set τf and τg to be 1.0 and, eventually, cs is the only parameter to adjust the stability of our computation. To solve the Poisson equation, a local equilibrium distribution function hα for pressure p is introduced as 1 hα n + 1(x + cαΔx) = hα n(x) − [hα n(x) − Eαpn (x)] τh 1 δu * − Eα i 3 δxi (10)

fα (x + cαΔt , t + Δt ) − fα (x , t ) 1 = − {fα (x , t ) − f αeq (x , t )} τf

(1)

gα (x + cαΔt , t + Δt ) − gα (x , t ) 1 1 = − {gα (x , t ) − gαeq (x , t )} + 3ωα ∇ τg ρ {ρν(∇u + u∇)}cα − 3ωα cαzg

(2)

p=

(3)

c Δt = Δx

{

k |∇φ|2 6

⎧ 9 3 gαeq (x , t ) = ωα ⎨1 + 3cαu + (cαu)2 − u 2 2 2 ⎩ k 3 + cα(∇u + u∇)cβ + ωα Gαβ (φ)cαcβ ρ 4 ⎫ 2 k − Fα ∇φ|2 ⎬ 3 ρ ⎭

Gαβ (φ) =

∂φ ∂φ 3 − |∇φ|2 δαβ ∂x α ∂xβ 2

u = u* −

ν=

∑ fα α

u* =

∑ cαgα α

φ − φG φL − φG

(νL − νG) + νG

⎛ φ − φ ⎞2 G ⎟⎟ σ = k ⎜⎜ L ρ − ρ ⎝ L G⎠

(4)

(13)

(14)

⎛ δφ ⎞2 ⎜ ⎟ dn −∞ ⎝ δn ⎠

∫

∞

(15)

where n is the normal direction of an interface and k is the parameter representing the interface tension used in eqs 4 and 5. The integral is eventually applied to only the lattices inside of a gas−water interface with finite numerical thickness, along the normal direction of which φ changes monotonically between φL and φG. In this study, the numerical thickness of the interface was kept at 4 lattice cells to minimize the thickness without losing the numerical stability. σ for the gas−water interface without MH membrane was set to be 72.75 mN/m, and the contact angle of water on the glass wall in the air was set at 26°, referring to a chemistry textbook. We modified this method to treat bubbles that do not coalesce when they come into contact with each other, by setting different color functions to individual bubbles, such as φG1, φG2, ..., φGm, where m is the number of all of the bubbles within the computational domain. When calculating the interface tension between water and gas with a particular color function, gases with different color functions are treated as water. Then, a bubble with the particular color function always tries to make a convex shape toward the outside of the bubble and never coalesces with the other bubbles. 3.2. Treatment of the MH Membrane. In this study, a numerical method to treat a thin MH membrane on the surface of methane bubbles was developed. First, fα, gα, and hα on the

(5)

(6)

(7)

(8)

For a common single-phase LBM, to correspond to the Navier−Stokes equation, the relaxation time τg is set to satisfy the following equation: ⎛ 1⎞ ν = ⎜τg − ⎟cs 2Δt ⎝ 2⎠

(12)

where the subscripts L and G indicate the liquid and gas phases. The interface tension σ is given as

The interfacial parameter φ and fluid velocity u* are given as

φ=

∇p ρ

ρ and ν are now given as φ − φG (ρ − ρG ) + ρG ρ= φL − φG L

}

+ 3ωαφcαu + ωαkGαβ (φ)cαcβ

(11)

α

where fα and gα are the local equilibrium distribution functions for mass conservation and momentum conservation, respectively, and cα (|cα| = c) indicates the discrete particle velocity in the direction toward α, which denotes each of the surrounding 14 lattice points, t is the time, Δt is the time step, ρ is the density, ν is the kinematic viscosity, and τf and τg are the relaxation times. The local equilibrium distribution function feq α and geq α are extensions of the Maxwell distribution to local equilibrium, which are the general kinetic theory of fluids and expressed as f αeq (x , t ) = Hαφ + Fα p0 − kφ∇2 φ −

∑ hα

(9) D


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Energy & Fuels lattices inside and outside of the MH membrane are calculated. To impose a moving no-slip boundary condition on the surface of the MH membrane, the methods of Mei et al.12 and Bouzidi et al.13 were applied in the propagation steps of fα, gα, and hα. Although, to express the movement of a membrane in fluid flow, the motion equation of the membrane should have been coupled with the two-phase flow equation system, we took a rather simple way to reduce the computational cost: the thickness of the MH membrane is not taken into account; a moving no-slip condition is imposed on the MH membrane at the interface for the fluids inside and outside the bubble; the velocity on the membrane is interpolated from the velocities of surrounding fluids; its component normal to the membrane is considered to be the moving speed of the membrane; and this normal velocity is used for the moving boundary condition. To do so, the interface tension of the MH membrane is needed. However, there have been little research about the tension. Here, the interface tension is regarded as the same as the surface strength of CO2 hydrate measured by Yamane et al.:14 100 mN/m. The contact angles of MH on the pipe wall in the surrounding gas were set to be 0° or 89.9° as case studies: 89.9° can be regarded as a case that the MH membrane breaks when it touches a wall, and 0° is a case in which it does not. Because the present experimental results show that there is almost no cohesion force between MH surfaces in the water and a study by Joseph et al.2 also suggests that the adhesion force of MH to the pipe wall is minuscule, we did not take into account the cohesion and adhesion forces of MH in the water in the present numerical simulation method. In this method, the only mechanism for MH to adhere to the pipe wall in the water is the breakup of the MH membrane when the contact angle is set to be 89.9°. However, it is still not clear how the MH membrane breaks against the wall. Therefore, the contact angles of 0° and 89.9° are both regarded as two extreme cases: either none of the bubbles break, or they all break against the wall, respectively. 3.3. Validation of the Present Numerical Method. Here, we tried validating the present numerical method for bubbles with the MH membrane rising in the water. Sato et al.15 conducted experiments to measure the terminal velocity of methane bubbles covered with the MH membrane. In the experiment, pressure and temperature are set to be 6 MPa and 4 °C, respectively, to maintain MH on the surface of the methane bubbles. Then, numerical simulations of a rising bubble covered with the MH membrane are performed under the same conditions: the diameter of the bubble is 7.8 mm. The pseudo-speed of sound cs in the method of Inamuro et al.8 is a representative velocity. A value of cs should be determined to satisfy a typical problem with theoretical solutions or experimental data without losing the numerical stability. In this study, the rising bubble with the MH membrane of Sato et al.15 was the case with experimental data and cs was set to be 400 m/s after several trials. The temporal change of the calculated rising speed of the bubble is shown in Figure 10 with the experimental result, 0.21 m/s. From the figure, it is thought that the present method is well-validated. 3.4. Simulation of Blockage by a Single Bubble within a Pipe. The numerical simulations were conducted for single methane bubbles, with and without the MH membrane, rising within a contracting pipe, whose diameter shrinks abruptly in the middle of the vertical direction, as shown in Figure 11. The

Figure 10. Temporal change of the rising speed of a single methane bubble covered with MH in the water. The sphere equivalent diameter of the bubble is set to be 7.8 mm. The dashed line indicates the measurements conducted by Sato et al.:15 0.21 m/s in the case that the diameter of the bubble is 7.8 mm. Pressure and temperature are set to be 6 MPa and 4 °C, respectively.

Figure 11. Schematic image of the contracting pipe used for the numerical simulations of the behaviors of rising bubbles with or without MH membranes on the bubble surfaces. The boundary conditions at the upper exit of the small pipe and at the lower exit of the large pipe are periodical.

boundary conditions at the upper outlet of the small pipe and at the lower inlet of the large pipe are periodically connected. Therefore, the small pipe is just like the narrow neck of a pipe. The blockage caused by rising bubbles covered with MH was simulated by changing the diameter of the contacting pipe: 6− 12 mm for the diameter of the small pipe and 30 mm for the larger pipe. Figures 12 and 13 show the temporal changes of the perspective images of the calculated behaviors of single bubbles covered with MH for the contact angles of 0° and 89.9°, respectively, under the condition that the sphere equivalent diameter of the bubble is 7.8 mm and the small pipe diameter is 6 mm at t = (a) 0.06 s, (b) 0.105 s, (c) 0.225 s, and (d) 0.450 s. Although the single bubbles clogged the pipe neck in both of the cases, the ways in which that happened look different: the bubble could not go into the small pipe at the neck in the case of 0° (Figure 12), while it blocked the flow inside of the small pipe in the case of 89.9° (Figure 13). Table 2 shows whether the single bubbles with a diameter of 7.8 mm pass the small-diameter neck or block the flow, “P” or “B”, respectively, depending upon the neck diameter. Moreover, “S” means that the bubble sticks to a part of the neck wall without blocking. The results showed that bubbles covered with MH tended to cause blockage more than those without membrane, and the cases in which the contact angle was 89.9° were more likely to cause blockage than those with 0°. E


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Table 2. Criteria of Blockage for a Rising Bubble within the Contraction Pipe small pipe diameter (mm) bubble property with MH membrane without MH membrane

contact angle (deg)

6.0

8.0

10.0

12.0

89.9 0.0 26.0

B B

B P P

P P P

S P P

Figure 12. Temporal change of the perspective images of the calculated behavior of a bubble covered with MH for the contact angle of 0°, under the condition that the sphere equivalent diameter of the bubble is 7.8 mm and the small pipe has a diameter of 6 mm, at t = (a) 0.060 s, (b) 0.090 s, (c) 0.135 s, and (d) 0.195 s.

Figure 14. Temporal change of the perspective images of the calculated behavior of a bubble covered with MH for the contact angle of 89.9°, under the condition that the sphere equivalent diameter of the bubble is 7.8 mm and the small pipe has a diameter of 8 mm, at t = (a) 0.060 s, (b) 0.105 s, (c) 0.150 s, and (d) 0.218 s.

is applied in the vertical direction, a bubble coming into the domain at the lower boundary is actually the top of the bubble at the upper boundary, as seen in Figure 14. It is seen that the single bubbles clogged the neck, when the neck diameters were 8 and 10 mm (Figures 14 and 15). However, in the case that the neck diameter was 12 mm, the bubble adhered (stuck) at a part of the neck wall and stopped rising and space still remains within the neck for water flow. This is the case indicated by “S” in Table 2. It should be noted that the “S” case may not always take place, even if the neck diameter is 12 mm or larger: it just depends upon the horizontal position of the bubble when it comes close to the neck. 3.5. Simulation of Blockage by Multiple Bubbles within a Pipe. Numerical simulations of multiple rising bubbles covered with MH were also performed. Results of the cohesion force measurement suggest that it is not necessary to take the cohesion force into consideration in the simulation. The sphere equivalent diameter of the bubble in the simulation was, again, set to be 7.8 mm; the neck diameter was 14 mm; and the contact angle of MH to the wall in the gas phase was 89.9°. Figures 17 and 18 show the perspective images of the calculated behaviors of six and eight bubbles, respectively, at t =


Figures 14−16 show the calculated bubble behaviors with the contact angle of 89.9°, when the neck diameters were 8, 10, and 12 mm, respectively. Because the periodical boundary condition F


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Figure 17. Temporal change of the perspective image of the calculated behaviors of six bubbles covered with MH for the contact angle of 89.9°, under the condition that the sphere equivalent diameter of the bubbles is 7.8 mm and the small pipe has a diameter of 14 mm, at t = 0.009 s viewed in the (a) radial direction and (b) vertical direction and t = 0.279 s in the (c) radial direction and (d) vertical direction.


Figure 18. Temporal change of the perspective image of the calculated behaviors of eight bubbles covered with MH for the contact angle of 89.9°, under the condition that the sphere equivalent diameter of the bubbles is 7.8 mm and the small pipe has a diameter of 14 mm, at t = 0.009 s viewed in the (a) radial direction and (b) vertical direction and at t = 0.252 s in the (c) radial direction and (d) vertical direction.

0.009 s viewed in the (a) radial direction and (b) vertical direction and t = 0.279 s in the (c) radial direction and (d) vertical direction in Figure 17 and at t = 0.009 s viewed in the

(a) radial direction and(b) vertical direction and at t = 0.252 s in the (c) radial direction and (d) vertical direction in Figure G


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(6) Aman, Z. M.; Brown, E. P.; Sloan, E. D.; Sum, A. K.; Koh, C. A. Interfacial Mechanisms Governing Cyclopentane Clathrate Hydrate Adhesion/Cohesion. Phys. Chem. Chem. Phys. 2011, 13, 19796−19806. (7) Aman, Z. M.; Joshi, S. E.; Sloan, E. D.; Sum, A. K.; Koh, C. A. Micromechanical Cohesion Force Measurements to Determine Cyclopentane Hydrate Interfacial Properties. J. Colloid Interface Sci. 2012, 376, 283−288. (8) Inamuro, T. Lattice Boltzmann Methods for Viscous Fluid Flows and for Two-phase Fluid Flows. Fluid Dyn. 2006, 38, 641−659. (9) Yan, Y. Y.; Zu, Y. Q. A Lattice Boltzmann Method for Incompressible Two-phase Flows on Partial Wetting Surface with Large Density Ratio. J. Comput. Phys. 2007, 227, 763−775. (10) Qian, Y. H.; D’Humières, D.; Lallemand, P. Lattice BGK models for the Navier-Stokes equation. Europhys. Lett. 1992, 17, 479−484. (11) Nash, R. W.; Carver, H. B.; Bernabeu, M. O.; Hetherington, J.; Groen, D.; Krüger, T.; Coveney, P. V. Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains. Phys. Rev. E 2014, 89, 023303. (12) Mei, R.; Shyy, W.; Yu, D.; Luo, L. S. Lattice Boltzmann Method for 3-D Flows with Curved Boundary. J. Comput. Phys. 2000, 161, 680−699. (13) Bouzidi, M.; Firdaouss, M.; Lallemand, P. Momentum Transfer of a Boltzmann-Lattice Fluid with Boundaries. Phys. Fluids 2001, 13, 3452−3459. (14) Yamane, K.; Aya, I.; Namie, S.; Nariai, H. Strength of CO2 Hydrate Membrane in Sea Water at 40 MPa. Ann. N. Y. Acad. Sci. 2000, 912, 254−260. (15) Sato, Y.; Kiyono, F.; Ogasawara, K.; Yamamoto, Y.; Sato, T.; Hirabayashi, S.; Shimizu, Y. An Experimental Study on the Dynamics of a Rising Methane Bubble Covered with Hydrates. J. MMIJ 2013, 129, 124−131 (in Japanese)..

18. In these cases, all of the bubbles adhered to the inlet of the neck and even to the inner shoulder of the contraction. It is easily understood that this is because of the breakage of the MH membranes when they attach to the wall as a result of the set contact angle.

4. CONCLUSION In this study, we measured the cohesion force of MH per unit contact area. Although, in the ambient methane gas, some values of the cohesion force were measured, it is almost zero at any contact force and time in the ambient water. Thus, it is strongly suggested that the cohesion force of MH in the ambient gas originates in the surface tension of water film existing on the MH surface and is undetectably small in the ambient water, actually, almost zero. Then, we developed a numerical method that can simulate the behaviors of methane bubbles covered with MH, within contraction pipes, and numerical simulations were performed on the behaviors of single and multiple rising bubbles covered with the MH membrane in the water within contraction pipes. The contact angles of MH on the wall in the gas were set to be 0° or 89.9° as case studies. In the case of the contact angle of 0°, the bubble clogs the contraction pipe when the neck diameter is less than that of the bubble. The adhesion of MH bubbles to the pipe wall in the present simulations depends upon whether the bubbles are broken up or not, namely, whether the contact angle is 89.9° or 0°. However, the breakup behavior of the bubbles covered with MH is still unknown. Further research is necessary for this phenomenon.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +81-4-7136-4726. Fax: +81-4-7136-4727. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by the Research Consortium for Methane Hydrate Resources in Japan (MH21 Research Consortium) of the Methane Hydrate Research and Development Program planned by the Ministry of Economy, Trade and Industry (METI).

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REFERENCES

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Cohesion Force Measurement of Methane Hydrate and Numerical

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