Molecular Dynamics Simulation of the Crystal Nucleation and Growth

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Molecular Dynamics Simulation of the Crystal Nucleation and Growth Behavior of Methane Hydrate in the Presence of the Porous Sediment Surface and Nanopore Ke-Feng Yan, Xiao-Sen Li, Zhao-Yang Chen, Zhi-Ming Xia, Chun-Gang Xu, and Zhiqiang Zhang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01601 • Publication Date (Web): 11 Jul 2016 Downloaded from http://pubs.acs.org on July 18, 2016

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Molecular Dynamics Simulation of the Crystal Nucleation and Growth Behavior of Methane Hydrate in the Presence of the Porous Sediment Surface and Nanopore KefengYan,†‡ Xiaosen Li,*†‡ Zhaoyang Chen,†‡ ZhimingXia,†‡ Chungang Xu,†‡ and Zhiqiang Zhang§ †

Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy

of Sciences, Guangzhou 510640, China ‡

Guangdong Key Laboratory of New and Renewable Energy Research and Development,

Guangzhou 510640, China §

College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, China

KEYWORDS molecular dynamics simulation; porous media; methane hydrate; formation mechanism

ACS Paragon Plus Environment

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ABSTRACT: The hydrate formation behavior in porous sediment has been widely studied because of the importance to the reservoirs and the drilling of natural gas hydrate. However, it is difficult to understand the nucleation and growth mechanism of hydrate in the porous media surface and nanopore by the experimental and numerical simulation method. In the work, a molecular dynamics simulation on the nucleation and growth of CH4 hydrate in the presence of the clay surface and nanopore is carried out. The molecular configurations and microstructure properties are analyzed with the systems containing 1 H2O layer hydrate (System A), 3 H2O layer hydrate (System B) and 6 H2O layer hydrate (System C) in the clay and the bulk solution. It is found that the formation of hydrate is more complex in the porous media than in the pure bulk solution. The cooperativity between hydrate growth and molecular diffusion is involved in the clay nanopore. The hydroxylated edge sites of the clay surface could serve as a source of CH4 molecules to facilitate the hydrate nucleation. The diffusion velocity of molecules is influenced by the growth of the block hydrate in the throats of the clay nanopore. Compared with the hydrate growth in the different pore sizes in the clay, it is found that the pore sizes play an important role in the hydrate growth and molecular diffusion in the clay. This simulation study provide the microscopic mechanism of hydrate nucleation and growth processes in the porous media, which can be favorable for investigation into the formation of natural gas hydrate in sediments.

1. INTRODUCATION Natural gas hydrate as a new clean energy source in the world is distributed widely in the ocean sediments and permafrost areas. The hydrate formation behavior in porous sediment is


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important to investigate the reservoirs and the drilling of natural gas hydrate. The knowledge of the hydrate formation in the porous sediments has been advanced substantially by the experimental researches1,

2, 3

. Some mathematical simulations have been carried out to

investigate the kinetic and equilibrium behaviors of the hydrate formation in the porous media4, 5, 6

. Smectite as one kind of the porous sediments is the most abundant mineral in the natural gas

hydrate bearing marine sediments, and a considerable amounts of CH4 was prove to be absorbed in the clay minerals in the marine sediments7. Besides, the hydrate formation condition in the smectite was experimentally demonstrated to be milder than that in pure water8, 9, i.e., CH4 hydrate can steadily intercalate into the smectite at low temperatures10, 11. However, the smectite has a relatively weak effect on improving the stability of hydrate formation 8, 9, 11. Till to now, it is difficult to understand the formation mechanism of hydrate in the porous media by the experiments and numerical simulations. The molecular dynamics simulation (MD) is employed to improve on understanding of the mechanisms of the crystal growth and formation in bulk natural gas hydrate. Recently, the mechanisms of the CH4 hydrate nucleation in the pure water or ice were carried out by MD simulation12,

13, 14

. Several molecular simulations provided the information of the growth

mechanisms of gas hydrate in the porous materials. In the fixed silica surfaces, CO2 hydrate formation was investigated by Bai et al.15. The microsecond MD simulation presented a threestage process of the CO2 hydrate nucleation, and the results indicated the H2O molecular structures near the silica surfaces were ice-like. Liang et al.16 investigated the crystal growth process of CH4 hydrate in the silica surfaces through MD simulation. Their simulation results showed H2O molecules neighboring the silica surface were disorderedly arranged. The hydroxylated silica surfaces were of benefit to promoting hydrate growth, and CH4 molecules


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appears to help stabilize these cage structures. The smectite as a possible fingerprint for natural gas hydrate in nature is widely spread in sediments. Park and Sposito investigated the stable interlayer CH4 clathrate structures in the Na-montmorillonite by the Monte Carlo(MC) and MD simulations recently17. They found the stable interlayer CH4 hydrate structures contain 0.5 CH4 per clay mineral unit cell. H2O molecules surrounded CH4 molecules to construct a hydrate-like structure, and CH4 molecules were nested on a hexagonal ring of the clay surface oxygen. Cygan et al.18 investigated the behavior of CH4 hydrate in the interlayer of the different smectite clays by MD simulation. The results indicated the CH4 hydrate structure in the clays was different from the CH4 in the aqueous solution and that in the bulk CH4 hydrate. Zhou et al.19 observed the behavior of CH4 hydrate in the clay interlayer with the different layer-charge distributions. The results showed that the important factor of forming hydrate-like structure was the sufficient interlayer water. Rao and coworkers20 have performed the grand-canonical Monte Carlo (GCMC) and MD simulation on the structure and dynamics of the H2O-CH4 fluids between Namontmorillonite clay surfaces. The simulations showed the clay swelling mechanism in the CH4 hydrate formation. It was found that CH4 molecules were not sufficiently coordinated by H2O molecules due to the low density of H2O content in the clay. However, there is not a clear understanding on the hydrate nucleation and growth on the clay surface and nanopore. The effects of pore size and gas-water ratio on the CH4 hydrate formation in the clay interlayer have been reported by our previous works21, 22. In the work, we focus on the nucleation and growth process of CH4 hydrate in the clay surface and nanopore, especially the diffusion behavior of the H2O-CH4 fluids between the clay interlayer and the dilute aqueous gas solution by MD simulation. We report the molecular configuration and microstructure properties with the systems containing 1 H2O layer hydrate (System A), 3 H2O layer hydrate (System B)


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and 6 H2O layer hydrate (System C) in the clay and the bulk solution. The effects of the clay surfaces edge sites and nanopore on the hydrate formation are also discussed.

2. MODEL AND SIMULATION METHOD Our simulated clay model is a generic Wyoming type Na-montmorillonite, and the montmorillonite lattice model is based on the structure of the pyrophyllite23. The Namontmorillonite structure is constructed from the previous simulation work21, which formula is the Na3(Si31Al) (Al14Mg2) O80(OH)16. 1 H2O layer hydrate, 3 H2O layer hydrate and 6 H2O layer hydrate in the montmorillonite model are investigated to understand the effect of the pore sizes on the hydrate growth in the clay. These H2O layer hydrates are defined from the previous researches of molecular simulation24, 25, 26. They correspond to 32, 96 and 192 H2O molecules in the unit cell. The corresponding initial basal spacings are listed in Table S1. The simulation cell along x-direction corresponds to the basal space of H2O layer hydrate. The simulated system in the work is a clay layer in contact with a bulk H2O-CH4 solution layer alone the (0 1 0) face of the clay (Figure 1). The clay layer contains the supercell (1×1×2) of Namontmorillonite model along the z-direction. The (0 1 0) edges is obtained by cutting the Namontmorillonite model. And the broken bonds are saturated with OH groups27, 28. The systems containing 1 H2O layer hydrate, 3 H2O layer hydrate, 6 H2O layer hydrate in the clay and the bulk solution are called System A, System B and System C respectively, in this work. The H2OCH4 bulk solution layer contains the relative number of CH4 molecules and H2O molecules, which are listed in Table S1. The density of the H2O-CH4 bulk solution is 0.948 g/cm3 which conforms to the density of the structure I (sI) CH4 hydrate single-crystal structure29. The density of the H2O solution in clay nanopore is approximately 0.97 g/cm3, which agrees with the density


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of the H2O solution in clay in the prior study26. Though the solubility of CH4 in liquid water is about 1 molecule for every 4000 H2O molecules, the concentration of CH4 in the solid hydrate lattice is more than 2 orders of magnitude higher than the solubility of CH4 in liquid water30. Thus, the bulk solution of this simulation is a CH4 supersaturated aqueous solution, which is consistent with many prior researches on the hydrate formation simulations15,

30, 31, 32

.

Meanwhile, the prior researches indicated the condition of CH4 supersaturated solution dramatically reduced the nucleation time33. The prior ice nucleation study indicated that the simulation system with the slightly lower density than the normal liquid water can increase the nucleation rate of ice34. So, the density of the H2O-CH4 bulk solution is feasible to the simulation of the hydrate nucleation and growth on the clay surface and nanopore. The MD simulations are performed using the DL_POLY MD simulation package35. The CLAYFF force field36 for the clay is used in the simulations. The CLAYFF force field has been widely used to the mineral surfaces with aqueous solutions and the simulation of the hydrated mineral systems18, 19. The interaction potentials of H2O molecules are treated as the TIP4P H2O model37, and CH4 molecules are represented by the OPLS all atom (OPLS-AA) model38. These interaction potentials have been successful used to study the hydrate growth in prior researches39, 40, 41, 42

. The Lorentz–Berthelot mixing rules are used to calculate the parameters of Lennard-

Jones potentials between different atom types. The rigidity of the model in the work is implemented with the SHAKE algorithm. A cutoff distance at half of the model cell length is used for the short-ranged interactions, while the long-range electrostatic interactions are calculated using the Ewald summation method. The Verlet Leapfrog algorithm is used to the equations of motion for translations and rotations with a timestep of 1 fs. Periodic boundary conditions are applied along all three directions of the systems.


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The simulations of the hydrate nucleation and growth process runs are maintained at 260 K by using the Nose-Hoover algorithm. The temperature of simulation at 260 K is above the ice melting point of TIP4P H2O model (around 232K43). Therefore, no ice crystal structure is found in the simulations. First, an isobaric-isothermal (NpT) relaxation process of 2 ns is performed to eliminate the effect of the initial configuration at 260 K and 10 MPa. Then, the simulations of the H2O-CH4 fluids and the hydrate formation on the timescale of 500 ns are performed using the constant volume (NVT) ensemble. In the NVT simulations, the positions of clay molecules were fixed. In the initial NPT simulation, volume is relaxation. The fluctuation of volume is small. In the next NVT simulation, the pressure value for the simulation box will oscillate significantly. This variation is entirely normal due to the fact that pressure is a macroscopic property and can only be measured properly as time average, while it is being measured and/or adjusted with pressure coupling on the microscopic scale. To reveal the structure transition of the simulation systems, we monitor the evolution of threebody structural order parameters and four-body structural order parameters. The angular order parameter (AOP)44 of a H2O molecule as a three-body structural order, the four-body order parameter (F4φOP)44,

45

as a function of the H-O......O-H torsion angle, and the Mutually

Coordinated Guest order parameter (MCGOP)46 as a new order parameter for tracking hydrate nucleation and growth have been successfully used to the simulation of the hydrate formation and dissociation15, 47, 48 (Figure S1, Equation S1-S2).

3. RESULTS AND DISCUSSIONS 3.1. The clathrate nucleation and growth in the bulk solution and the clay nanopore


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The crystal nucleation and growth simulations of CH4 hydrate have been performed in the system containing a clay layer and a bulk solution layer. The molecular configurations of System A during the simulation at 260 K are shown in Figure 1. As seen in Figure 1, the initial configuration (0 ns) for System A is composed of a H2O-CH4 bulk solution layer and a clay layer. The clay is a hydrated aluminosilicate, which is comprised of layers. Each layer formed by one central octahedral Al oxide layer sandwiched between two tetrahedral silicate layers. Therefore, the clay is described as 2:1 hydrated aluminosilicate or TOT (tetrahedral octahedral tetrahedral) layer mineral. In the asymmetrical TOT structure, the tetrahedral sites of occupied Si are substituted by Al, and the octahedral sites of occupied Al are substituted by Mg. Therefore, the TOT structure holds the net negative structural charge, which is balanced by the interlayer Na+ ions. Some H2O molecules intercalate on the interlayer of the clay. In the H2O-CH4 bulk solution region, some CH4 molecules gather to form a bubble (seen in Figure S2). CH4 molecules subsequently dissolve in the solution and the CH4 bubbles disappear. An amorphous cluster of these dissolved CH4 molecules and H2O molecules continually arranges to form irregular cages. As the cages formation, the irregular cages have been rearranged, before the clathrate structure is completely formed finally. It can be seen from the molecular configuration at 500 ns in Figure 1 that the arrangement of CH4 molecules and H2O molecules are quite regular. The clathrate CH4 hydrate structure clearly appears in the bulk solution region. Regrettably, none of CH4 molecules move into the clay nanopore due to the small pore size in 1 H2O layer hydrate of the clay. On the other hand, the hydrogen bonds form in the entrance to the clay nanopore between by H2O molecules and the hydroxyls on the clay surface, which obstruct the access of CH4 molecules. The result agrees with that obtained by Rao et al.20. Rao et al. reported that CH4 molecules did not enter clay interlayer, and the basal spacing was less than 1.2 nm.


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Figure 1. Molecular configurations at 0 ns, 50 ns and 500 ns of a crystal nucleation and growth simulation of the CH4 hydrate in System A at x-z plane at 260 K. Yellow sphere indicates CH4 molecules; red stick and white stick indicate O and H atoms of H2O molecules, respectively; blue sphere indicates Na+ ions; yellow stick and purple stick indicate Si and Al atoms of montmorillonite molecule, respectively; the blue dashed line represents the hydrogen bonds.

Clearly showing the clathrate hydrate structure, we delete some molecules in the system A at 500 ns to exhibit the cage configurations, as seen at the bottom of Figure 1. The clear clathrate structure parallels with the (0 1 0) crystal face of the clay. The regular 512 cages (12 pentagonal faces) and 51262 cages (12 pentagonal and 2 hexagonal faces) present in the bulk solution region in the system, which also present in a typical sI hydrate. Clathrate hydrate connects the clay surface with the ice-like structural H2O molecules, which is the same as the ice-like hydrate structure near the silica surfaces15. As mentioned in the earlier hydrate formation study in the


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presence of a bentonite surface, the solid surface can absorb H2O molecules and provides a nucleation site to promote the faster and greater hydrate crystal growth49. Meanwhile, H2O molecules have a strong tendency to solvate the clay surfaces, and form strong hydrogen bonds between H2O molecules and the clay surfaces25, which results a strong interaction between the clay surface edge sites and H2O molecules. Then, the hydroxyls of the clay surface edge sites and H2O molecules cooperatively organize into a stable semi-cage structure with the adsorbed CH4 molecules on the clay edge sites. The semi-cage structure is the clathrate-like structure containing a cluster of pentagonal or hexagonal rings and a cluster of irregular rings. These irregular rings are formed by the hydroxyls of the clay surface edge sites and H2O molecules. In the early stages of the nucleation, the few semi-512 cages form on the entrance to clay nanopore, and the few semi-51262 cages form on the clay surface edge sites. Subsequently, the regular 512 cages (small cages) and the 51262 cages (large cages) together with the semi-512 cages and semi51262 cages are gradually formed. Then hydrate grows from cages on the clay surface edge sites. It means that H2O molecules around the adjacent cage sites consequently form another small cages and large cages on the bulk solution when cages are formed on the clay surface edge sites. The clathrate hydrate may continuously grow with the formation of a stacking fault until the growth of the CH4 hydrate crystal completes. Notably, some irregular cages such as 5126471 cages, 4151062 cages grow at this simulation. As shown in Figure 1, the quadrangular face of 4151062 cages is shown with the blue line at the bottom, and the similar result was present in the references13, 32. The result reflects that the structure of the crystal has defects in the simulation system at 500 ns, and the clathrate structure is misaligned with respect to the ideal hydrate crystal. Cages are dynamic in nature and undergo continuous structural rearrangements47. It would be rearranged to form ideal hydrate crystal in a long time simulation. The results of


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simulation by Walsh et al. also implicated that the hydrate nucleation must be investigated for a long time.30 The CH4 mole fraction (xm) in the aqueous solution is one key factor to hydrate nucleation and growth. The prior researches on hydrate nucleation indicated that hydrate formation was triggered when xm in the aqueous solution was above certain minimal value33,

50

. In this

simulation, xm is about 0.17 in System A, System B and System C, which is consistent with xm in an ideal sI CH4 hydrate. Two simulations with the different xm (0.07 and 0.11) in the bulk solution in System A are carried out to analyze the influence of xm on hydrate nucleation and growth on clay system,. The molecular configurations of CH4 hydrate in System A with different xm at y-z plane at 300 ns at 260 K are shown in Figure S3. The results imply that a significant effect of xm on the crystal growth of CH4 hydrate on clay system. In the condition of high xm, the CH4 bubbles appear in the initial hydrate formation (seen in Figure 1 and Figure S2). They may reduce the chance of hydrate nucleation and growth. However, the CH4 bubbles are transient with the CH4 molecules dissolution. The effect of CH4 bubbles for reducing hydrate nucleation and growth is weak. On the other hand, CH4 molecules can promote the stability of cages with the condition of high xm51. Therefore, the condition of high xm in the aqueous solution can promote the hydrate nucleation and growth. The results are consistent with experimental results52, 53. The CH4 molecules are difficult to diffuse from the bulk solution into the clay nanopore region in System A for its small pore size, however they can move in System B and C because their relatively large pore sized make them can offer relative large entrance. Figure 2 shows the snapshots taken from the crystal nucleation and growth simulation of CH4 hydrate in System C at 0 ns, 50 ns and 500 ns at 260 K. As seen in Figure 2, System C has larger pore size than System


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A. In larger pore size system, CH4 molecules transfer from the bulk solution region into the clay nanopore region. While CH4 molecules diffuse, some cages form in the bulk region. However, the arrangement of cages in the bulk solution region in System C is not regular as that in System A because of the decreased xm by the diffusion of CH4 molecules. There are many empty cages formed in the bulk solution region in System C, which cause the instability of those cages. In the same time, the CH4 molecules diffusion, caused by the concentration gradient of CH4 molecules between the bulk solution region and the clay nanopore region, breaks the network of the unstable cages. Therefore, the velocity of the hydrate formation in the clay is determined by the cages growth and the molecular diffusion. To make the cage structures in System C clear, we delete some molecules in this system at 500 ns to illustrate the cage configurations at the bottom of Figure 2. The hydroxyls of the clay surface edge sites and H2O molecules cooperatively organize into the stable cage structures on the clay edge sites. A semi-512 cages and a semi-51262 cages form on the clay edge sites. The cages continue to grow not only in the bulk solution region but also in the clay nanopore region with the formation of a stacking fault. In the bulk solution region, the cages mainly present the 512, with some half-complete cages containing pentagon and hexagon and some empty cages. In the clay nanopore region, H2O molecules connect with the Si-O ring of the clay nanopore surface and the nearest-neighboring H2O molecules to form the network by the hydrogen bonds. CH4 molecules near the clay nanopore surface are surrounded by the network to form cages in the clay nanopore surface. The Na+ ions, as the cations which balance the charge of the clay, disperse in the clay interlayer and form cages with H2O molecules. These cages distort under the steric effect of cations. This steric effect comes from a fact that the cations occupy the space which should be occupied by H2O molecules to construct the network of cage in the clay nanopore. Therefore, the steric effect affects the


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structure of cage. As seen at the bottom of Figure 2, a Na+ ion (blue sphere) occupies one site of a cage. Hydrate has the crystal defect in this cage. In the interlayer of the clay nanopore, a cage is formed by a CH4 molecule surrounded by the “interlayer H2O molecules”21. These results reflect that CH4 molecules diffuse into in the clay nanopore region and enter the irregular cage, while hydrate grows in the bulk solution region. In the bulk solution region, the formation of the empty and irregular cages is attributed to the decreased xm. In the clay nanopore region, the formation of the irregular cages is attributed to the steric effect of the cations21. Therefore, the hydrate formation process is related to the hydrate nucleation and growth process as well as the molecular diffusion process in the porous media.

Figure 2. Molecular configurations at 0 ns, 50 ns and 500 ns of a crystal nucleation and growth simulation for CH4 hydrate in System C at x-z plane at 260 K.


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Figure 3 shows the molecular configuration of System C at 500 ns at 260 K, the z-profile for the density of H2O molecules at the top of the configuration, and the z-profile for the F4φOP of H2O molecules at the bottom of the configuration. All these profiles in Figure 3 are averaged over the simulation trajectory from 450–500 ns. The densities of H2O molecules in Figure 3 are recorded by using the center of mass for each molecule. As seen in Figure 3, in the bulk solution region, the z-profile of the density profile of H2O molecules shows the typical periodic oscillations, which is clear for the crystalline hydrate phases. In the clay nanopore region, the zprofile of the density profile of H2O molecules shows slightly fluctuant, which is essential for the aqueous solution. The value of the F4φOP in the bulk solution region approach that value in the hydrate region (0.7), which imply H2O molecules present the solid structure in this region. However, the profile of the F4φOP on the interface of the bulk solution and the clay nanopore falls suddenly due to the effect of the edge sites of the clay for the torsion angle of the H2O-H2O pairs. Then, the profile of the F4φOP rises from the 3.5 nm to 4.0 nm in the z direction again. It reflects the solid arrangement of H2O molecules presents in this region. The result indicates that some cages form in the entrance of the clay nanopore region, which had been proved in Figure 2. In the internal clay nanopore, the value of the F4φOP approaches to that value in the liquid region (-0.04). It implies that the liquid arrangement of H2O molecules exists in this region.


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Figure 3. Molecular configuration of System C at 500 ns at 260 K, the z-profile density of H2O molecules at the top of the configuration and the z-profile for the F4φOP of H2O molecules at the bottom of the configuration.

In our simulation, there are three types of cages (large cage, small cage and incomplete cage), which are defined by Tung et al.41, 48. Figure S4 shows the time evolution of large cages, small cages and half-complete cages in System C at 260 K. In the bulk solution region, some halfcomplete cages form in the initial simulation (Figure S4(a)). The cages in the bulk solution region initiate from the spontaneous formation of amorphous water clusters. H2O molecules of amorphous water clusters form half-complete cages through the fluctuating formation and dissociation of hydrogen-bonded. The result is consistent with the result of the simulation by Vatamanu et al.13, who indicated that the disordered solid containing the mixture of symmetric and irregular water cages (half-complete cages) appear in the first stage of hydrate nucleation. And, H2O molecules cooperate with CH4 molecules toward ordering. Half-complete cages gradually turn to completely cages. After ~60 ns, CH4 molecules around the pentagonal rings of


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H2O molecules occupy cage sites to form complete small cages in the bulk solution region. Then, the number of half-complete cages decreases, while small cages appear. Large cages appear at about 300ns. However, large cages follow to intermittently disappear and appear. It illustrates that small cage is more stable than large cages in the bulk solution region, which is consistent with priors suggestion that small cages are locally preferred in the formation stage30. On the other hand, in the clay nanopore region, half-complete cages only present during this simulation, as shown in Figure S4(b). This result indicates no perfect cage forms in the clay nanopore region. The steric effect of the cations may be the one reason for the imperfect cages, and the slowing hydrate growth may be the other reason for the imperfect cages in this region. 3.2. Effect of the pore size on the hydrate formation Figure 4 shows the order parameters of the simulation trajectories in System A, System B and System C at 260 K. These order parameters have high resolution traces to the hydrate formation, which can make identification of the hydrate nucleation and growth events. The related descriptions of these order parameters are presented in the Supporting Information. In the bulk solution region, as shown in Figure 4, the precipitous rises of the F4φOP and the MCGOP, and the decreasing slop of the AOP present the hydrate growth process in the bulk solution region, which also indicate the arrangement of H2O molecules from liquid to solid in this region. Compared with these order parameters in System A, System B and System C in Figure 4, it is found that the slopes of these order parameters are sharper in System A than those in System B and System C during 0-50 ns period in the bulk solution region. After 50 ns, these order parameters in System A tend to the values fluctuate around an average value in the bulk solution region. The result indicates that the hydrate crystal formation in System A is faster than those in System B and System C. It is due to the high xm in the bulk solution promote the hydrate


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nucleation and growth in the system with small pore size clay. Thus, the result illustrates that the diffusion process in pore is a key factor to affect the hydrate formation in the porous media with different pore size.

Figure 4. F4φOP, AOP and MCGOP for the trajectory of the simulations at 260 K in (a) System A, (b) System B and (c) System C.

In the clay nanopore region, the F4φOP and AOP both fluctuate on the melt reference line, as seen in Figure 4. It shows that H2O molecules present in the form of liquid in the clay nanopore region. However, it can be seen from Figure 4(c) that the MCGOP gradually appear, which indicates few MCG clusters present in the clay nanopore region in System C. This implies that some cages form in this region. At 500 ns, there are approximately 3 guest molecules in the MCG cluster in this region, which indicating that CH4 molecules and H2O cluster form the incomplete or irregular cages in the clay nanopore during the hydrate formation. Similarly, the MCGOP trace illustrates the long crystal growth period in this region. In our simulation, it


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demonstrates that MCGOP, which combines the uses of the guest and solvent molecules, have higher resolution traces for quantifying the hydrate nucleation and growth than the F4φOP and AOP. The F4φOP and AOP of CH4 hydrate nucleation and growth in pure water systems (without clay) are also shown in Figure 4. Under the same conditions, the concentrations of these systems are about 0.948 g/cm3 which is same as the concentrations of System A, System B and System C in the bulk solution region. In Figure 4(a), the slopes of the F4φOP and AOP are sharper in the bulk solution region in System A than those in the pure water system during 0-50 ns period. After 50 ns, the F4φOP rises continuously and the AOP descend continuously in the pure water system. Until 100 ns, the F4φOP and AOP of the pure water system fluctuate around an average value. These results indicate that the hydrate crystal growth in aqueous solution system with the small pore size clay is faster than that in pure system. It implies the hydroxylated edge sites of the small pore size clay surface can promote hydrate growth. At the same time, the slopes of the F4φOP and AOP in the bulk solution region in System B are the same as those in the pure water system as shown in Figure 4(b)), and the slopes of the F4φOP and AOP in the pure water system are sharper than those in the bulk solution region in System C (seen in Figure 4(c)). These results show that the promotion effect for the hydrate growth in clay surface is weakened by the diffusion effect on big pore size clay. The growth speeds of hydrate in the aqueous solution region with the big pore size clay system are slower than those in the pure water system. Because the hydrate nucleation is a stochastic process, the several simulations under same conditions in System A, System B and System C are carried out to present the sampling of several nucleation events. In the Figure S5 in the Supporting Information, the results among the sequence of repeated simulations agree well, indicating a good reliability in this work. As mentioned above,


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the hydrate nucleation is a stochastic process. The above-mentioned hydrate nucleation and growth in System A, System B, System C and pure system may be a special case in the hydrate formation process. It is insufficient to make an evaluation on the hydrate stochastic nucleation process in the clay surface and nanopore. However, the trend of hydrate growth rate in System A, System B, System C and pure system reflects that the clay surface, the molecular diffusion and the pore size of the clay are a significant effect on hydrate growth in clay. Figure 5 shows the radial distribution functions (RDFs) of the simulation systems at 260 K. It can be seen from Figure 5(a)-5(c) that the first, second and third peaks for gO-O(r) in the bulk solution region have the H2O-H2O distances of about 0.27 nm, 0.45 nm and 0.64 nm, respectively. The result agrees with that of gO-O(r) for the stable pure CH4 hydrate54, 55, indicating the clathrate-like arrangement of H2O molecules in this region in System A, System B and System C. However, in Figure 5(a), the second peak for gO-O(r) is lower and broader in the clay nanopore region than that in the bulk solution region, and the third peak for gO-O(r) almost disappears in the clay nanopore region in System A. It indicates that H2O molecules present the liquid-like arrangement in the clay nanopore region in System A. The same result is found in the clay nanopore region in System B in Figure 5(b). As shown in Figure 5(c), the peak profile for gO-O(r) in the clay nanopore region is similar to that in the bulk solution, though the peak height in the clay nanopore region is broader than that in the bulk solution. This result indicates that the arrangement of H2O molecules in the clay nanopore region in System C approaches that the arrangement of H2O molecules in the clathrate. Comparing with the gO-O(r) in System A, System B and System C, we can find that the regular arrangement of H2O molecules in the clay nanopore increase with the increase of the pore size. Due to no CH4 molecules in the clay nanopore region in System A, this work only analyzes the RDFs between CH4 molecules (gC-C(r)) in System B


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and System C, as seen in Figure 5(d) and Figure 5(e). In Figure 5(d), the clear different profile for gC-C(r) in the bulk solution region and the clay nanopore region in System B can be found. The first peak value in the clay nanopore region approaches the peak value of gC-C(r) in liquid56, while the first peak value in the bulk solution region approaches the peak value of gC-C(r) in CH4 hydrate54, 55. In Figure 5(e), the peak profiles of gC-C(r) not only in the clay nanopore region but also in the bulk solution approach the peak profile of gC-C(r) in CH4 hydrate. As above analyzed, the conclusion can be made that the clathrate-like structures are easily formed in the clay nanopore region with big pore size. The pore size is a key factor to affect hydrate formation in the sediment. These results are in agreement with the experimental phenomena: the hydrate formation conditions in the clay are mainly affected by the pore sizes9, 57.

Figure 5. RDFs of the simulation systems at 260 K (a) gO-O(r) in System A, (b) gO-O(r) in System B, (c) gO-O(r) in System C, (d) gC-C(r) in System B (e) gC-C(r) in System C.

3.3. Molecular diffusion in the hydrate formation Figure 6 shows the trajectory of a CH4 molecule migrating from the bulk solution into the clay nanopore over a period of 0-500 ns (yellow line) in System C at 260 K. In the bulk solution


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region, CH4 molecule firstly moves in the bulk solution, and then moves towards the clay nanopore region. When reaching the clay interface, the CH4 molecule occupies a cage site around by H2O molecules at a certain position. The cage is half-complete cage41, 48 which is formed by H2O molecules of amorphous water clusters through the fluctuating formation and dissociation of hydrogen-bonded in the first stage of hydrate nucleation. The half-complete cage is unstable. Then, the CH4 molecule diffuses to other site while the half-complete cage is broken. Whereafter, CH4 molecule tends to diffuse into the clay nanopore on account of the concentration

gradient of CH4 molecules between the bulk solution region and the clay nanopore. In the clay nanopore, CH4 molecule is surrounded by H2O molecules which forming irregular cages in the clay nanopore surface. After 200 ns by the simulation, the hydrate gradually forms in the bulk solution region, which is reflected in Figure 4 (c). Some cages form in the entrance of the clay nanopore region, which had been proved in Figure 2. The diffusion of CH4 molecules in the entrance of the clay nanopore region is processed by frequently forming and breaking these cages, so it is slow. In the same time, the amount of CH4 molecules fluctuates around an average value after 200 ns, which is reflected in Figure S6 in the Supporting Information. It means that the migration of CH4 molecules from the bulk solution region to the clay nanopore region is slow after the hydrate formed in the bulk solution region. This low frequency for the transfer of CH4 molecules reflects the obstruction of the hydrate crystals in the entrance of the clay nanopore and the slow hydrate growth in the clay nanopore. Therefore, there are only small amount of CH4 molecules diffusing into the clay nanopore, as seen in Figure 2. The xm is approximately 0.046 in the clay nanopore at 500 ns. This value is much lower than the value of the ideal CH4 hydrate (0.17), and is lower than the value of CH4 hydrate in the clay (0.083)22. Moreover, because of the cation effect on the hydrate formation in the clay22, the formation of hydrate is difficult in the


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clay nanopore. It means that the complete hydrate formation in the clay nanopore requires a long simulation time.

Figure 6. Snapshot of trajectory of a CH4 molecule migrating from the bulk solution into the clay nanopore over a period of 0-500 ns in System C at 260 K.

The time dependence of the number of H2O molecules and CH4 molecules dispersing in the solution and the clay pore in System C at 260 K are shown in Figure S6. The results from Figure S6 reflect that more CH4 molecules diffuse in bulk rather than near the pores. The diffusion of CH4 molecules is hindered by the formation of hydrates at the nanopore entrance. H2O molecules outside the clay nanopore frequently exchange with H2O molecules inside the clay nanopore until the formation of the block hydrate in the entrance of the clay nanopore. As CH4 molecules and H2O molecules transfer in and out the clay nanopore, the hydrogen bond networks are frequently formed and broken by H2O molecules around CH4 molecules. In the bulk solution region, the number of the hydrogen bonds increases with the increase of H2O molecules at 260 K (Figure S7). When the transfer of H2O molecules is stable, the average number of the hydrogen bonds per H2O molecule is approximately 3.74 in the bulk solution region and approximately 3.22 in the clay nanopore, respectively. These values indicate that the number of hydrogen bonds per H2O molecule in the bulk solution region is equal to the number in the solid water at 248 K (=3.76)58, and the number of hydrogen bonds per H2O molecule in the clay nanopore region is


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slightly smaller than the number in the bulk liquid water at 298 K (=3.3)59. This result indicates H2O molecules present in the form of the solid in the bulk solution region and the in the form of the liquor in the clay nanopore region. As mentioned above, The results suggests that the diffusion rate of CH4 molecules are influenced by the growth of the block hydrate in the throats of the clay pores, which agrees with the result of the CH4 hydrate formation experiments in the porous media57, 60. The experiments indicated that the hydrate particles tend to block the pore channels, and the decrease of permeability was caused by the decrease of the effective porosity in the porous media. Therefore, this phenomenon suggests that the hydrate crystals tend to be firstly deposited in the throats of the pores.

4. CONCLUSION In this work, the molecular-scale nucleation and growth process of clathrate hydrate in the system containing a clay layer and a bulk solution layer are investigated by MD simulation. From the simulation of the structural arrangements of these systems, the nucleation and growth of the clathrate hydrate occur via the following processes: the dissolution of CH4 molecules migrate to the clay surface with forming semi-cages; clathrate hydrate grows with the formation of a stacking fault in the bulk solution region; CH4 molecules diffuse into the clay nanopore to form the “interlayer hydrate” and the “surface hydrate”. In the simulation systems, the hydroxylated edge sites of the clay surface could serve as a source of CH4 molecules to facilitate the hydrate nucleation. By analyzing the density profile and the order parameters of H2O molecules in System C, we found that the formation of hydrate is more complex in the porous media than in the pure bulk solution, involving the cooperativity between hydrate growth and molecular diffusion. In the clay nanopore, the molecular diffusion is slow on account of the


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blocking of hydrate crystals in the entrance of the clay nanopore, and cages are irregular because of the steric effect of the cations in the clay. Compared with the nucleation and growth processes of hydrate in System A, System B and System C, the diffusion of CH4 molecules is one key factor for determining the hydrate growth process, and the pore size is other one key factor for affecting hydrate formation in sediments. The diffusion processes of CH4 molecules and H2O molecules in System C reveal that the hydrate crystals tend to block the pore channels, and the diffusion rate of CH4 molecules are influenced by the growth of the block hydrate in the throats of the clay pores. The results illustrates that the hydrate crystals tend to be firstly deposited in the throats of the pores. This simulation study provide the microscopic mechanism of hydrate nucleation and formation processes in the porous media, and it can be favorable for investigating into the reservoir formation for natural gas hydrate in sediments.

ASSOCIATED CONTENT Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org. Basal spacing data in montmorillonite model (Table S1), order parameters of simulation (Equation 1-2, Figure S1), initial molecular configuration of System A (Figure S2), influence of xm on hydrate nucleation and growth on clay system (Figure S3), number of cages in System C (Figure S4), the sampling of several nucleation events (Figure S5), molecular diffusion in the hydrate formation (Figure S6) and number of the hydrogen bonds (Figure S7) (PDF)


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes Any additional relevant notes should be placed here.

ACKNOWLEDGMENT This work was supported by National Science Fund for Distinguished Young Scholars of China (51225603), National Natural Science Fund (51376184, 51276182), International S&T Cooperation Program of China (2015DFA61790), and Science & Technology Program of Guangzhou (y307j21001), which are gratefully acknowledged.

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Molecular Dynamics Simulation of the Crystal Nucleation and Growth

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