Grand Canonical Monte Carlo Simulations on Phase Equilibria of

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Grand Canonical Monte Carlo Simulations on Phase Equilibria of Methane, Carbon Dioxide and its Mixture Hydrates Nianxiang Qiu, Xiaojing Bai, Ningru Sun, Xiaohui Yu, Longbin Yang, Yanjun Li, Minghui Yang, Qing Huang, and Shiyu Du J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b04551 • Publication Date (Web): 02 Oct 2018 Downloaded from http://pubs.acs.org on October 3, 2018

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The Journal of Physical Chemistry

Grand Canonical Monte Carlo Simulations on Phase Equilibria of Methane, Carbon Dioxide and its Mixture Hydrates Nianxiang Qiu1, Xiaojing Bai1, Ningru Sun1, Xiaohui Yu2, Longbin Yang3, Yanjun Li3, MinghuiYang4, Qing Huang1, and Shiyu Du*1 1

Engineering Laboratory of Nuclear Energy Materials, Ningbo Institute of Industrial Technology,

Chinese Academy of Sciences, Ningbo, Zhejiang 315201, P. R. China. 2

National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Science,

Beijing 100190, China 3

College of Power and Energy Engineering, Harbin Engineering University, Harbin, Heilongjiang,

150001 China. 4

Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo,

Zhejiang 315201, P. R. China. *Corresponding Author: E-mail: [email protected]

ABSTRACT: The cage occupancy plays a crucial role in thermodynamic stability of clathrate hydrates and is an important quantity for understanding the CO2-CH4 replacement phenomenon. In this work, the occupancy isotherms of pure CH4, pure CO2 and their mixture in sI and sII hydrates are studied by GCMC+MD simulations. The adsorption of CH4 and CO2+CH4 in the sI and sII hydrates can be categorized as the one-site Langmuir type. The calculated occupancy ratio θL/θS and the abundance ratio of CO2 to CH4 vary with the temperature and pressure, which provide the prerequisite information for prediction of CH4 recovery yield at different conditions in the CO2-CH4 gas exchange process. The phase equilibria of clathrate hydrates of pure gases and mixtures are explored and the corresponding heat of dissociation and hydration numbers are determined. The current investigation provides new perspectives to understand the mechanism behind the gas adsorption behavior of clathrate hydrates.

1. INTRODUCTION Gas hydrates are crystalline, non-stoichiometric compounds, in which gas molecules are trapped inside polyhedral cages formed by hydrogen-bonded water molecules1. There are three most common hydrate structures: cubic structure I (sI), cubic structure II (sII) and hexagonal structure H (sH). The sI crystal is composed of pentagonal dodecahedron (512) and tetrakaidecahedron (51262) cages, the sII hydrate consists of 512 and hexakaidecahedron (51264) cages and the structure sH contains 512, irregular dodecahedron (435663) and icosahedron (51268) cages. There is a huge amount of natural gas hydrates in ocean sediments and permafrost regions with methane as the major guest molecule, and they have received wide attention as a `

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future energy resource2,3. Moreover, gas hydrates are also relevant to various potential applications such as CO2 capture4-6, H2 storage7-9 and gas separations10-12. In the past few years, an interesting gas exchange method has been developed, which is commonly known as CH4-CO2 replacement, in order to exploit methane from natural gas hydrates. The replacement of CH4 with CO2 in gas hydrates can convert the CH4 hydrate into a stable CO2 hydrate and would serve double duty as CH4 source extraction and greenhouse gas CO2 sequestration12-21. As the fundamental principle behind it, the formation condition of pure CO2 hydrate is milder than that of pure CH4 hydrate1,13, which has been verified by many experimental studies14-20. Ohgaki et al. illustrated the feasibility of the replacement scheme and suggested that the heat released with the formation of the CO2 hydrate is more than that demanded to decompose the CH4 hydrate14. Hence, this process may be self-sustaining as long as CO2 supply is maintained. Lee et al. estimated that 64% of CH4 can be produced from the methane hydrate after its reaction with CO2 and predicted a CO2/CH4 ratio of about 1.8 in the product hydrate at 270 K15. Lee et al. studied the thermal properties of the intermediates in CH4-CO2 replacement of gas hydrates using a differential scanning calorimeter, and found no noticeable dissociation or formation of gas hydrates during the replacement process20. In order to study the CH4-CO2 replacement mechanism, many works have also been conducted on the hydrate phase equilibria of various CH4+CO2 compositions as well as the compositional change in both the gas and hydrate phases 13,14,21-23. Spectroscopic observations indicated that CO2 molecules prefer substituting CH4 in sI large cages, due to its more appropriate molecule size to enter the sI large cages15-18,24. CO2 molecules are preferentially encaged into the large cages of the hydrate phase as compared with CH4 molecules. With the boost of the computational power, molecular simulations have been playing a more and more significant role in exploring the behavior of gas hydrates. By this method, the cavity occupation in clathrate hydrates can be directly monitored at the molecular level. Recently, quite a few theoretical studies on gas adsorption in clathrate hydrates have been performed, which consider versatile gases such as hydrogen25-27, neon28,29, xenon30, nitrogen31, methane32-40, carbon dioxide39-41, carbon monoxide42, ammonia43 and the CO+N2 mixture44. Lasich et al.34 and Henley et al.36 claimed that the adsorption of CH4 in sI hydrates can be interpreted in terms of a single type Langmuir adsorption, and there is no apparent distinction between small and large cavities for CH4 molecules. However, Papadimitriou et al. demonstrated that the occupancy isotherm of CH4 in sI hydrates as well as sII hydrates can be described not only by a Langmuir isotherm but also by a two-site occupancy isotherm, and they pronounced the OPLS-UA (united-atom) methane model, which overestimated the total and small cage occupancies with the TIP4P/Ice water model, and could provide larger cage occupancy compared with OPLS-AA (all-atom) five-site methane model36-38. Glavatskiy et al.39 reported that carbon dioxide tend to occupy large cages first as compared with methane molecules that have no clear preference between small and large cage types. Moreover, they suggested that the mole fraction of CO2 in the hydrate phase is less than that in the gas phase of the mixture CO2+CH4, which is in contrast with experimental results17-23, and again the Langmuir-type adsorption `


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model do not fit the occupancy isotherms of pure CO2 or CH4 hydrates. Waage et al suggested that the adsorption of pure CO2 or CH4 in sI hydrates are both two-site isotherms, and they reported that the fractional occupancies decrease as the applied pressure increases due to the compression of the hydrate structure41. Although the above investigations provide important insights into the adsorption of gas molecules in clathrate hydrates, the occupancy isotherm and phase equilibria of hydrates for pure CH4 and CO2 as well as CO2+CH4 mixtures are not yet well understood and debates apparently persist. Grand Canonical Monte Carlo (GCMC) simulation in particular is a useful tool to study the occupancy of gas molecules within clathrate hydrates as well as the spatial distribution of gas adsorbed in cages25-44. Phase equilibria of gas hydrates can be estimated using the predicted cage occupancies by GCMC simulations according to the van der Waals-Platteeuw (vdWP) theory45, which has successfully predicted phase behaviors for many hydrates46-53. In this paper, the occupancy isotherms for both single-component and mixture hydrates are investigated using the GCMC and molecular dynamics (MD) hybrid (GCMC+MD) simulations. It is found that the adsorption of CH4 and CO2+CH4 mixtures in sI hydrates can be approximately described in terms of a one-site Langmuir-type adsorption. The calculated phase equilibria and the heat of dissociation for gas hydrates are comparable to experiments.

2. THEORY AND METHODS 2.1 Simulation details In our work, GCMC simulations are performed using the LAMMPS package, which is distributed as an open source code for massively parallel simulations54. The lattice parameters of cubic unit cells of sI and sII hydrates are 12.0 and 17.3Å, respectively55. 3×3×3 and 2×2×2 unit cells of sI and sII hydrates are considered in the present GCMC (µVT) simulations, which have 216 and 192 cages, respectively. Furthermore, all atoms in the simulation cells are allowed to move using regular time integrations, resulting in a hybrid GCMC+MD simulation. The constant temperature and constant volume (NVT) MD simulation runs are performed by the Nosé-Hoover algorithm56 with a timestep of 1 fs. The total simulation time depends on the adsorbed gas pressures and temperatures to provide well equilibrated states for the system, which is typically 5~50 ns. Meanwhile, a Monte Carlo (MC) cycle is attempted in every 50 timesteps by the Metropolis scheme57. The MC cycle includes exchanges (insertions or deletions) of adsorbed gas atoms or molecules, and moves (translations and molecule rotations) of gas. For MC exchanges of gases, the probabilities of both insertions and deletions are 50%. For MC moves, translations and rotations are each attempted with 50% probability. The number of MC exchanges and moves per cycle varies depending on the number of particles adsorbed in the systems with a minimum of 50. The maximum allowed displacement distance is 1Å, while the maximum molecular rotation angle is 10º. In GCMC simulations, the chemical potential of each component is manually imposed to calculate the equilibrium number of particles58. To calculate the gas phase `



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fugacity, Peng-Robinson equation of state (PR-EoS) is found to be satisfactory for the fluid phase far from the critical points59. The values of critical temperature, critical pressure and acentric factor of physical properties, required for PR-EoS, are 190.56 K, 4592.0 kPa and 0.008 for CH4 as well as 304.13 K, 7375.0 kPa and 0.225 for CO2.60 For a gas mixture, the van der Waals mixing rules are applied to describe the crossed influence between the components, which convert fugacities from pure gas phases to values for mixtures. The binary interaction parameter kij of components CH4 and CO2 is 0.12.61 The TIP4PEw water model is used in our simulations62, which is a reparameterization of TIP4P with a long-range Coulombic solver, and is considered as a reliable pair potential for predicting water properties63 as well as cage occupancy compared to experimental measurements34,35. The bond length and angle of the water model are constrained with the SHAKE algorithm. CO2 molecules are modeled by the EPM2 potential64, which has been successfully used in many simulations65. CH4 molecules are modeled with the DACNIS united-atom (UA) potential66 and the TraPPE all-atom (AA) potential67,68. The force field parameters used in this study are presented in Table 1. The unlike parameters of Lennard-Jones potentials are determined by the Lorentz-Berthelot combining rule. Short-range interactions are calculated with a cutoff distance of 12.5Å, while the Coulombic long-range interactions are calculated using the PPPM algorithm69. Periodic boundary conditions are imposed in all three Cartesian directions. Table 1. Force filed parameters used in this study. Model

Atom

ε/kB(K)

σ (Å)

q (e)

DACNIS-UA TraPPE-AA

CH4 C(CH4) H(CH4) C(CO2) O(CO2) O(H2O) H(H2O) M(H2O)

158.500 51.167 8.646 28.129 80.507 81.900 0.000 0.000

3.720 3.350 2.610 2.757 3.033 3.164 0.000 0.000

0 -0.5720 0.1430 0.6512 -0.3256 0 0.5242 -1.0484

EPM2 TIP4PEw

2.2 Phase equilibria of gas hydrates The prediction on the phase equilibria of clathrate hydrates employing the chemical potential equivalence between the hydrate phase and the coexisting water phase provides a bridge between molecular structures (e.g. cavities and their occupancies) and macroscopic properties (e.g. temperature and pressure). For a gas hydrate at equilibrium, the chemical potential of water in the hydrate phase equals to that in the ice phase: = (1) If the chemical potential of empty hydrate phase ( ) is used as a reference state, equation (1) can be expressed as: Δ = Δ (2) `


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where Δ =- and Δ = - . Δ is determined by equation (3):45 Δ = ∑ 1 ∑ (3) where νi is the number of type i cavities per water molecule in the lattice. θji is the fractional occupancy of a cavity of type i by a molecule of type j. By the vdWP approach, the fractional occupancy θji is calculated by the Langmuir constant of cavity i adsorbed by gas component j and the fugacity of gas component j. In this study, fractional occupancies of cavities by gas species can be obtained directly by GCMC+MD simulations. By use of a reference hydrate, the chemical potential difference Δ can be 70 calculated by the following well established relationship: $

#

Δ & = Δ & $ ∆ ⁄ ∆ %

⁄ !

"

(4)

where Δ is the difference in chemical potential between the empty hydrate lattice and ice at reference state (T0=273.15 K, P0=0 Pa). The ∆hw and ∆Vw are the differences in enthalpy and volume between the empty hydrate lattice and ice, respectively. And aw is the activity of water in ice phase, whereas the term lnaw is omitted in ice phase without significant error as adopted in the literature51. The enthalpy term ∆hw is a function of temperature and is expressed as follow: $

∆ = ∆ $ ∆'(,

%

(5)

and the temperature dependency of heat capacity term ∆Cp,w is given as: ∆'(, = ∆'(, α′ 273.15 (6) where the constant α' is the fitted parameter. The values in equation (4) used to calculate phase equilibria are provided by Chen and Gao52. Thus, the phase equilibria are predicted according to equation (3) by adjusting the temperature or pressure as required.

`



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Figure 1. Snapshots of the united-atom methane sI (a) and sII (b) clathrate hydrates and carbon dioxide sI (c) and sII (d) clathrate hydrates at 270 K and 100 kPa after 5×106 MC moves. The united-atom methane and carbon atoms are represented by green balls, and the oxygen and hydrogen atoms are represented by red and white balls, respectively.

3. RESULTS AND DISCUSSION 3.1 Occupancy isotherms for single components The GCMC+MD simulations of pure CH4 and CO2 are firstly performed and the snapshots are provided in Figure 1 for visualization purpose. To investigate the structures of sI and sII hydrates obtained after the encapsulation of CH4, CO2, and CH4+CO2 (introduced in section 3.2), the tetrahedral order parameter F4 is used to distinguish the liquid-like disordered water molecules and hydrate-like ordered ones, which is defined as71 3

12 = 4 ∑4

93 56738

(7)

where φ is the H-O⸱⸱⸱O-H torsional angle for the water-water pairs within the distance RO,O of 3.5 Å, in which the hydrogen atoms is the outmost hydrogens in the water-water pairs. N is the number of the water-water pairs. The average F4 values for the perfect clathrate hydrate and liquid water are 0.7 and -0.04, respectively. For the sI (sII) clathrate hydrates encapsulated by CH4, CO2, and CH4+CO2 at 270 K and 100 kPa, the calculated values of F4 are 0.61 (0.65), 0.61 (0.66), and 0.61 (0.63), respectively, all of which are greater than 0.6 and close to 0.7. Therefore, the sI and sII hydrates obtained after the encapsulation of CH4, CO2, and its mixture maintain the clathrate hydrate structures and are not simple amorphous solutions even at the high temperature of 270 K. The occupancy isotherms of both sI and sII hydrates are investigated at four different temperatures (200K, 230K, 260K and 270K) and the gas pressures studied in occupancy isotherms are confirmed to be lower than the CH4 and CO2 liquefaction pressures. As shown in Figure 2, the cage occupancy of single components in both sI and sII hydrates decreases as the system temperature rises, while the encapsulation of CH4 and CO2 increases when the gas pressure increases until the occupancy isotherms reach the plateaus. In general, the cage occupancy of single components in sI hydrates is higher than that in sII hydrates under the same conditions except for the case of the double occupancy of CO2 occurring in the sII hydrate at 200K, indicating that adsorption capacities of both CH4 and CO2 in sI hydrates are generally stronger than those in sII hydrates. As one can see from Figure 2a and 2b, the cage occupancies of CH4 in sI and sII hydrates are not lager than 1, implying the single occupancy is dominant in different cavity types even at relatively high pressures. The occupancy isotherms of CH4 using methane UA and AA models in sI and sII hydrates can all be approximately described in terms of single site adsorption, indicating there is no clear preference between small and large cages. This may be attributed to the rather small diameter (4.36 Å) of a methane molecule compared with the small and large cage diameters of sI (sII) hydrates, which are 7.90 (7.82) Å and 8.66 (9.46) Å, respectively,1 and weak interaction between methane and `


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water in the cages. The occupancies obtained from the methane UA model are evidently higher than those obtained from the AA model, which is consistent with the previous simulations32,36-38, suggesting that the intermolecular interaction between methane and water molecules described by the UA model is stronger than that of the AA model. It is generally believed that AA models may provide more details on the molecular motion, while UA models exhibit better computational efficiency.72 Therefore, in order to find the intermolecular potential mimicking the UA model with similar adsorption behavior predicted by the AA model, we modified the cross-interaction term of the UA model between the methane molecule and the other atoms in the system by: : = ; ?

(9)

>? #

where the Langmuir constant (Kji) is temperature dependent and is given by:51 A = B / DEFG /

(10)

For the gas component j entering a cavity of type i, Aji and Bji can be fitted by the Langmuir-type adsorption isotherms. The encapsulation of CH4 in both sI and sII hydrates can be considered as one-site Langmuir-type adsorption, and the fitted A and B parameters for calculating the Langmuir constant are presented in Table 2. From the table, the sI methane hydrate manifests stronger adsorption capacities from the values of the parameters obtained by all the three models as compared to the sII methane hydrate. Specifically, the values of A and B for the sI methane hydrate are both greater than those for the sII hydrate by the UA and AA models. And the UA0.88 model predicts the very similar results for parameters with those of the AA model as expected. As seen from Figure 4, the occupancy ratio (θL/θS) between large and small cages of CH4 and CO2 in sI and sII hydrates tends to decrease with increasing gas pressure, but increase as the temperature rises, the trend of which is consistent with the experimental observations77 and previous simulation results36,40. The value of θL/θS for the sII hydrates is greater than that for the sI hydrate due to the larger size ratio between large and small cages. The occupancy ratio obtained by methane UA0.88 model is again similar to that of AA model and thus is not shown here. The values of θL/θS in sI and sII hydrates both approach 1.0 (1.00 for UA model and 1.01 for AA model at 200 K and 10 MPa) at the high enough pressures, implying the small cages `


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are filled after the large ones. The calculated θL/θS in the sI methane hydrate at 270 K and 6 MPa according to the Langmuir-type fractional occupancy isotherms (the fitted parameters are presented in Table 3) are 1.16 for the UA model and 1.40 for the AA model, which are in good accordance with the experimental values of ~1.26 at 270 K15 and 1.13~1.15 at 268 K73-75. Figure 4b shows that the occupancy ratios θL/θS of CO2 in sI and sII hydrates are rather large at low pressures, indicating that the small cages probably start to encapsulate the CO2 molecules after most of the large cages have been occupied. The values of θL/θS of CO2 in sI and sII hydrates are about 3.13 and 5.13 at 270 K and 1.5 MPa, respectively, comparable to experimental value of 8.333 at 273.15 K and 1.2 MPa78 and the predicted values of 1.908 and 1.347 by the CSMGem and CSMHYD programs79 at 273.15 K and 1.2 MPa for sI CO2 hydrate. Altogether, the calculated results are in reasonable agreement with the experimental data, demonstrating that our GCMC+MD simulations are valid for studying the adsorption of CH4 and CO2 in clathrate hydrates.

Figure 4. The occupancy ratios θL/θS of methane molecules (a) and carbon dioxide molecules (b) in large and small cages of the sI and sII hydrates as a function of temperatures and pressures.

The parameters Aji and Bji in Eq(10) can also be determined by the fractional occupancy isotherms of the gas species j in the cavity type i. Table 3 shows the values of the parameters Aji and Bji for the adsorption of pure CH4 and CO2 in both sI and sII hydrates, which can be compared with those reported calculation results80. The Langmuir constants Kji of pure CH4 and CO2 in large cages of both sI and sII hydrates are larger than those in small cages, and the temperature dependences of Langmuir constant calculated by different models are found consistent. The values of Bji in small and large cages are almost equal from all models for the sI methane hydrate, while the Aji values in large cages are larger than those in small cages. The UA0.88 model well resembles the AA model, and the UA model exhibits apparent differences compared with the AA and UA0.88 models. As a general trend for the methane sII hydrates from the table, the Aji values of the large cages are much greater than the small cages while the Bji values present the opposite trend, which is consistent with the MC simulations of Papadimitriou et al.37. Similar to the UA methane model, the parameters Aji and Bji for the adsorption of CO2 in large cages of the sI hydrate are apparently higher than those in small cages, and the distinction in Aji values between the large and small `



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cages for the CO2 sII hydrate is found even more significant than CH4. Table 3. The fitted parameter Aji (10-6 K·kPa-1), Bji (103 K), ∆ha (kJ/mol) and ∆s (J mol-1K-1) from fraction occupancy isotherms of different cavity types obtained from GCMC+MD simulations. Gas

Force Field

Structure

Small cavity A

CO2

CH4

EPM2

UA

AA

UA0.88

Mixture

B

∆ha

Large cavity ∆s

A

B

∆ha

∆s

sI

2.617

2.785

-24.956

-121.517

20.658

3.171

-28.391

-105.300

sII

1.513

2.781

-24.930

-126.124

657.029

2.379

-21.601

-75.672

sI

7.180

2.751

-24.711

-113.633

27.101

2.800

-25.189

-102.626

sII

3.412

2.868

-25.653

-119.370

172.367

2.428

-22.001

-86.761

sI

6.699

2.472

-22.371

-113.818

31.209

2.475

-22.387

-100.965

sII

4.101

2.522

-22.778

-117.823

213.670

2.090

-19.203

-85.035

sI

6.378

2.490

-22.528

-114.233

31.683

2.463

-22.284

-100.832

sII

3.685

2.551

-23.045

-118.838

188.327

2.142

-19.631

-86.071

sI

6.854

2.728

-24.485

-113.518

17.569

3.101

-27.957

-107.234

sII

1.473

2.990

-26.891

-127.311

156.406

2.617

-23.803

-88.567

EPM2+

sI

5.432

2.583

-23.303

-115.567

18.997

3.029

-27.237

-106.130

UA0.88

sII

1.030

2.842

-26.365

-133.305

0.311

4.033

-19.942

-73.674

EPM2+UA

Figure 5. The occupancy isotherms of the CO2+CH4 sI and sII hydrates at the CO2 concentration of 50% in the gas phase as a function of temperatures and pressures obtained by EPM2+UA (a) and EPM2+UA0.88 (b) models. The lines are the Langmuir-type isotherm-fitted curves.

In order to clarify the physical implication behind the fitted parameters, the Langmuir constant K has also been determined by the adsorption thermodynamic parameters here:81 A=

3

#%

exp K

∆L& ∆7 & M

(11)

where P0 is the standard pressure. ∆ha and ∆s are the respective heat and standard entropy of adsorption, which are fitted from the Langmuir-type curves describing the cage occupancies from the GCMC+MD simulations. ∆s reflects the restriction of the molecular mobility. From Table 3, ∆ha and ∆s for adsorption of CO2 in small and large cages in the sI hydrates are larger, i.e. more negative, than those of CH4, which `


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indicate that both the interaction energies of CO2 in small and large cages are stronger than those of CH4, and translational and rotational degrees of freedom for CO2 are more limited, being consistent with the results of quantum chemistry calculations82. From the table, the predictions from the AA and UA0.88 CH4 models are in excellent agreement. The values of ∆ha (-24.711 and -25.189 kJ/mol) in small and large cages of the sI hydrate obtained by CH4 UA model are more negative than those of -22.4~-22.5 and -22.3~-22.4 kJ/mol obtained by CH4 AA and UA0.88 models, respectively. From the current data, it is difficult to distinguish the small and large cages in the sI CH4 hydrate from the adsorption heat alone. Meanwhile, the values of ∆s (-113.6~-114.2 J/mol/K) in small cages of the sI hydrates are apparently more negative than those (-100.8~-102.6 J/mol/K) in large cages from all models, indicating that the adsorption of CH4 in large cages may be mainly entropy driven. As a result, all the adsorption capacities of large cages obtained from different methane models are only slightly stronger than that of small cages. Although the adsorption characteristics of CO2 in sI hydrates is similar to that of CH4, the discrepancy of the adsorption heat between large and small cages (-28.391 vs. -24.956 kJ/mol) is evidently larger as compared to CH4. Therefore, CH4 has moderate preference between the small and large cages of the sI hydrate, while the CO2 more strongly prefers to fill the large cages. For the sII hydrate, the values of ∆ha for CH4 and CO2 in large cages are smaller than those in small cages, implying that CH4 and CO2 do not prefer to occupy the large cages of the sII hydrate energetically. However, the adsorption entropy of -75.7~-86.8 J/mol/K is much larger in large cages, resulting in their stronger capacity. This can be understood by the large enough size of 51264 cages as compared with the molecular diameters of CH4 and CO2 to allow molecular motions. Therefore, the adsorption thermodynamics obtained from occupancy isotherms by the GCMC+MD simulations can well describe the adsorption mechanism of CH4 and CO2 encapsulated in clathrate hydrates.

3.2 Occupancy isotherms for gas mixture The occupancy isotherms of 1:1 mixtures of CO2 and CH4 in the gas phase for sI and sII hydrates obtained by the CO2 EPM2 model plus the CH4 UA or UA0.88 models (EMP2+UA or EMP2+UA0.88) are shown in Figure 5. As seen in the figure, the occupancy isotherms of sI and sII hydrates for mixtures are between those for pure CO2 and CH4, but the occupancy isotherms of CO2+CH4 obtained by the EPM2+UA0.88 model are similar to CO2 and the occupancy isotherms of CO2+CH4 by the EPM2+UA model resemble CH4 better. There are only single occupancies for the adsorption of CO2+CH4 in clathrate hydrates studied by the EPM2+UA model, while double occupancies of two CO2 molecules encapsulated in large cages of the sII hydrate can be found at low temperatures by the EMP2+UA0.88 model (in Figure S2). The adsorption of CO2+CH4 into sI and sII hydrates studied using the EPM2+UA model can be approximately described in terms of Langmuir-type adsorption. On the contrary, the occupancy isotherms of mixtures in sII clathrate hydrates by the EPM2+UA0.88 model appear to be two-site adsorptions. Actually, these deviations of adsorption behaviors between EPM2+UA and EPM2+UA0.88 models can be readily `



Page 14 of 35

understood from the fact that the capacity difference between the EPM2 carbon dioxide and UA0.88 methane models are much larger than that between the EPM2 and UA models from Table 3. The adsorption capacity of the gas mixture in sI hydrates is stronger than that in sII hydrates in most cases. The exception only appears at low temperature about 200 K and a pressure above 1500 (1000) kPa as shown in Figure 5a (5b). It indicates that the CO2+CH4 hydrate still stabilizes in form of the sI structure at ambient conditions. This prediction by EPM2+UA model as well as the EPM2+UA0.88 methane model is consistent with the experimental observations1. The fitted parameters A and B for the occupancy isotherms of CO2+CH4 studied by the EPM2+UA model are presented in Table 2 (The parameters for EPM2+UA0.88 are not shown since the adsorption does not well follow a Langmuir isotherm). From the data one may deduce that the higher occupancy of mixture in the sI hydrate rises from the much larger B value in the exponential term. As presented in Table 3, the adsorption heat and entropy of the gas mixture in small and large cages of sI and sII hydrates are similar to those of pure CH4 or CO2. The ∆ha and ∆s values of mixtures in sI hydrate by EPM2+UA and EPM2+UA0.88 models are coincident, although the adsorption thermodynamic parameters between UA methane and UA0.88 methane models are different. According to the calculation results on occupancies, the adsorption capacity of mixtures in large cages of both the sI and sII hydrates is stronger than that in small cages. One can also see that the difference of capacity between the large and small cages obtained by EPM2+UA0.88 model is higher than that of the EPM2+UA model, which may lead to a deviation from Langmuir-type adsorption model. To be explicit, even a two-site adsorption is apparently obtained at high temperatures by the EPM2+UA0.88 model for sII hydrate from Figure 5b. In addition, more detailed inspection finds from Table 3 that the adsorption thermodynamic parameters of mixture sI hydrates in small and large cages resemble those of pure CH4 in small cages and pure CO2 in large cages, respectively, irrespective of the model is adopted. This suggests that CO2 of mixtures prefers to occupy the large cages and CH4 tends to occupy the small cages at conditions near saturation, which is consistent with the results of accommodation rate provided in Figure S3, and the molar ratios of CO2 to CH4 in small and large cages of the sI hydrate at 270 K and 3 MPa obtained by the EMP2+UA (EMP2+UA0.88) models are 0.17 (0.26) and 2.46 (2.61). Then we investigated the abundance ratio of CO2 to CH4 and the CO2 molar concentration in the hydrate phase of the CO2+CH4 sI and sII hydrates. The O

U

abundance ratio of CO2 to CH4 is defined as: N = KOPQR M&KUPQR M, where yCO2 and yCH4 PST

PST

are the mole fractions of CO2 and CH4 in the hydrate phase, xCO2 and xCH4 are their mole fractions in the gas phase. As seen in Figure 6, both the abundance ratio of CO2 to CH4 and the CO2 concentration in the hydrate phase decrease as the pressure increases, which is in good agreement with the experimental observations22. The abundance ratio of CO2 to CH4 and the CO2 concentration in the hydrate phase of the sI hydrate are both greater than that of the sII hydrate, indicating that it is not conducive to operate the CO2-CH4 replacement process directly in the sII hydrate. `


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This is probably the result from the smaller number percentage (1/3) of the large cages in the total cages of the sII hydrate. Moreover, both the values of S and yCO2 obtained by the EPM2+UA0.88 model are larger than those obtained by the EPM2+UA model since the interaction between CH4 and H2O of the cages is weaker for the UA0.88 methane model. Correspondingly, the abundance ratio of CO2 to CH4 in the sI hydrate varies from 4.01 (23.85) to 1.03 (3.14) obtained by the EPM2+UA (EPM2+UA0.88) model, and the CO2 concentration in the hydrate phase varies from 0.80 (0.96) to 0.51 (0.76) in this study, which are all greater than the value of 0.50 in gas phase. The values of S and yCO2 in the sI hydrate are about 1.86 and 0.65 for the EPM2+UA model and 4.94 and 0.83 for the EPM2+UA0.88 model under the equilibrium pressure at 270 K, respectively, while the corresponding experimental values are ~1.8 and 0.6415,18,20. The results may suggest that the methane UA model provides better prediction than the AA model (represented by UA0.88) to study the adsorption of CH4 and its mixture in clathrate hydrates. In order to better understand the behavior of the gas mixture in the hydrate phase, the accommodation rate is also investigated at 270K using the UA model and the discussions are provided in the supporting information.

Figure 6. The abundance ratio (black symbols) of CO2 to CH4 and the CO2 concentration (red symbols) in the hydrate phase of the CO2+CH4 sI and sII hydrates obtained by the methane UA (a) and UA0.88 (b) models as a function of pressures and temperatures.

3.3 Phase equilibria for single-component gas and mixtures in clathrate hydrates In this section, the phase equilibria of gas hydrates by statistical thermodynamics are predicted from the calculated fractional occupancy (θij) using equation (3) as mentioned above. The Ice-Hydrate-Vapor (I-H-V) coexistence conditions of pure CH4, CO2 and their mixture (CO2:CH4=1:1 in the gas phase) from the GCMC+MD simulations are shown in Figure 7 along with experimental measurements1,13,83-89 as well as the results from previous MD90-96 and MC97-99 simulations. The phase equilibria of CH4 and CO2+CH4 clathrate hydrates predicted by the methane UA model are in good accord with the experimental results and are better than those predicted by the methane UA0.88 and AA models, while the phase equilibria of the CH4 hydrate calculated by methane UA0.88 model are almost identical as that calculated by the AA model. For CH4 sI hydrate in Figure 7(a), the phase diagrams below the ice point using TIP4PEw and UA models in the current study are fairly `



comparable to the free energy calculations in combination with semigrand MC simulations of Jin et al. using TIP4P/Ice and UA models99, and are apparently better than the direct-coexistence simulations of Conda et al.90 and Waage et al.98 and free energy calculations of Jin et al.99 using TIP4P/2005 and UA models since the TIP4P/2005 model underestimates the melting temperature of methane hydrate by ~20 K90-92. Noteworthy, it seems that the interpolation of our work using TIP4PEw and UA models to higher temperatures follows the similar trend with the direct-coexistence simulations of Tung et al94 performed by TIP4PEw and AA models which are in agreement with the experimental data and previous MD and MC simulations using TIP4P/Ice and UA models. This may be due to the adjustment in parameters made by Tung et al to describe the methane-water potential. As shown in Figure 7(b), the current simulations for CO2 sI hydrates are in good agreement with the experiments.1 Since Míguez et al91 suggested that the CO2 model has a much smaller effect on phase diagram compared with the water model, the adopted TIP4PEw water model can yield a better description for the phase equilibria of CO2 hydrates as compared with TIP4P/Ice and TIP4P/2005 models. Although the simulations of CO2+CH4 clathrate hydrates in this study (Figure 7(c)) are difficult to compare to the experiments directly due to the lack of measurement data below ice point, the overall trend of pressure-temperature phase curve is consistent with the experimental measures1 (48%~51% methane concentration in gas phase) and direct-coexistence results (60% methane concentration in gas phase) of Michalis et al.96. Moreover, from Figure 7a and 7c, the discrepancies of dissociation pressures between the EPM2+UA and EPM2+UA0.88 models are smaller than the ones between the UA and UA0.88 models. In other words, the predictions by UA0.88 model appear better after the encapsulation of CO2 molecules since the CO2-H2O interactions are stronger than the CH4-H2O interactions so that the difference between the UA and UA0.88 methane models is weakened. Therefore, the GCMC+MD simulation using TIP4PEw water, DACNIS-UA methane and EPM2 carbon dioxide models is a valid method to study the phase equilibria. Not surprisingly, the dissociation pressure of the CO2 clathrate hydrate is lower than that of CH4 clathrate hydrate at the same temperature, and the dissociation pressure of the CO2+CH4 clathrate hydrate is between those of CO2 and CH4 hydrates in this study. For the CH4 clathrate hydrate, the dissociation pressure of the sI hydrate is higher than that of the sII hydrate at low temperature, while it becomes less than that of the sII hydrate at high temperature according to our results. Hence, the CH4 sI hydrate is more stable at high temperature but it is possible to transform it to the sII hydrate by adjusting the temperature. Especially, the predicted conversion temperature is ~248 K, in agreement with the condition of natural gas hydrate reserved in ocean sediments and permafrost at 278~293 K100. For both the CO2 and CO2+CH4 clathrate hydrates, the sI hydrates are determined to possess lower dissociation pressure and thus are more stable than the sII hydrates. Moreover, the difference between the dissociation pressures of the sI and sII hydrates appears to be increased with the increasing temperature, indicating that the CO2 and CO2+CH4 sI hydrates are more likely to be formed relative to the sII hydrates and the relative `


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stability is enhanced at high temperatures. Namely, the mixing of CO2 into CH4 may have stabilization effect on sI hydrate below the ice point.

Figure 7. Temperature-pressure phase equilibria of (a) the CH4 sI and sII hydrates, (b) the CO2 sI and sII hydrates and (c) the CO2+CH4 sI and sII hydrates. The red symbols represent the calculations from the current GCMC+MD simulations; the violet symbols represent the 1,13,83-89

experimental data ; the calculated phase equilibria from the previous direct-coexistence simulations90-96 and GCMC simulations97-99 using TIP4PEw, TIP4P, TIP4P/2005, and TIP4P/Ice water models, different guest models are denoted as blue/black square, down triangle, diamond, and star symbols, respectively.

3.4 Dissociation heat of clathrate hydrates The heat of dissociation (∆hd) for the clathrate hydrates, which is defined as the enthalpy change to dissociate hydrate phase to a vapor and ice, can be calculated by Clausius-Clapeyron equation101: V WX #

V3⁄$

=

∆YZ [\

(12)

Here z is the compressibility factor of the gas and is set to unity in this study since this would not cause a significant difference in the calculated value of ∆hd.33 The heats of dissociation have been determined by the slope of the linear fitting of lnP versus 1/T and the calculated results for CH4, CO2 and CO2+CH4 sI and sII hydrates are presented in Table 4 with the experimental values displayed for comparison. As listed, ∆hd calculated from phase equilibria data by the UA methane model (or EPM2+UA) are in good agreement with the experimental results, and appear to be more satisfactory than those by the AA and UA0.88 models. ∆hd of CO2 hydrates are larger `



Page 18 of 35

than that of CH4 hydrates, further confirming that the CO2 hydrates are more stable than the CH4 hydrates. Furthermore, the dissociation heat of CO2+CH4 hydrates resembles that of CO2 hydrate better, which is slightly larger than those reported by Lee at al20 with yCO2=58.2% and by Kwon et al.102 with yCO2=~60% due to the more concentration of CO2 in hydrate phase in current study, indicating again that the replacement of CH4 with CO2 in CH4 hydrates will stabilize the clathrate hydrate. This can be readily understood from the calculation results that the sI clathrate hydrate with CO2 in large cages and CH4 in small cages has the lowest configurational energy compared with the fully occupied pure CH4 and CO2 sI hydrates103. It should be noted that the current GCMC+MD simulations using TIP4PEw water model can provide better results of ∆hd (14.57~16.32 kJ/mol) for methane sI hydrate compared with the experimental data of 17.47~18.12 kJ/mol104,105 (Table 4) than those (45.77~50.65 kJ/mol) predicted by free energy calculations in combination with MC simulations using TIP4P/2005 or TIP4P/Ice water model,99 which is another indication that the TIP4PEw model appears to have better predictability for the heat of dissociation of clathrate hydrates. In addition, ∆hd for the sII hydrates are greater than that of the sI hydrates for all gases, which is consistent with previous calculation results,26 owing to the more number of cage per water molecule in the sII hydrate. This may imply entropy is a decisive factor for the formation of hydrates. 3.5 Hydration number Finally, the equilibrium hydration number n (the water molecules per guest molecule) can be determined based on the enthalpies of formation for hydrates from gas and ice (∆H1), and from gas and water (∆H2) proposed by de Forcrand112: Gas + nH2O(I) ↔ Gas·nH2O (H) ∆H1 Gas + nH2O(L) ↔ Gas·nH2O (H) ∆H2 nH2O(I) ↔ nH2O(L) ∆H3 The I, L, and H in parentheses represent the ice, liquid water, and hydrate phases, respectively. Apparently, ∆H3 = ∆H1 - ∆H2, which is the fusion enthalpy of water, and is well known to be 6.008n kJ/mol at 273.15 K1. Thus one has =

∆] ^∆R _.`

at ~273K,

where ∆H1 is calculated from the current work and equal to -∆hd (Table 4), and the ∆H2 values of pure CH4, pure CO2, and CO2+CH4 sI hydrates are -54.1, -57.1 and -55.5 kJ/mol, respectively, taken from experimental measurements20. The hydration number of sII hydrate are estimated from the results of GCMC+MD simulations at 270 K and its equilibrium pressure. As shown in Table 4, the calculated hydration number of the CH4, CO2 and CO2+CH4 sI hydrates by the UA methane model (or or EPM2+UA) are in good agreement with the previous experimental and theoretical studies at ~273 K20,74,102,104-111, and the UA methane model provides better results compared with the other two methane models. It can be found that the hydration number of the CO2+CH4 sI hydrate is less than those of both the CO2 and CH4 sI hydrates, indicating that the adsorbed gas of sI hydrate from the mixture is more than that in the single component system under equilibrium condition. The hydration number of methane sII hydrates are larger than that of sI hydrate from the UA model, `


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which appears to provide more reasonable prediction than the AA and UA0.88 models. The hydration number of CO2 and CO2+CH4 sII hydrates are larger than those of sI hydrates and the values by the UA0.88 and UA models are in good accord. By calculating the n values, one can obtain a clear description on solvation of the gases in hydrates. Particularly, the difference in the n value between sI and sII hydrates for CO2 and CO2+CH4 mixture is apparently greater than CH4, which provides a direct view to the difference in phase stability for different gases or mixtures. Table 4. The heat of dissociation and hydration number for the CO2, CH4 and CO2+CH4 clathrate hydrates. Gas component CH4

Structure sI

Force field Expt.

∆hd (kJ/mol)

n 104

17.73,18.12±0.27

,

105

17.47±0.10

sII

CO2

sI

6.05,6.00±0.01104,5.90±0.30105, 6.2±0.2106, 5.99±0.07107,5.9574

UA

16.32

6.29

AA

15.13

6.49

UA0.88

14.57

6.58

UA

18.30

6.59

AA

16.77

6.17

UA0.88

17.71

6.27

Expt.

21.13,23.77±0.40108

5.99,6.6±0.3108,7.0109, 6.07110,6.21111

CO2+CH4

EPM2

20.22

6.14

sII

EPM2

21.75

9.83

sI

Expt.

18.5520,20.28102

6.1520

EPM2+UA

20.48

5.83

EPM2+UA0.88

21.38

5.68

EPM2+UA

21.82

7.49

EPM2+UA0.88

25.63

7.59

sII

4. CONCLUSIONS In this paper, the occupancy isotherms of CH4, CO2 and their mixture in the sI and sII hydrates are studied using hybrid GCMC+MD simulations with the TIP4PEw water, DACNIS-UA/modified UA0.88/TraPPE-AA methane and EPM2 carbon dioxide models. The modified UA0.88 model well reproduces the thermodynamics predicted from the TraPPE-AA model and thus the UA0.88 model can replace the AA model to study the adsorption of its mixtures with better computational efficiency. We have obtained the occupancy ratio θL/θS, the abundance ratio of CO2 to CH4 and the CO2 concentration in hydrate phase, all of which are in good agreement with the experimental results. A temperature-dependent Langmuir-type adsorption model is fitted to the present occupancy isotherms from GCMC+MD simulations. It is found that the encapsulation of CH4 and CO2+CH4 in the sI and sII hydrates can be approximately described in terms of a one-site adsorption. The adsorption parameters are predicted by which one may gain new insight into the thermodynamics for `



formation of different hydrates. The phase equilibria of the CH4, CO2 and CO2+CH4 sI and sII hydrates are predicted from the fractional occupancy isotherms in cavity types. The calculated phase equilibria can be favorably compared with the experimental measures and the previous MD and MC simulations. The phase equilibria of the CO2+CH4 hydrates are located between that of the CH4 and CO2 hydrates and the mixing of CO2 into CH4 may have stabilization effect on sI hydrate below the ice point according to our data. The heat of dissociation and hydration number of CH4, CO2 and CO2+CH4 hydrates are estimated from their phase equilibria, which are consistent with the previous experimental and predicted results. It can be found that the heat of dissociation and hydration number for the sII hydrates are larger than that of the sI hydrates. Therefore, the hybrid GCMC+MD simulations with the TIP4PEw water, DACNIS-UA methane and EPM2 carbon dioxide models can provide accurate description on the adsorption of CH4, CO2 and CO2+CH4 into clathrate hydrates and can be used to determine clathrate hydrate phase equilibria and the other thermodynamics data for the CO2-CH4 replacement phenomenon.

ASSOCIATED CONTENT S Supporting Information ○ The Supporting Information about the comparisons of cage occupancies for CH4 sII hydrate and CO2 sI hydrate from the current study with the experimental data and previous MC simulations, the structure for the double occupancy of two CO2 enclathrated in 51264 cage of the sII hydrate obtained by the EMP2+UA0.88 model and the accommodation rate of gas mixture in hydrate phase is provided in doc file.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. (S.D.) ORCID Shiyu Du: 0000-0001-6707-3915 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The authors acknowledge the support of the National Key Research and Development Program of China (No. 2016YFB0700100), National Science Foundation for Young Scientists of China (Grant No. 21707147), the Foundation of State Key Laboratory of Coal Conversion (Grant No. J15-16-301), Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC037), National Science Foundation for Post-doctoral Scientists of China (Grant No. 2017M612045), Natural Science Foundation of Ningbo (Grant Nos. 2014A610006, 2016A610273), One Thousand Youth Talents plan, the key technology of nuclear `


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energy, 2014, CAS Interdisciplinary Innovation Team and K.C.Wong Education Foundation (rczx0800). The authors also acknowledge the support of Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) (U1501501 to Juan Li and Aiguo Wu) and ITaP at Purdue University for computing resources.

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