CO2 and CH4 Hydrates: Replacement or Co-growth?

thermodynamic equilibrium studies, 4 while the production level in many ... Most. 57 recently, we reported the evolution of hydrate cages in the regio...
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CO and CH Hydrates: Replacement or Co-Growth? Guozhong Wu, Linqing Tian, Daoyi Chen, Mengya Niu, and Haoqing Ji J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00579 • Publication Date (Web): 19 Apr 2019 Downloaded from http://pubs.acs.org on April 19, 2019

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CO2 and CH4 Hydrates: Replacement or Co-growth?

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Guozhong Wu†, ‡, Linqing Tian†, ‡, Daoyi Chen†, ‡, Mengya Niu†, ‡, Haoqing Ji †, §, *

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† Division of Ocean Science and Technology, Graduate School at Shenzhen,

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Tsinghua University, Shenzhen 518055, China

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‡ School of Environment, Tsinghua University, Beijing 100084, China

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§ College of Energy, Soochow University, Suzhou 215006, China

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ABSTRACT

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Replacement of CH4 with CO2 in gas hydrates is a promising option for producing CH4

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and sequestrating CO2 simultaneously, but it remains debatable if the CH4 hydrate

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dissociate or convert to the CH4-CO2 mix hydrates during the replacement. To gain

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insights into the underlying micro-mechanisms, molecular dynamics simulations were

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performed in this study at six temperatures (250 K - 275 K) and three pressures (20 bar,

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50 bar, 100 bar) by systematic analysis of the hydrate cages. Results demonstrated that

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it was possible to destabilize the CH4 hydrates by decreasing the adsorption of CO2 on

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the CH4 hydrate surface or increasing the interfacial area for the contact between CO2

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and CH4 hydrates. However, the simultaneous dissociation of CH4 hydrates and

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formation of CO2 hydrates was not observed or only last for a very short time, while

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the released CH4 would form CH4-CO2 mix hydrates even though the driving force was

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suitable for breaking up CH4 hydrate cages and forming CO2 hydrate cages. Moreover,

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this study revealed that the coalescence of CH4 hydrate particles was mainly contributed

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by the linkage from 512 cages in the region between the two CH4 hydrate particles which

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was further stabilized by the 51263 cages.

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1. INTRODUCTION

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Natural gas hydrate has been identified as a huge potential resource for future energy in

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which the amount of carbon stored is estimated to be twice more than all fossil fuels

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combined. 1 The replacement of CH4 with CO2 in gas hydrates is a method of increasing

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research interest, because it is able to harvest CH4 for energy production and sequestrate

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CO2 for climate change mitigation. More importantly, the hydrate structure will not be

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significantly changed during the replacement reaction.2 Therefore, the geological stability

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problem caused by hydrate dissociation in traditional methods (e.g. thermal stimulation,

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depressurization and inhibitor injection) can be potentially avoided, which is essential for

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guaranteeing a large-scale safe exploitation. The feasibility of this method has been well

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proven from both kinetic and thermodynamic points of view 3, but the slow recovering

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rate and the low production efficiency make it challenging for commercial application.

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For example, the expected methane recovery is estimated to be below 70% from the

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thermodynamic equilibrium studies, 4 while the production level in many experimental

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practices are below 50%.

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microscopic mechanisms of CH4-CO2 replacement in gas hydrates.

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It is assumed that the replacement took place by the first dissociation of CH4 hydrates

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followed by the formation of CO2 hydrates where the production of free water is a

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significant feature during the replacement on the macro level.

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might become a quasi-static equilibrium at the liquid-hydrate interface rather than in the

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free gas.13 However, there are also strong evidences that revealed no detectable

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dissociation of CH4 hydrates during the CH4-CO2 exchange process, instead, substantial

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portion of the CH4 hydrates converted to the CH4-CO2 mix hydrates without significant

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hydrate dissociation.14-16 An interesting research question raised from these controversial

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This highlights the demands for works focusing on the

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The hydrate growth

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results is whether the “replacement” would really occur if the temperature and pressure

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can provide adequate driving force for both CH4 hydrates dissociation and CO2 hydrate

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formation. If not, what is the main factor preventing the CH4 hydrates from dissociation

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and driving the co-growth of CH4-CO2 hydrates, and how it differs against the reaction

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conditions such as the initial phase state of CO2, the concentration of CO2, and the

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interfacial area between CO2 and CH4 hydrates.

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Another research question of particular interests is the molecular mechanisms for the

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coalescence of hydrate particles during the replacement or co-growth process. Most

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recently, we reported the evolution of hydrate cages in the region between two CH4

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hydrate surfaces and highlighted the role of the adsorption and spreading dynamics of

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water droplet on the above process.

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oil-dominated system, while previous study indicated that the magnitude of inter-particle

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interactions of hydrates in water were relatively low and the hydrate aggregation

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mechanism was different from that in the oil- or gas-dominated systems.18 Lee and Sum

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19

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C2H6 mix hydrates) had no influence on the cohesive force between hydrate particles.

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These studies provided direct evidences for the strength of hydrate-hydrate interactions

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by artificially pulling two hydrate particles together, but it remained unclear when and

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how the two hydrate particles would spontaneously move towards each other and how

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the resulted hydrate aggregates were stabilized by specific cage links. It becomes more

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complicated during the CO2 replacement reaction due to the coexistence of multiple

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processes such as CO2 hydrate formation, CH4 hydrate dissociation and re-formation. The

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two CH4 hydrate particles may link together to form a larger particle and then the CO2

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replacement took place on the outer surface, otherwise, the CO2 hydrates would fast form

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However, the above study was performed in the

further suggested that the hydrate structure (sI with CO2 hydrates and sII with CH4-

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on the surface of each of the two CH4 hydrate particles and then merged to a larger one.

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It demands future works on cage analysis at molecular-level to gain insights into these

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processes, which benefits for better understanding the mass transfer resistance for the CO2

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replacement reaction.

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Accordingly, molecular dynamics (MD) simulations were performed in this study to

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address the above issues. Specific objectives were to identify (i) the effects of CO2 state

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(i.e., gas or solution), CO2 concentration and the number of interfaces between CO2

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solution and CH4 hydrates on the hydrate evolutions in a number of temperature and

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pressure conditions, and (ii) the dynamic evolution of typical hydrate cages during the

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coalescence process of two hydrate particles immersing in the CO2 environment.

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2. METHODOLOGY

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2.1 Model construction and molecular dynamics simulation

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MD simulations were performed with an open source software Gromacs (version 5.0.5).

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20

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was replicated to form a 3 × 3 × 3 super cell to represent a cubic hydrate particle. Two

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scenarios were setup to compare the one-dimensional and three-dimensional reactions

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with different interfacial area between CO2 and CH4 hydrates. In Scenario 1, the hydrate

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particle was placed at the bottom of the simulation box, while the gaseous CO2 (300 CO2

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molecules) or the dissolved CO2 (mixture of 100 CO2 molecules and 1400 water

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molecules) was placed on the top, respectively. In this case, the hydrate particle was only

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truncated and contacted with CO2 in the z-dimension, while the continuity in the x-y plane

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was maintained with periodic boundary conditions. In Scenario 2, two hydrate particles

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with an initial spacing of 1.3 nm were immersed in the CO2 solution. The mole

The unit cell of structure I CH4 hydrate was obtained from Lenz and Ojamäe,21 which

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concentration of CO2 in the solution was set as 6.1% and 9.1% by mixing 432 or 660 CO2

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molecules with 6600 water molecules, respectively. The spatial continuity of the hydrate

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particles was truncated in all dimensions. The initial configurations of the simulation

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systems are shown in Fig. S1 in the supporting information.

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Water was modeled with TIP4P model,

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united-atom (UA) model

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between water and CO2 were obtained from Duan et al.,

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between other unlike atom pairs were calculated by the standard Lorentz-Berthelot

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mixing rules.

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Coulombic interactions were calculated by the particle mesh Ewald method with a Fourier

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spacing of 0.12 nm. 27 The leap-frog algorithm was employed to integrate the equations

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of motion.

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dimensional reaction simulation, respectively.

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The initial conformations were firstly energy-minimized with the steepest descent

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algorithm, followed by a 30 ps NPT (constant number of atoms, pressure and temperature)

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equilibration. Subsequently, MD simulations were performed at NPT ensemble. During

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the one-dimensional reaction simulation, totally 9 groups of P-T conditions (temperatures:

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265 K, 270 K, 275 K, pressures: 20 bar, 50 bar, 100 bar) were employed. During the

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three-dimensional reaction simulation, a series of trial runs were performed to determine

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the P-T conditions (temperatures: 250 K, 255 K, 260 K, 265 K, pressures: 20 bar, 50 bar,

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100 bar). Temperature and pressure were controlled by the Nose-Hoover thermostat

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and Parrinello-Rahman barostat 30, respectively. The simulation duration was 3000 ns and

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300 ns for the one-dimensional and three-dimensional reaction simulation, respectively.

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The simulations were manually terminated if all hydrate cages dissociated in the

28

26

23

22

while CH4 and CO2 were modeled with the

and EPM2 model

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respectively. Non-bonded parameters 25

while cross interactions

Short-range interactions were truncated at 1.2 nm, while long-range

The time step was 1 fs and 2 fs for the one-dimensional and three-

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simulation systems.

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2.2 Data Analysis

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The face-saturated incomplete cage analysis method developed by Guo et al.

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employed to quantify the hydrate cage compositions, the free or adsorption state of CH4

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and CO2 molecules, and the cage linking structures of hydrates. Briefly, the complete

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cage (CC) was identified as the cage with every vertex shared with at least three edges

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and every edge shared with exactly two faces. CCs included standard cages (e.g. 512, 51262,

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51264, 51268, 435663) and other cages (e.g. 51263, 4151062, 4151063, 4151064). Each cage face

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had an adsorption site, which was along the normal vector (outward) crossing the face

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center and was 3 Å away from the center. The CH4 or CO2 molecules were identified as

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adsorbed molecules (if it was within 3 Å from the adsorption site of a cage face), guest

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molecules (if it was in a hydrate cage), or free molecules. The linkages between each two

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hydrate cages through a cage face were classified into structure I (sI) links, structure II

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(sII) links and structure H (sH) links. The linkage between a 512 cage and a 51262 cage

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was recognized as an sI link because such linkage only existed in the sI hydrate structures,

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while the linkage between two 512 cages could be either sII or sH. To intuitively display

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the hydrate evolution during simulations, the algorithm developed by Jacobson et al.

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was employed to illustrate the cage distribution in a system.

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was

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3. RESULTS AND DISCUSSIONS

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3.1 One-dimensional reaction

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The evolution of hydrate cages during interaction with CO2 gas are shown in Fig. 1. It

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demonstrated the fast dissociation of CH4 hydrate cages and the formation of CO2 hydrate

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cages during the first 100 ns at 265 K (Figs. 1a – 1c). Such replacement process stopped 7

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after 100 ns, which resulted in the loss of about 50 complete CH4 hydrate cages and the

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appearance of about 85 free CH4. Only a small portion of the dissociated CH4 hydrates

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were ‘replaced’ by the CO2 hydrates, because only 10 - 20 CO2 hydrate cages appeared.

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These findings were independent on the initial pressure (20 - 100 bar) and differed little

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when the temperature increased to 270 K (Figs. 1d – 1f), but 275 K was obviously not

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suitable for the hydrate replacement as it was high enough to destroy both CH4 and CO2

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hydrate cages (Figs. 1g – 1i). It should be noted that the equilibrium points of gas hydrate

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in the MD simulation were different from that in the experiments. Since both water-water

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and water-guest interactions affects the equilibrium conditions, recent studies had been

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carried out to calculate the host-guest interactions and the three-phase equilibrium

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conditions of pure CH4, pure CO2 and their mixture hydrates using different combination

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of molecular models.

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CH4 hydrate (TIP4P water + UA methane) and CO2 hydrate (TIP4P water + EPM2 CO2)

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was 247 K ± 3 K (P = 100 bar) and 275 K ± 2 K (P = 100 bar), respectively.

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Accordingly, there was strong tendency for the dissociation of CH4 hydrate at 275 K and

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100 bar as the driving force was about 28 K, while the driving force for the CO2 hydrate

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formation was almost zero.

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When the initial state of CO2 was changed to solution, an obvious change was the state

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of CH4 and CO2 molecules after reaction at 265 K. For example, the free CH4 was about

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83% less and the adsorbed CH4 was more than doubled after changing the CO2 gas to CO2

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solution (Figs. 1 - 4). Another finding was that the CH4 hydrates were less stable when

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contacting with CO2 solution than with CO2 gas. For example, the CH4 hydrate cages

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remained stable at 270 K after interaction with CO2 gas (Figs. 1d – 1f) but completely

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dissociated in presence of CO2 solution (Figs. 3d – 3f). This could be further evidenced

33-38

As previously reported, one of the equilibrium point for the

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by the faster dissociation rate at 275 K. For example, it took 140 ns to completely melt

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the CH4 hydrate cages by CO2 gas under 20 bar (Fig. 1g), while the corresponding time

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cost was only 80 ns by CO2 solution (Fig. 3g).

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The above finding was attributed to the different spatial distribution of CO2 molecules in

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gas and solution which led to different capability for stabilizing the CH4 hydrates. The

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CO2 molecules in the gas state were concentrated and close to each other, making them

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easy to densely adsorb onto the hydrate surface. This portion of CO2 molecules

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contributed to stabilize the interfacial hydrate structure according to the ‘cage adsorption’

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mechanism that the hydrate cages could absorb guest molecules and in turn be stabilized

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by such adsorption. 41 This was supposed to increase the mass transfer resistance for the

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escape of CH4 molecules from the hydrate cages. Moreover, the CH4-occupied small 512

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cages would initiate the nucleation of CH4-CO2 mix hydrates in a local liquid phase with

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a high gas concentration. 42 By contrast, the CO2 molecules dispersed in water were less

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concentrated than in the gas state making them more scattered on the hydrate surface.

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This was confirmed by the 50% decrease in the number of adsorbed CO2 when the initial

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state of CO2 was changed from gas to solution (Figs. 2d and 4d). The weakened

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adsorption of CO2 allowed the faster dissociation of the CH4 hydrate cages, while the

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latter also resulted in the fast collapse of the CO2 hydrate cages at around 400 ns at 270

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K (Figs. 3e and 3f). This was attributed to the fact that the driving force for the CO2

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hydrate formation was only 5 K, which was insufficient to ensure its thermodynamic

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stability and therefore made it susceptible to be perturbed by the diffusion of the CH4

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molecules released from the continuous break-up of CH4 hydrate cages. Based on the

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above results, we used CO2 solution in the subsequent studies.

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3.2 Three-dimensional reaction 9

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3.2.1 Reaction with high concentration CO2 solution

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Since both CH4 and CO2 hydrates dissociated at 270 K and 275 K but remained stable at

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265 K during the one-dimensional reactions with CO2 solution, we first tested the three-

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dimensional reactions at 265 K under 100 bar. Results demonstrated that all the CH4

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hydrate cages disappeared during the first 10 ns (Fig. 5a and 5b). Such dissociation rate

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was even faster than that in the one-dimensional reaction at 275 K under the same pressure

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(Fig. 1i). It should be noted that the mole concentration of CO2 in this case (9.1%) was

200

higher than that in the one-dimensional reaction (6.7%). The CH4 hydrates should have

201

been more stable at high concentration, because the number of the adsorbed CO2

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molecules increased to 150 in the early stage (Fig. 6b) which was about 3.8-fold of that

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in the one-dimensional reaction (Fig. 4d). However, the number of interfaces between the

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CH4 hydrate and CO2 solution increased from 1 in the one-dimensional reaction to 12 in

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the three-dimensional reaction, while the corresponding interface area increased from

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about 13 nm2 to 156 nm2. Accordingly, the number of the adsorbed CO2 molecules per

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unit area was indeed decreased by increasing the dimension of reaction. Therefore, the

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reduced stability of CH4 hydrates was mainly attributed to the increased area of CH4

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hydrates exposed to CO2 solution. However, little CO2 hydrate was formed in this case,

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suggesting that such P-T condition (265 K, 100 bar) was not suitable for an effective

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replacement of CH4 hydrates from the kinetic point of view (Fig. 5c).

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Therefore, we decreased the initial temperature to 260 K without changing the pressure

213

to test if the hydrate replacement process took place. Results demonstrated that such P-T

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condition (260 K, 100 bar) made it possible to synthesis CO2 hydrates as the cages

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occupied by CO2 increased to 200 quickly (Fig. 5c). However, the number of CH4

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hydrates also increased although there was 13 K driving force for the dissociation of CH4 10

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hydrates (Fig. 5b). The observed increased number of CH4 hydrates at early stage was

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due to the fact that the edges of the hydrate supercell were not continuous in the initial

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model. This meant that some CH4 molecules were adsorbed on the external surface of the

220

hydrate supercell rather than being well-entrapped inside the complete hydrate cages (Fig.

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S2). This portion of CH4 molecules tend to form hydrate cages if the reaction conditions

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were suitable for CH4 hydrate formation, which was further stabilized by the formation

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of CO2-CH4 mixed hydrates. Accordingly to the stabilization energy calculations by Geng

224

et al.,

225

hydrates alone.

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Subsequently, we decreased the initial pressure to 50 bar without changing the

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temperature (260 K). It was found that all the CH4 cages melted during the first 50 ns

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(Fig. 5b) while the small amount of the initially formed CO2 cages also disappeared (Fig.

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5c). Further tests indicated that the stability of both CO2 and CH4 hydrates could be

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preserved at 250 K or 255 K even when the pressure was decreased to 20 bar (Fig. 5).

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Since 250 K and 20 bar were very close to the reported phase equilibrium condition of

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CH4 hydrates, further decrease of temperature might provide little driving force for the

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dissociation of CH4 hydrates. Therefore, four P-T conditions were employed in the

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subsequent study including (255 K, 20 bar), (255 K, 50 bar), (250 K, 20 bar) and (250 K,

235

50 bar). The co-growth of CH4 and CO2 hydrates were observed in all these conditions,

236

which was similar to that found at (260 K, 100 bar) (Fig. 5).

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the CO2-CH4 mixed hydrates was more stable than the CH4 hydrates or CO2

237 238

3.2.2 Reaction with low concentration CO2 solution

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When the initial mole concentration of CO2 in the solution was decreased to 6.1%, it was

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interesting to find that the CH4 hydrates dissociated very fast and no CO2 hydrates were 11

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formed at 260 K under 100 bar (Fig. 7), which was opposite to the co-growth tendency

242

observed at high initial concentration of CO2 (Fig. 5). This might be associated with the

243

role of CO2 adsorption on the stability of CH4 hydrates. As shown in Fig. 8b, the number

244

of CO2 molecules adsorbed onto the hydrate surface started to decrease from 150 to 50,

245

which was supposed to be insufficient to stabilize the CH4 hydrate structure. By contrast,

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the number of the adsorbed CO2 molecules kept stable at about 200 during the reactions

247

with high CO2 concentration under the same P-T conditions (Fig. 6b).

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Similar to the previous subsections, we tested the reactions with low concentration CO2

249

solution under (255 K, 20 bar), (255 K, 50 bar), (250 K, 20 bar) and (250 K, 50 bar). The

250

number of both CH4 and CO2 hydrate cages increased at the end of reactions under these

251

conditions, which was similar to that observed at high concentration CO2 solution.

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However, it was interesting to notice at 255 K that the number of CH4 hydrate cages

253

decreased sharply during the first 50 ns before rising. This indicated a successful

254

replacement of the CH4 hydrates by the CO2 hydrate at the beginning of reaction with low

255

CO2 concentration, but the released CH4 molecules were converted to hydrates again

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which resulted in the co-growth of CH4-CO2 mixed hydrates. To gain insights into the

257

reactions with low concentration CO2 at 255 K, the evolution of hydrate cages during the

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initial 100 ns was analyzed and discussed in the following subsection.

259 260

3.2.3 Cage linkage between hydrate particles

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The snapshots of the hydrate cages (512, 51262, 51263, 51264) evolution under 20 bar and 50

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bar at 255 K are shown in Fig. 9. An interesting finding was that the two hydrate particles

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started to link together at about 10 ns and eventually merged into one particle at about 50

264

ns under 20 bar. The volume of the resulted particle was obviously smaller than the sum 12

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of the initial two particles. However, the top particle was fast melted and completely

266

disappeared at 60 ns under 50 bar where the particles coalescence phenomenon observed

267

under 20 bar did not take place (Fig. 9). To clarify the different findings between the two

268

initial pressures, we quantified the number of different type of hydrate cages and

269

fractionated them into the ones filled by CH4 or CO2, respectively, under 20 bar and 50

270

bar (Fig. 10).

271

Results indicated that the two CH4 hydrate particles were linked by three 512 cages at 10

272

ns under 20 bar, probably because the 512 cage was easy to form due to the small deviation

273

from the tetrahedron structure (Fig. 9a). It should be noted that the links between 512 cages

274

belonged to the sII hydrate, which did not match the sI structure of the CH4 hydrates

275

initially located in the system. We also noted that the 51263 cages appeared at about 20 ns

276

and fast increased at 75 ns (Fig. 10a), which belonged to neither sI or sII hydrate but was

277

able to connect and stabilize these two structures. This agreed with previous study which

278

demonstrated the presence of 51263 cages during the formation of CO2 and CH4 mixed

279

hydrates and suggested that such cages acted as a linker at the interface of sI and sII

280

hydrates.42 By contrast, the number of the 51263 cages was negligible under 50 bar (Fig.

281

10b).

282

Moreover, the sum of the number of the 512 and 51262 cages filled with CO2 exceeded 20

283

during the initial 50 ns under 20 bar (Fig. 10a), which was less than 10 at 50 bar (Fig.

284

10b). These cages were preferentially located near the linking area between the two

285

hydrate particles since they could be stabilized by the two CH4 hydrate particles. During

286

the first 50 ns, the number of both 51262 and 512 cages filled with CH4 sharply decreased

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under 50 bar (Fig. 10b), but the decline of the number of 512 CH4 cages was gently under

288

20 bar (Fig. 10a). The stronger degree of the 51262 cage dissociation was attributed to the 13

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weaker thermodynamic stability than 512 cages, which was consistent with previous study

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that the 51262 cages dissociated prior to the 512 cages during replacement. The less

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dissociation degree of both cages under 20 bar than under 50 bar might be attributed to

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the stabilization effects from the 51263 cages on the hydrate structure under 20 bar as

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aforementioned. As shown in Fig. 9, the location of the 51263 cages changed from the

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linking area of the two hydrate particles (t = 20 ns) to the position with 2 – 3 cages far

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away from the linking area (t = 30 ns), after which their position kept on changing and

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the corresponding cage number increased. This helped to stabilize the remaining 512 cages.

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Enlarged snapshots are shown in Fig. S3 for better illustrating this process. After 75 ns,

298

considerable amount of 51263 and 51264 cages were observed under 20 bar (Fig. 10a) and

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the sII links obviously increased (Fig. 10c). This was due to the fast formation of 512 cages

300

before 50 ns which kinetically favored the formation of sII hydrate. By contrast, the sII

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links were almost negligible under 50 bar (Fig. 10d), which was attributed to the

302

simultaneous dissociation of both 512 and 51262 CH4 cages aforementioned.

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4. CONCLUSIONS

305

This study clearly demonstrated the capability of CO2 to stabilize CH4 hydrate by surface

306

adsorption. For example, the CH4 hydrate was more stable when contacting with CO2 gas

307

than with CO2 solution, because the number of adsorbed CO2 was significantly higher

308

when the hydrate was exposed to CO2 gas compared with CO2 solution. Similarly, the

309

CH4 hydrate structure was much more susceptible to collapse when six surfaces rather

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than only one surface was exposed to CO2 solution, because the number of the adsorbed

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CO2 per unit surface area significantly decreased by increasing the reaction dimensions.

312

Results further demonstrated that only a very small portion (~ 20%) of the dissociated 14

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CH4 hydrates were really “replaced” by CO2 in all tests even though there was enough

314

driving force for both CH4 hydrate dissociation and CO2 hydrate formation. It was more

315

likely to form CO2-CH4 mix hydrates due to the low stabilization energy especially when

316

the concentration of CO2 solution was high. The simultaneous decrease of CH4 hydrate

317

cages and increase of CO2 hydrate cages were observed in presence of low concentration

318

CO2 solution, but the released CH4 molecules were quickly trapped in hydrate cages

319

resulting in co-growth of mix hydrates again. These findings suggested the necessary to

320

timely extract the recovered CH4 gas before continuous CO2 injection to ensure an

321

effective replacement reaction. Overall results suggested that the CH4 hydrates would

322

either dissociate to release free CH4 gas or directly convert to the CH4-CO2 mix hydrates

323

without significant dissociation, while the former last for a short time and the

324

“replacement” would eventually turn to “co-growth” process.

325 326

SUPPORTING INFORMATION

327

Initial molecular configurations of the simulation systems (Figure S1), Configurations of

328

the CH4 molecules at the edge of the hydrate supercell (Figure S2), Snapshots showing

329

the movement of the 51263 hydrate cages during the reaction with 6.1% CO2 solution (255

330

K, 20 bar) (Figure S3).

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Telephone/Fax: +86-0755-26030544 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This study was financially supported by the Shenzhen Peacock Plan Research Grant (No. KQJSCX20170330151956264), Natural Science Foundation of Guangdong Province (No. 2018A030313899), and the Development and Reform Commission of Shenzhen Municipality (No. DCF-2018-64).

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Fig. 1 Number of total complete cages (CC), complete cages filled by CH4 (CCCH4), complete cages filled by CO2 (CCCO2), and free CH4 molecules during the onedimensional reaction with CO2 gas

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Graphical Abstract

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