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Microsecond molecular dynamics simulation of methane hydrate formation in the humic acid amended Na-montmorillonite Haoqing Ji, Guozhong Wu, Mucong Zi, and Daoyi Chen Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01544 • Publication Date (Web): 16 Aug 2016 Downloaded from http://pubs.acs.org on August 21, 2016
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Microsecond molecular dynamics simulation of methane hydrate
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formation in the humic acid amended Na-montmorillonite
3 4
†
†
Haoqing Ji , Guozhong Wu , Mucong Zi, Daoyi Chen *
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Division of Ocean Science and Technology, Graduate School at Shenzhen, Tsinghua
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University, Shenzhen 518055, China
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ABSTRACT:
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Natural gas hydrate in marine sediments is a promising energy resource while the
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atomic level understanding of its formation on the organo-mineral complex remains
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limited. Microsecond molecular dynamics simulations were performed to investigate
12
the methane hydrate growth in the sodium montmorillonite interlayer in presence of
13
natural sediment organic matter (Leonardite humic acid, LHA) at mass concentration
14
of 2% and 11%, respectively. The hydrate growth were characterized by the global
15
and local four-body order parameter, surface distribution function, snapshots of
16
molecular configurations and face-saturated incomplete cage analysis. It clearly
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demonstrated the kinetic inhibition effects of LHA on hydrate formation on clay
18
minerals especially when the self-aggregation of LHA took place at high
19
concentration. Overall results highlighted the role of methane adsorption on LHA
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aggregates on the observed inhibition phenomenon, which changed the pathway of
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gas molecules by complex dynamic processes such as aggregates deformation, cage
22
break and cage re-formation.
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1. INTRODUCTION
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Natural gas hydrate (NGH) is a promising candidate for energy resource with a carbon
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quantity twice more than the combination of all fossil fuels.1 Methane hydrate is the most
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widespread type of NGH in which methane molecules are encaged in the water cages
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formed by hydrogen bonds. It was estimated that the hydrate resource in the marine
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sediments outnumbered that in the permafrost environment by more than two-order of
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magnitude.2 Geochemical data further indicated that the smectite, a group of 2:1 clay
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minerals such as sodium montmorillonite (Na-MMT), was the most abundant mineral in the
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oceanic hydrate-bearing sediments.3,
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explore the interactions between gas hydrate and clay minerals. It is known that the mineral
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surface can facilitate hydrate crystallization and stabilize the hydrate cages by providing
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nucleation sites.5,
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intercalation of NGH in the clay mineral interlayers, because the hydrate formation varied
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against the surface hydrophobicity,7 surface charge,8 surface area,9 pore size distribution,10
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particle size and chemical compositions of minerals.11
6
4
Therefore, there are increasing investigations to
Nevertheless, scientific knowledge remains incomplete about the
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Moreover, it becomes more complicated when natural soil organic matters (e.g. humic
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substances, lignins and compounds with amide and amine groups) are present in the clays.
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For example, it was demonstrated that the organic matters inhibited the hydrate formation
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kinetics by forming hydrogen bonds with water and disrupting the hydrogen bond network
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of water.12, 13 They might also inhibit the hydrate re-formation from the partial hydrate cages
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and dissolved gas by eliminating the memory effect which is a phenomenon that gas and
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water with previous hydrate history is easier to form hydrates.14, 3
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By contrast, the
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hydrophobic groups like alkyl chains in the organic matters decreased the inhibition effects
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and even accelerated the hydrate growth by strengthening the local water structure.12 More
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interestingly, experimental results demonstrated that the soil organic matter played a key
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role as kinetic inhibitor during hydrate formation, but it turn to enhance the hydrate
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nucleation kinetics by up to one-order of magnitude after adsorption on the Na-MMT
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compared with that on bare Na-MMT or in bulk water.16-18 These results implied the
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existence of complex interactions between gas hydrate and organo-minerals, which
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demands future works for better understanding the hydrate evolution mechanism in the
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hydrate-bearing clay sediments.
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Additionally, majority of current studies attributed the inhibition or promotion effects of
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organic matters to their interactions with water molecules. Relatively less attention was paid
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to their influences on the gas transport, because the organic matters previously used were
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relatively small molecules without taking into account the formation of large clusters by
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self-aggregation. Humic substances such as humic acids in the seawater or oceanic
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sediments have a strong tendency to aggregate from monomer to supramolecule by direct
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assembling or molecular bridging mediated by water or multivalent cation.19 This process
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was critical for the adsorption and diffusion of hydrocarbons, which was supposed to affect
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the hydrate formation and disassociation.
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On this basis, we performed molecular dynamics (MD) simulations in this study to
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investigate the influence of humic acids on the methane hydrate formation in the Na-MMT
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interlayer at atomic level. Specific objectives were to identify the distribution of gas and
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water around the monomer or nanoaggregates of humic acids, and evaluate its effects on the 4
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global and local rate of hydrate formation in the organo-clay pore water.
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2. METHODOLOGY
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2.1 Modeling and simulation. MD simulations were performed using the open source
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software Gromacs (version 5.0.5).20 The montmorillonite unit cell with a stoichiometry of
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[Al3Mg1][Si8O20][OH]4 was used in this study (a = 0.516 nm, b = 0.897 nm, c = 0.935 nm, α
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= 91.2°, β = 100.5°, γ = 89.6°), which was obtained from the American Mineralogist crystal
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structure database.21 It was expanded to a supercell structure (9 × 4 × 1). A liquid slab
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(initial thickness: 3.3 - 3.5 nm) consisted of 36 sodium ions, 1628 water and 160 methane
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was intercalated in the expanded montmorillonite (interlayer space: 4.3 nm). The sodium
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ions were used to compensate the negative charges in the montmorillonite, while the
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molecular ratio of methane to water was chosen to ensure enough water for hydrating all the
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methane and interlayer cations.5 Hydrate cages were not pre-built in the initial configuration
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in order to minimize artificial effects during model construction. Organo-clay models were
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also constructed by loading one and six Leonardite humic acid (LHA, C31H26O12) molecules
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into the Na-MMT interlayer, respectively.22 The corresponding mass concentration of LHA
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in the pore water in these two scenarios was 2% and 11%, respectively.
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The ClayFF force field was used to model Na-MMT.23 The corresponding bond and
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nonbond parameters are listed in Tables S1 and S2, respectively, in the supporting
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information. The LHA was modelled using the CHARMM36 force field which had proven
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to be compatible with ClayFF.24, 25 Parameters for LHA were manually adjusted according
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to analogue structures in the CHARMM36 force field database. Partial charges in LHA 5
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molecule are illustrated in Figure S1. Methane was modelled using the united-atom
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Lennard-Jones model while the TIP4P-ice model was used for water.26 Lorentz-Berthelot
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mixing rules were implemented to calculate the cross interactions between different
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molecules.27 Short-range interactions were truncated at 1.2 nm. Long-range electrostatic
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interactions were calculated using the particle mesh Ewald method with a Fourier spacing
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of 0.12 nm.28 The leap-frog algorithm with a time step of 1 fs was used to integrate the
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motion equations.29
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Energy minimization was performed using the steepest descent algorithm before
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simulation, which was followed by 200 ps NPT runs for equilibration under constant
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temperature (250 K) and pressure (500 bar). This step was followed by 3 µs production run
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at NPT ensemble using the Nose-Hoover thermostat and Parrinello-Rahman barostat.30, 31
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Semi-isotropic pressure coupling was used to barostat the system along the z direction
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separately from the x and y dimensions. This allowed the the pressure component normal to
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the clay layer to fluctuate independently from the tangential pressure components.
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Three-dimentional periodic boundary condition was applied throughout simulations.
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2.2 Data Analysis. The degree of methane hydrate formation was quantified by the four-body order parameter F4φ,32 which was calculated as follows: F
1 = cos 3φ
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where n is the total number of H2O-H2O pairs with the distance between oxygen atoms less
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than 3.5 Å, φi is the H-O···O-H torsion angle between oxygen atoms and two outermost
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hydrogen atoms in the ith H2O-H2O pair. The average F4φ values for ice, liquid water and
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hydrate are -0.4, -0.04, 0.7, respectively.33 6
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The face-saturated incomplete cage analysis (FSICA) method was used to determine the
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changes in the cage water and gas methane during simulation.34 Particularly, a gas methane
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molecule was identified if the number of the surrounding water molecules was less than 16
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within a sphere of 0.54 nm radius.
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The intensity of LHA aggregation was quantified by the intermolecular contacts, which
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was counted if the minimum distances between each two LHA molecules were ≤ 0.5 nm as
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suggested by Zhu et al.35
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3. RESULTS AND DISCUSSION
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3.1 Influence of LHA monomer on the hydrate formation. The equilibrium
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conformations of different molecules in the Na-MMT interlayer are shown in Fig. 1. The
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corresponding density profiles along the normal direction of the Na-MMT surface are
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shown in Fig. 2. Two sharp peaks were found at 1.0 and 4.1 nm, respectively, suggesting the
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formation of a dense water film on the Na-MMT surface. This portion of water was
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supposed to contribute little to the formation of methane hydrate because (i) the thermal
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motion of sodium ions on the Na-MMT surface would decrease the water activity and
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disrupt the formation of hydrogen-bonded water networks,16, 36 and (ii) the hydrophobic and
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nonpolar methane molecules on the hydrophilic Na-MMT surface were inadequate for
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hydrate formation (Fig. 2).
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It appeared that the LHA monomer was immobilized by the surrounding methane hydrate
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cages. It was unlikely to move towards the Na-MMT surface although it contained a couple
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of hydroxyl and carboxyl groups with affinity to the oxygen and siloxy on the Na-MMT 7
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surface. Nevertheless, the overall results demonstrated the kinetic inihibition effects of the
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LHA on the methane hydrate formation in the Na-MMT pore. For example, the global F4φ
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parameter during the initial 600 ns decreased by up to 16% when one LHA molecule was
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added in the pore water (Fig. 3A). This was also supported by the less number of cage water
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(Fig. 3B) and higher fractions of gas methane (Fig. 3C) after the addition of LHA. The
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effects of space constraints after LHA addition on the decreased rate of hydrate formation
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could be excluded, because the simulation box was flexible to stretch throughout the NPT
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simulation. This inihibition tendency was inconsistent with Kyung et al.16 which reported
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the accelerated hydrate induction on the organo-mineral complexes in presence of glycine.
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The different findings were due to the fact that the thermal flucturation of Na+ on MMT
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surface was suppressed after coordinating with the –COO- in the zwitter-ionic glycine, but
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the LHA in this study was neutral without significantly altering the distribution of Na+ (Fig.
146
2).
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In order to identify whether such inihibition effects were resulted from the changes in the
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thickness of the water film aforementioned, we divided the pore water into various slices
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according to the distance to Na-MMT surface. Each two neighbour slices shared an overlap
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region of 0.27 nm width and the local F4φ parameter was then calculated in each slice. As
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shown in Fig. 4, slice “n” represents the water slice ranging from 0.03 (n-1) to 0.3 + 0.03
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(n-1) nm from the Na-MMT surface. The thickness of the water slice with little contribution
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to the hydrate formation was determined by the position where the local F4φ values
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increased suddenly. For example, the F4φ values almost kept constant in the first five slices
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with less than 0.42 nm far from the Na-MMT surface, while explicit increase in the F4φ was 8
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noticed in the sixth slice. It suggested that the water film on the Na-MMT surface was about
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0.42 nm thick, which varied little after LHA addition (Fig. 4). Nevertheless, the hydroxyl
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and carboxyl groups in the LHA molecule were expected to interact with water and
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therefore delay the hydrate formation. As shown in Fig. 5A, the first peak was found at 0.28
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nm in the RDF between oxygen in LHA (OL) and oxygen in water (OW), corresponding to
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the distance between two hydrogen-bonded oxygen atoms. Similar phenomenon was
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reported by Xu et al.,13 which attributed the inhibition effects of natural product pectin on
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hydrate formation to the hydrogen bonding. It was inferred that the contribution of this
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mechanism to the inhibition effects of LHA was less pronounced than pectin at the same
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concentration, because the mass fraction of oxygen in LHA (32%) was lower than that in
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pectin (55%).
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For better elaborating the influence of LHA-water interactions on the dynamics of local
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hydrate formation, we divided the overall water into several sections according to the
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distance to the geometry center (COG) of LHA (Fig. 6). Particularly, water within a sphere
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of 1.2 nm radius from the COG of LHA was defined as adjacent water while the rest was
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defined as nonadjacent water. The cut-off value of 1.2 nm was selected because it was
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enough to include all the water molecules being affected by LHA molecules, since the
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distance between the two outermost atoms in a LHA molecule was about 1.8 nm and a
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hydrogen bond length was about 0.3 nm. Overall, the closer to the LHA, the slower rate of
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hydrate formation for the adjacent water. It should be noted that the nonadjacent water also
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included the aforementioned water film near the Na-MMT surface where hydrate rarely
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formed, therefore the average F4φ value for nonadjacent water was lower than that of the 9
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adjacent water especially at the end of the simulation (Fig. 6A). An interesting finding was
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that the hydrate formation rate for the adjacent water decreased remarkably at 200 ns and
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greatly fluctuated until 1600 ns. It suggested that the inhibition by hydrogen-bonds
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formation aforementioned was not the predominant mechanism at the late-stage of hydrate
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growth. Otherwise, the hydrate growth pattern for the adjacent water should have been
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similar to that of the nonadjacent water without substantial fluctuation, because the number
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of hydrogen bonds between LHA and water was almost constant over the course of
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simulation (Fig. 5C).
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A possible reason for this finding was that the presence of LHA affected the fate and
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transport of methane in the pore water. In order to identify these changes, the surface
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distribution function (SDF) for methane near the LHA surface was plotted in Fig. 7A. The
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first three peaks were characterized at around 0.35, 0.6 and 1.0 nm, respectively.
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Accordingly, three compartments were defined including the internal, middle and external
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regions for the partitioning of methane molecules. Results clearly demonstrated the
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movement of methane away from the LHA surface throughout the simulation. For example,
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the intensity of the first peak decreased with time and even disappeared during the last 1000
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ns, which resulted in an increase in the intensity of the remaining two peaks (Fig. 7A). More
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details could be gained from the changes in the number of methane molecules with time in
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each region (Fig. 8A). The sharp peak located at about 140 ns in the number of methane in
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the internal region suggested a fast initial accumulation of methane near the LHA surface,
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which was mainly attributed to the affinity of methane to the hydrophobic functional groups
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such as phenyl and alkyl groups in the LHA molecule. This portion of methane molecules 10
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were unlikely to form hydrate directly, because they were too close to the LHA surface to
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form complete cages and the number of the surrounding water molecules was also
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inadequate to form hydrate structures. To confirm this, a snapshot of the water molecules
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within 0.6 nm from each methane molecule in the internal region is shown in Fig. 9A. The
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distance of 0.6 nm was chosen because the average cavity for a standard 512 cage (the most
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common cage type for methane hydrate) was approximately 0.4 nm, while 0.6 nm was large
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enough to involve the possible hydrate structure around a methane molecule. Results
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indicated that none of the methane molecules accumulated near the LHA surface was
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surrounded by an explicit water cage (Fig. 9A). Additionally, the methane in the internal
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region become less stable when the hydrate started to form in the external region that would
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facilitate the separation of methane from the LHA surface by the cage adsorption
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mechanisms.37 Therefore, there was a quick decrease in the number of methane in the
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internal region (Fig. 8A). However, the decreasing rate became much slower after 200 ns.
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This was contributed by the formation of explicit hydrate cages in the internal region, which
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made it harder for methane molecules to escape from LHA surface to the neighbor region
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(Fig. 9B) due to the increased diffusion resistance of methane.38 A continuous diffusion of
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methane molecules would result in the destruction and reconstruction of the hydrate cages
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along the diffusion pathway, which accounted for the significant fluctuations found in the
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local F4φ curves after 200 ns (Fig. 6A). As is known, the breakup and re-formation or
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re-arrangements of water cages is a normal phemomenon during hydrate growth.39, 40 The
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release and diffusion of methane would facilitate this process, because it would influence
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the stable environment between water cages and bulk water pre-built by the adsorbed 11
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methane.41
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3.2 Influence of LHA nanoaggregates on the hydrate formation. Results demonstrated
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that the kinetic inhibition effects of LHA on hydrate formation was more pronounced at
225
higher concentration. The global F4φ value during the initial 400 ns was up to 10% smaller
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when six LHA molecules than a LHA monomer was added in the Na-MMT pore water (Fig.
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3A). Similar trend was observed in the percentage of cage water (Fig. 3B). Additionally, the
228
distribution of the six LHA molecules close to the Na-MMT surface led to much smaller
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values of local F4φ for the water adjacent to LHA aggregates than to a LHA monomer (Fig.
230
6B), because the water film close to the Na-MMT surface was hard for hydrate formation
231
and its thickness was not influenced by LHA concentration (Fig. 4).
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The enhanced inhibition at high concentration was partially attributed to the increased
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association of water with LHA, because the number of hydrogen bonds between LHA and
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water increased by about 5-fold when the mass fraction of LHA increased from 2% to 11%
235
(Fig. 5C). However, the enhanced inhibition was obviously not proportional to the increased
236
number of hydrogen-bonds. It was inferred that the inhibition resulted from hydrogen
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bonding mechanism was counterbalanced to some extent by the formation of LHA
238
nanoaggregates. This was evidenced by an increase in both the degree of LHA aggregation
239
(Fig. 10) and the local F4φ for the water adjacent to LHA (Fig. 6B) at around 1350 ns.
240
Results also suggested that the increased local F4φ was due to the desorption of methane
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from the LHA driven by LHA aggregation. As shown in Fig. 8B, a sharp decrease in the
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number of methane molecules in the internal region of LHA was found at 1200 ns, which
243
was not observed when only a LHA monomer was present in the pore water. Moreover, the 12
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structure deformation of LHA aggregates also resulted in the release of methane. For
245
instance, the methane molecules were trapped in a small hydrophobic space formed by four
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LHA molecules at 540 ns (Fig. 9C), which made it hard for the methane to transport out
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from the internal region resulting in the appearance of a plateaus between 540 and 1000 ns
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(Fig. 8B). The number of methane in the internal region restarted to decrease after 1200 ns
249
when the structure of LHA aggregates become less tight (Fig. 9D).
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In order to track the pathway of the released methane, we randomly selected one of such
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methane and compared the snapshots at different time (Fig. 11). It clearly showed the
252
moving of the released methane towards the hydrate cages near the LHA surface (399 - 404
253
ns), local breakdown of the hydrate cages (413 ns), penetration of methane through the
254
resulted open channel (443 ns) and re-formation of the hydrate cages (452 ns). A closer
255
examination of the above processes indicated the transition from two linked hexagonal faces
256
to an octagonal face when the methane approached the cages (Figs. 11A and B). Such
257
structure transformation was favorable for methane penetration, because there was a large
258
potential mean force barrier at the center of the hexagonal faces preventing methane from
259
crossing which completely disappeared in the octagonal face.42 It should be noted that the
260
penetration of methane was along a zigzag pathway accompanied by the fast break down
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and re-formation of cage faces in different directions. Nevertheless, it was an irreversible
262
process that the passed methane was unlikely to transport back to the LHA surface when the
263
bottom cage faces were self-enclosed (Fig. 11E). The above findings suggested that the
264
hydrate formation at the late-stage was mainly inhibited by the mass transfer resistance for
265
methane through the hydrate cages already formed in the external regions. 13
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4. CONCLUSIONS
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Overall results demonstrated the inhibited methane hydrate growth in the Na-MMT after
269
amendment of humic acid. A summary of the processess influencing methane hydrate
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growth observed in this study is shown in Fig. 12. The presence of LHA had little influence
271
on the distribution of sodium ions or the thickness of the water films close to the MMT
272
surface that were adverse for hydrate formation. It also suggested that the disruption of
273
water networks by forming hydrogen-bonds with pore water was not the predominant
274
mechanism for the observed inhibition by LHA addition. Instead, it was mainly contributed
275
by the adsorption of methane on LHA which made it hard for methane to form hydrate
276
directly near LHA surface or adsorbed by the water cages already formed in the external
277
region. This portion of methane tended to release from LHA again, which was driven by the
278
LHA aggregation, deformation of LHA aggregates and the competition between LHA
279
adsorption and cage adsorption. The circuitous diffusion of the released methane through
280
the solid cages by cage break and cage re-formation became the main factor limiting the
281
continue growth of hydrate.
282 283
SUPPORTING INFORMATION
284
Nonbond parameters for the CLAYFF force field (Tables S1), bond parameters for the
285
CLAYFF force field (Tables S2), partial charges for atoms in typical functional groups in
286
LHA molecule (Figure S1)
287 14
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AUTHOR INFORMATION
289
†
290
Corresponding Author
291
*E-mail:
[email protected]. Telephone/Fax: +86-0755-26036290.
292
Notes
293
The authors declare no competing financial interest.
These authors contributed equally to this work
294 295
ACKNOWLEDGEMENTS
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This study was finacially supported by National Natural Science Foundation of China (No.
297
21307069) and the Economy, Trade and Information Commission of Shenzhen Municipality
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(Project Nos. HYCYPT20140507010002 and 201411201645511650).
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2005, 19, (2), 459-470.
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Letters 2013, 575, 54-58. 19
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A
C
B
401 402 403 404
Fig. 1 Equilibrium conformations of simulation systems (a) without LHA, (b) with 2% LHA and (c) with 11% LHA. Na+: grey; Si: yellow; O: red ; H: white; Al: blue; Mg: pink; CH4: cygan; LHA: red sticks; H2O: blue lines; hydrogen bonds: blue dashed lines.
405
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120 Number density (nm-3)
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C
+
Na LHA CH4
80
O in H2O
60 40 20 0
407 408
B
A 100
0
1
2
3
4
5 0
1
2 3 4 Z-coordinate (nm)
5 0
1
2
3
4
Fig. 2 Number density profiles of species in the systems (a) without LHA, (b) with 2% LHA, and (c) with 11% LHA.
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409 80
50
B
A
0.3 0.2 0.1
C
40
60
Gas methane (%)
Cage water (%)
0.4
F4ϕ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
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0% LHA 2% LHA 11% LHA
30 20 10
0.0
0
0 0
600
1200
1800
2400
Time (ns)
3000
0
600
1200
1800
2400
Time (ns)
3000
0
600
1200
1800
2400
Time (ns)
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Fig. 3 Changes in the (a) global F4φ, (b) percentage of cage water, and (c) percentage of gas methane. Curves in (a) and (b) were smoothed using
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the 30-point adjacent-averaging method.
412 413 414
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0.06
0.04
F 4ϕ
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water on top Na-MMT 0.02
0.00
water on bottom Na-MMT
-0.02 1
2
3
4
5
6
7
8
9
10
Slice 416
Fig. 4 F4φ order parameters of different water slices in the systems without LHA
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(square), with 2% LHA (circle) and with 11% LHA (triangle), respectively.
418 419
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420
A
6
OL-OW OW-OW
B
OL-OW OW-OW
5
5
4
g(r)
4 3
3
2
2
1
1
0 0.0
90
Number of H-bonds
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g(r)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
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0.6
0.9
r (nm)
1.2
1.5
1.8
C
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2% LHA 11% LHA
70 60 50 40 10
0 0.0
0.3
0.6
0.9
1.2
1.5
r (nm)
1.8
0 0
500
1000
1500
2000
2500
3000
Time (ns)
421
Fig. 5 Radial distribution functions between oxygen in water (OW) and oxygen in LHA (OL) and between OW and OW in the system with (a) 2%
422
and (b) 11% LHA. Number of hydrogen bonds between LHA and water is shown in (c).
423 424
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0.5
0.4
0.4
0.3
F4ϕ
0.3
F4ϕ
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0.2
0.2
A
0.0 0
0.1
r=0-0.9 nm r=0-1.0 nm r=0-1.1nm r=0-1.2 nm r>1.2 nm
0.1
500
1000
1500
2000
2500
B
0.0
3000
0
500
1000
1500
2000
2500
Time (ns)
Time (ns) 426
r=0-0.9 nm r=0-1.0 nm r=0-1.1 nm r=0-1.2 nm r>1.2nm
Fig. 6 Local F4φ for systems with (a) 2% LHA and (b) 11% LHA. Curves were smoothed by 30-point adjacent-averaging method.
427 428
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429 430
160
internal
middle
external
120
120
internal
80 40
0-200 ns 200-1000ns 1000-2000 ns 2000-3000 ns
A
0 0.0
external
0.3
0.6
0.9
1.2
1.5
60 0-200 ns 200-1000ns 1000-2000 ns 2000-3000 ns
30 0 0.0
1.8
B 0.3
0.6
0.9
1.2
1.5
1.8
r (nm)
r (nm) 431 432 433 434
middle
90
g(r)
g(r)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
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Fig. 7 Surface distribution functions for CH4 on (a) LHA monomer and (b) LHA aggregates. Curves were smoothed by 30-point adjacent-averaging method.
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A
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B
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internal region middle region external region
Number of methane
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Number of methane
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40 30 20 10
internal region middle region external region
60 50 40 30 20 10
0 0
500
1000
1500
2000
2500
3000
0
1000
1500
2000
2500
Time (ns)
Time (ns) 436 437
500
Fig. 8 Number of methane molecules in different regions from the COG of (a) LHA monomer and (b) LHA aggregates
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A
200 ns
140 ns
D
C
540 ns 438 439
1200 ns
Fig. 9 Selected snapshots of the simulation systems with (a-b) 2% and (c-d) 11% LHA. White ball: methane; White line: water; Red line: LHA 29
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Number of intermolecular contacts
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440 441
500
1000
1500 2000 Time (ns)
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3000
Fig. 10 Number of intermolecular contacts between LHA molecules
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B
399 ns
404 ns
E
D
C
443 ns
413 ns 442 443
452 ns
Fig. 11 Snapshots of methane (yellow ball) penetration through hydrate cages after release from the LHA surface. (Red : LHA; White: hydrate cages; Green: specific cage faces. Remainng molecules are not shown to highlight the structure of interest) 31
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mineral surface water film (~ 0.4 nm thick) methane
(a) nucleation & growth (b) CH4 adsorption (c) HA aggregation (d) H-bonding (e) HA deformation (f) CH4 desorption (g) cage adsorption (h) cage break (i) cage re-formation (j) CH4 diffusion
a
b
g
pore water
h i
f c e HA
j
f
d water
water film (~ 0.4 nm thick) mineral surface 444 445
Fig. 12 Schema of the processes influencing methane hydrate formation in the clay
446
pores in presence of humic acid (HA)
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