Molecular dynamics simulation of CO2hydrates: Prediction of three phase coexistence line

A Molecular Dynamics Study on Xe/Kr Separation Mechanisms Using Crystal Growth Method

The separation of xenon/krypton gas mixtures is a valuable but challenging endeavor in the gas industry due to their similar physical characteristics and closely sized molecules. To address this, we investigated the effectiveness of the hydrate-based gas separation method for mixed Xe-Kr gas via molecular dynamics (MD) simulations. The formation process of hydrates facilitates the encapsulation of guest molecules within hydrate cages, offering a potential strategy for gas separation. Higher temperatures and pressures are advantageous for accelerating the hydrate growth rate. The final occupancy of guest molecules and empty cages within 512, 51264, and all hydrate cages were thoroughly examined. An increase in the pressure and temperature enhanced the occupancy rates of Xe in both 512 and 51264 cages, whereas elevated pressure alone improved the occupancy of Kr in 51264 cages. However, the impact of temperature and pressure on Kr occupancy within 512 cages was found to be minimal. Elevated temperature and pressure resulted in a reduced occupancy of empty cages. Predominantly, 51264 cages were occupied by Xe, whereas Kr showed a propensity to occupy the 512 cages. With increasing simulated pressure, the final occupancy of Xe molecules in all cages rose from 0.37 to 0.41 for simulations at 260 K, while the final occupancy of empty cages decreased from 0.24 to 0.2.

Computer Simulation of Three-Phase Equilibria for Some Water/n-Alkane Binary Systems

In this work, the vapor-liquid-liquid equilibrium (VLLE) of the water/n-pentane, water/n-hexane, water/n-octane, and water/n-decane binary systems is calculated by computer simulation using the NVT-Gibbs ensemble (in the version of three simulation boxes) combined with the configurational bias Monte Carlo method. The combination of both methods, the molecular potential models used, and the simulation details allowed us to calculate the triphasic equilibrium properties of the systems studied: the densities of the three phases in equilibrium, their compositions, and potential energies. In previous works, these simulations were not carried out at a temperature range nor water/n-alkanes systems simulated in this work, probably because they are highly nonideal systems; so, to the best of our knowledge, this is the first time that this phenomenon is studied in detail. The results from VLLE simulations of the water/n-pentane system for temperatures from 343.2 to 435 K, the water/n-hexane system for temperatures from 373.11 to 473.15 K, the water/n-octane system for temperatures from 310.9 to 500 K, and for the water/n-decane system for temperatures from 374.15 to 525 K are reported here. The temperature range was selected in concordance with the experimental data available for an adequate study of the VLLE simulation results. The subcritical densities (vapor and liquid rich in n-alkane phases) at various temperatures fit well with the scaling law and the law of rectilinear diameters, allowing the estimation of upper critical end point temperature and density of the VLLE. The simulation results show a good prediction with experimental data reports in the literature.

Three-phase equilibria of hydrates from computer simulation. II. Finite-size effects in the carbon dioxide hydrate

In this work, the effects of finite size on the determination of the three-phase coexistence temperature (T3) of the carbon dioxide (CO2) hydrate have been studied by molecular dynamic simulations and using the direct coexistence technique. According to this technique, the three phases involved (hydrate-aqueous solution-liquid CO2) are placed together in the same simulation box. By varying the number of molecules of each phase, it is possible to analyze the effect of simulation size and stoichiometry on the T3 determination. In this work, we have determined the T3 value at 8 different pressures (from 100 to 6000 bar) and using 6 different simulation boxes with different numbers of molecules and sizes. In two of these configurations, the ratio of the number of water and CO2 molecules in the aqueous solution and the liquid CO2 phase is the same as in the hydrate (stoichiometric configuration). In both stoichiometric configurations, the formation of a liquid drop of CO2 in the aqueous phase is observed. This drop, which has a cylindrical geometry, increases the amount of CO2 available in the aqueous solution and can in some cases lead to the crystallization of the hydrate at temperatures above T3, overestimating the T3 value obtained from direct coexistence simulations. The simulation results obtained for the CO2 hydrate confirm the sensitivity of T3 depending on the size and composition of the system, explaining the discrepancies observed in the original work by Míguez et al. [J. Chem Phys. 142, 124505 (2015)]. Non-stoichiometric configurations with larger unit cells show a convergence of T3 values, suggesting that finite-size effects for these system sizes, regardless of drop formation, can be safely neglected. The results obtained in this work highlight that the choice of a correct initial configuration is essential to accurately estimate the three-phase coexistence temperature of hydrates by direct coexistence simulations.

Three-phase equilibria of hydrates from computer simulation. I. Finite-size effects in the methane hydrate

Clathrate hydrates are vital in energy research and environmental applications. Understanding their stability is crucial for harnessing their potential. In this work, we employ direct coexistence simulations to study finite-size effects in the determination of the three-phase equilibrium temperature (T3) for methane hydrates. Two popular water models, TIP4P/Ice and TIP4P/2005, are employed, exploring various system sizes by varying the number of molecules in the hydrate, liquid, and gas phases. The results reveal that finite-size effects play a crucial role in determining T3. The study includes nine configurations with varying system sizes, demonstrating that smaller systems, particularly those leading to stoichiometric conditions and bubble formation, may yield inaccurate T3 values. The emergence of methane bubbles within the liquid phase, observed in smaller configurations, significantly influences the behavior of the system and can lead to erroneous temperature estimations. Our findings reveal finite-size effects on the calculation of T3 by direct coexistence simulations and clarify the system size convergence for both models, shedding light on discrepancies found in the literature. The results contribute to a deeper understanding of the phase equilibrium of gas hydrates and offer valuable information for future research in this field.

Three-phase equilibria of hydrates from computer simulation. III. Effect of dispersive interactions in the methane and carbon dioxide hydrates

In this work, the effect of the range of dispersive interactions in determining the three-phase coexistence line of the CO2 and CH4 hydrates has been studied. In particular, the temperature (T3) at which solid hydrate, water, and liquid CO2/gas CH4 coexist has been determined through molecular dynamics simulations using different cutoff values (from 0.9 to 1.6 nm) for dispersive interactions. The T3 of both hydrates has been determined using the direct coexistence simulation technique. Following this method, the three phases in equilibrium are put together in the same simulation box, the pressure is fixed, and simulations are performed at different temperatures T. If the hydrate melts, then T > T3. Conversely, if the hydrate grows, then T < T3. The effect of the cutoff distance on the dissociation temperature has been analyzed at three different pressures for CO2 hydrate: 100, 400, and 1000 bar. Then, we have changed the guest and studied the effect of the cutoff distance on the dissociation temperature of the CH4 hydrate at 400 bar. Moreover, the effect of long-range corrections for dispersive interactions has been analyzed by running simulations with homo- and inhomogeneous corrections and a cutoff value of 0.9 nm. The results obtained in this work highlight that the cutoff distance for the dispersive interactions affects the stability conditions of these hydrates. This effect is enhanced when the pressure is decreased, displacing the T3 about 2-4 K depending on the system and the pressure.

Modeling oceanic sedimentary methane hydrate growth through molecular dynamics simulation

The crystallization process of methane hydrates in a confined geometry resembling seabed porous silica sedimentary conditions has been studied using molecular dynamics simulations. With this objective in mind, a fully atomistic quartz silica slit pore has been designed, and the temperature stability of a methane hydrate crystalline seed in the presence of water and guest molecule methane has been analyzed. NaCl ion pairs have been added in different concentrations, simulating salinity conditions up to values higher than average oceanic conditions. The structure obtained when the hydrate crystallizes inside the pore is discussed, paying special attention to the presence of ionic doping inside the hydrate and the subsequent induced structural distortion. The shift in the hydrate stability conditions due to the increasing water salinity is discussed and compared with the case of unconfined hydrate, concluding that the influence of the confinement geometry and pore hydrophilicity produces a larger deviation in the confined hydrate phase equilibria.

Mechanical properties of amorphous CO2 hydrates: insights from molecular simulations

Understanding physicochemical properties of amorphous gas hydrate systems is of great significance to reveal structural stabilities of polycrystalline gas hydrate systems. Furthermore, amorphous gas hydrates can occur ordinarily in the nucleation events of gas hydrate systems. Herein, the mechanical properties of amorphous carbon dioxide hydrates are examined by means of all-atom classical molecular dynamic simulations. Our molecular simulation results reveal that mechanical strengths of amorphous carbon dioxide hydrates are evidently governed by temperatures, confining pressures, and ratios of water to carbon dioxide molecules. Notably, under compressive loads, amorphous carbon dioxide hydrates firstly exhibit monotonic strain hardening, followed by an interesting distinct phenomenon characterized by a steady flow stress at further large deformation strains. Furthermore, structural evolutions of amorphous carbon dioxide hydrates are analyzed on the basis of the N-Hbond DOP order parameter. These important findings can not only contribute to our understanding of the structural stabilities of amorphous gas hydrate systems, but also help to develop fundamental understandings about grain boundaries of gas hydrate systems.

Understanding the effect of moderate concentration SDS on CO2 hydrates growth in the presence of THF

Hypothesis Additives like Tetrahydrofuran (THF) and Sodium Dodecylsulfate (SDS) improve Carbon Dioxide (CO2) hydrates thermal stability and growth rate when used separately. It has been hypothesised that combining them could improve the kinetics of growth and the thermodynamic stability of CO2 hydrates. Simulations and Experiments We exploit atomistic molecular dynamics simulations to investigate the combined impact of THF and SDS under different temperatures and concentrations. The simulation insights are verified experimentally using pendant drop tensiometry conducted at ambient pressures and high-pressure differential scanning calorimetry. Findings Our simulations revealed that the combination of both additives is synergistic at low temperatures but antagonistic at temperatures above 274.1 K due to the aggregation of SDS molecules induced by THF molecules. These aggregates effectively remove THF and CO2 from the hydrate-liquid interface, thereby reducing the driving force for hydrates growth. Experiments revealed that the critical micelle concentration of SDS in water decreases by 20% upon the addition of THF. Further experiments in the presence of THF showed that only small amounts of SDS are sufficient to increase the CO2 storage efficiency by over 40% compared to results obtained without promoters. Overall, our results provide microscopic insights into the mechanisms of THF and SDS promoters on CO2 hydrates, useful for determining the optimal conditions for hydrate growth.

Cage occupancies of CH4, CO2, and Xe hydrates: Mean field theory and grandcanonical Monte Carlo simulations

We propose a statistical mechanical theory for the thermodynamic stability of clathrate hydrates, considering the influence of the guest-guest interaction on the occupancies of the cages. A mean field approximation is developed to examine the magnitude of the influence. Our new method works remarkably well, which is manifested by two sorts of grandcanonical Monte Carlo (GCMC) simulations. One is full GCMC, and the other is designed in the present study for clathrate hydrates, called lattice-GCMC, in which each guest can be adsorbed at one of the centers of the cage. In the latter simulation, only the guest-guest interaction is explicitly treated, incorporating the host-guest interaction into the free energy of the cage occupation without other guests. Critical phenomena for guest species, such as large density fluctuations, are observed when the temperature is low or the guest-guest interaction is strong.

Efficiency and energy balance for substitution of CH4 in clathrate hydrates with CO2 under multiple-phase coexisting conditions

Many experimental and theoretical studies on CH4-CO2 hydrates have been performed aiming at the extraction of CH4 as a relatively clean energy resource and concurrent sequestration of CO2. However, vague or insufficient characterization of the environmental conditions prevents us from a comprehensive understanding of even equilibrium properties of CH4-CO2 hydrates for this substitution. We propose possible reaction schemes for the substitution, paying special attention to the coexisting phases, the aqueous and/or the fluid, where CO2 is supplied from and CH4 is transferred to. We address the two schemes for the substitution operating in three-phase and two-phase coexistence. Advantages and efficiencies of extracting CH4 in the individual scheme are estimated from the chemical potentials of all the components in all the phases involved in the substitution on the basis of a statistical mechanical theory developed recently. It is found that although substitution is feasible in the three-phase coexistence, its working window in temperature-pressure space is much narrower compared to the two-phase coexistence condition. Despite that the substitution normally generates only a small amount of heat, a large endothermic substitution is suggested in the medium pressure range, caused by the vaporization of liquid CO2 due to mixing with a small amount of the released CH4. This study provides the first theoretical framework toward the practical use of hydrates replacing CH4 with CO2 and serves as a basis for quantitative planning.

Molecular Dynamics Simulation of the Three-Phase Equilibrium Line of CO2 Hydrate with OPC Water Model

The three-phase coexistence line of the CO2 hydrate was determined using molecular dynamics (MD) simulations. By using the classical and modified Lorentz-Berthelot (LB) parameters, the simulations were carried out at 10 different pressures from 3 to 500 MPa. For the OPC water model, simulations with the classic and the modified LB parameters both showed negative deviations from the experimental values. For the TIP4P/Ice water model, good agreement with experimental equilibrium data can be achieved when the LB parameter is adjusted based on the solubility of CO2 in water. Our results also show that the influence of the water model on the equilibrium prediction is much larger than the CO2 model. Current simulations indicated that the H2O-H2O and H2O-CO2 cross-interactions' parameters might contribute equally to the accurate prediction of T3. According to our simulations, the prediction of T3 values showed relatively higher accuracy while using the combination of TIP4P/Ice water and EPM2 CO2 with modified LB parameter. Furthermore, varied χ values are recommended for accurate T3 estimation over a wide pressure range. The knowledge obtained in this study will be helpful for further accurate MD simulation of the process of CO2/CH4 replacement.

On the phase behaviors of CH4-CO2 binary clathrate hydrates: Two-phase and three-phase coexistences

We develop a statistical mechanical theory on clathrate hydrates in order to explore the phase behaviors of clathrate hydrates containing two kinds of guest species and apply it to CH4-CO2 binary hydrates. The two boundaries separating water and hydrate and hydrate and guest fluid mixtures are estimated, which are extended to the lower temperature and the higher pressure region far distant from the three-phase coexisting conditions. The chemical potentials of individual guest components can be calculated from free energies of cage occupations, which are available from intermolecular interactions between host water and guest molecules. This allows us to derive all thermodynamic properties pertinent to the phase behaviors in the whole space of thermodynamic variables of temperature, pressure, and guest compositions. It is found that the phase boundaries of CH4-CO2 binary hydrates with water and with fluid mixtures locate between simple CH4 and CO2 hydrates, but the composition ratios of CH4 guests in hydrates are disproportional to those in fluid mixtures. Such differences arise from the affinities of each guest species to the large and small cages of CS-I hydrates and significantly affect occupation of each cage type, which results in a deviation of the guest composition in hydrates from that in fluid on the two-phase equilibrium conditions. The present method provides a basis for the evaluation of the efficiency of the guest CH4 replacement to CO2 at the thermodynamic limit.

Microscopic insights on clathrate hydrate growth from non-equilibrium molecular dynamics simulations

Clathrate hydrates form and grow at interfaces. Understanding the relevant molecular processes is crucial for developing hydrate-based technologies. Many computational studies focus on hydrate growth within the aqueous phase using the 'direct coexistence method', which is limited in its ability to investigate hydrate film growth at hydrocarbon-water interfaces. To overcome this shortcoming, a new simulation setup is presented here, which allows us to study the growth of a methane hydrate nucleus in a system where oil-water, hydrate-water, and hydrate-oil interfaces are all simultaneously present, thereby mimicking experimental setups. Using this setup, hydrate growth is studied here under the influence of two additives, a polyvinylcaprolactam oligomer and sodium dodecyl sulfate, at varying concentrations. Our results confirm that hydrate films grow along the oil-water interface, in general agreement with visual experimental observations; growth, albeit slower, also occurs at the hydrate-water interface, the interface most often interrogated via simulations. The results obtained demonstrate that the additives present within curved interfaces control the solubility of methane in the aqueous phase, which correlates with hydrate growth rate. Building on our simulation insights, we suggest that by combining data for the potential of mean force profile for methane transport across the oil-water interface and for the average free energy required to perturb a flat interface, it is possible to predict the performance of additives used to control hydrate growth. These insights could be helpful to achieve optimal methane storage in hydrates, one of many applications which are attracting significant fundamental and applied interests.

Effect of pressure on the carbon dioxide hydrate-water interfacial free energy along its dissociation line

We investigate the effect of pressure on the carbon dioxide (CO2) hydrate-water interfacial free energy along its dissociation line using advanced computer simulation techniques. In previous works, we have determined the interfacial energy of the hydrate at 400 bars using the TIP4P/Ice and TraPPE molecular models for water and CO2, respectively, in combination with two different extensions of the Mold Integration technique [J. Colloid Interface Sci. 623, 354 (2022) and J. Chem. Phys. 157, 134709 (2022)]. Results obtained from computer simulation, 29(2) and 30(2) mJ/m2, are found to be in excellent agreement with the only two measurements that exist in the literature, 28(6) mJ/m2 determined by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)] and 30(3) mJ/m2 determined by Anderson et al. [J. Phys. Chem. B 107, 3507 (2002)]. Since the experiments do not allow to obtain the variation of the interfacial energy along the dissociation line of the hydrate, we extend our previous studies to quantify the effect of pressure on the interfacial energy at different pressures. Our results suggest that there exists a correlation between the interfacial free energy values and the pressure, i.e., it decreases with the pressure between 100 and 1000 bars. We expect that the combination of reliable molecular models and advanced simulation techniques could help to improve our knowledge of the thermodynamic parameters that control the interfacial free energy of hydrates from a molecular perspective.

Solubility of carbon dioxide in water: Some useful results for hydrate nucleation

In this paper, the solubility of carbon dioxide (CO2) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and the TraPPE model for CO2. In particular, the solubility of CO2 in water when in contact with the CO2 liquid phase and the solubility of CO2 in water when in contact with the hydrate have been determined. The solubility of CO2 in a liquid-liquid system decreases as the temperature increases. The solubility of CO2 in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar (T3). We compare the predictions with T3 obtained using the direct coexistence technique in a previous work. The results of both methods agree, and we suggest 290(2) K as the value of T3 for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrates along the isobar. The new approach is based on the use of the solubility curve of CO2 when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO2, providing reliable values for the driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of dispersive interactions and the occupancy of CO2 on the driving force for nucleation of the hydrate.

Chemical Promoter Performance for CO2 Hydrate Growth: A Molecular Perspective

Carbon dioxide (CO₂) hydrates, which contain a relatively large amount of captured CO₂ (almost 30 wt % of CO₂ with the balance being water), represent a promising CO₂ sequestration option for climate change mitigation. To facilitate CO₂ storage via hydrates, using chemical additives during hydrate formation might help to expedite formation/growth rates, provided the additives do not reduce the storage capacity. Implementing atomistic molecular dynamics, we study the impact of aziridine, pyrrolidine, and tetrahydrofuran (THF) on the kinetics of CO₂ hydrate growth/dissociation. Our simulations are validated via reproducing experimental data for CO₂ and CO₂ + THF hydrates at selected operating conditions. The simulated results show that both aziridine and pyrrolidine could perform as competent thermodynamic and kinetic promoters. Furthermore, aziridine seems to exceed pyrrolidine and THF in expediting the CO₂ hydrate growth rates under the same conditions. Our analysis unveils direct correlations between the kinetics of CO₂ hydrate growth and a combination of the free energy barrier for desorption of CO₂ from the hydrate surface and the binding free energy of chemical additives adsorbed at the growing hydrate substrate. The detailed thermodynamic analysis conducted in both hydrate and aqueous phases reveals molecular-level mechanisms by which CO₂ hydrate promoters are active, which could help to enable the implementation of CO₂ sequestration in hydrate-bearing reservoirs.

Molecular Simulation of CO2 and H2 Encapsulation in a Nanoscale Porous Liquid

In this study we analyse from a theoretical perspective the encapsulation of both gaseous H2 and CO2 at different conditions of pressure and temperature in a Type II porous liquid, composed by nanometric scale cryptophane-111 molecules dispersed in dichloromethane, using atomistic molecular dynamics. Gaseous H2 tends to occupy cryptophane-111's cavities in the early stages of the simulation; however, a remarkably greater selectivity of CO2 adsorption can be seen in the course of the simulation. Calculations were performed at ambient conditions first, and then varying temperature and pressure, obtaining some insight about the different adsorption found in each case. An evaluation of the host molecule cavities accessible volume was also performed, based on the guest that occupies the pore. Finally, a discussion between the different intermolecular host-guest interactions is presented, justifying the different selectivity obtained in the molecular simulation calculations. From the results obtained, the feasibility of a renewable separation and storage method for CO2 using these nanometric scale porous liquids is pointed out.

Phase equilibria molecular simulations of hydrogen hydrates via the direct phase coexistence approach

We report the three-phase (hydrate-liquid water-vapor) equilibrium conditions of the hydrogen-water binary system calculated with molecular dynamics simulations via the direct phase coexistence approach. A significant improvement of ∼10.5 K is obtained in the current study, over earlier simulation attempts, by using a combination of modifications related to the hydrogen model that include (i) hydrogen Lennard-Jones parameters that are a function of temperature and (ii) the water-guest energy interaction parameters optimized further by using the Lorentz-Berthelot combining rules, based on an improved description of the solubility of hydrogen in water.

Solubility of Methane in Water: Some Useful Results for Hydrate Nucleation

In this paper, the solubility of methane in water along the 400 bar isobar is determined by computer simulations using the TIP4P/Ice force field for water and a simple LJ model for methane. In particular, the solubility of methane in water when in contact with the gas phase and the solubility of methane in water when in contact with the hydrate has been determined. The solubility of methane in a gas-liquid system decreases as temperature increases. The solubility of methane in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the triple point T₃ at a certain pressure. We also determined T₃ by the three-phase direct coexistence method. The results of both methods agree, and we suggest 295(2) K as the value of T₃ for this system. We also analyzed the impact of curvature on the solubility of methane in water. We found that the presence of curvature increases the solubility in both the gas-liquid and hydrate-liquid systems. The change in chemical potential for the formation of hydrate is evaluated along the isobar using two different thermodynamic routes, obtaining good agreement between them. It is shown that the driving force for hydrate nucleation under experimental conditions is higher than that for the formation of pure ice when compared at the same supercooling. We also show that supersaturation (i.e., concentrations above those of the planar interface) increases the driving force for nucleation dramatically. The effect of bubbles can be equivalent to that of an additional supercooling of about 20 K. Having highly supersaturated homogeneous solutions makes possible the spontaneous formation of the hydrate at temperatures as high as 285 K (i.e., 10K below T₃). The crucial role of the concentration of methane for hydrate formation is clearly revealed. Nucleation of the hydrate can be either impossible or easy and fast depending on the concentration of methane which seems to play the leading role in the understanding of the kinetics of hydrate formation.

Modeling of Structure H Carbon Dioxide Clathrate Hydrates: Guest-Lattice Energies, Crystal Structure, and Pressure Dependencies

We performed first-principles computations to investigate the complex interplay of molecular interaction energies in determining the lattice structure and stability of CO₂@sH clathrate hydrates. Density functional theory computations using periodic boundary conditions were employed to characterize energetics and the key structural properties of the sH clathrate crystal under pressure, such as equilibrium lattice volume and bulk modulus. The performance of exchange-correlation functionals together with recently developed dispersion-corrected schemes was evaluated in describing interactions in both short-range and long-range regions of the potential. Structural relaxations of the fully CO₂-filled and empty sH unit cells yield crystal structure and lattice energies, while their compressibility parameters were derived by including the pressure dependencies. The present quantum chemistry computations suggest anisotropy in the compressibility of the sH clathrate hydrates, with the crystal being less compressible along the a-axis direction than along the c-axis one, in distinction from nearly isotropic sI and sII structures. The detailed results presented here give insight into the complex nature of the underlying guest-host interactions, checking earlier assumptions, providing critical tests, and improving estimates. Such entries may eventually lead to better predictions of thermodynamic properties and formation conditions, with a direct impact on emerging hydrate-based technologies.

Simulation of the carbon dioxide hydrate-water interfacial energy

HYPOTHESIS

Carbon dioxide hydrates are ice-like nonstoichiometric inclusion solid compounds with importance to global climate change, and gas transportation and storage. The thermodynamic and kinetic mechanisms that control carbon dioxide nucleation critically depend on hydrate-water interfacial free energy. Only two independent indirect experiments are available in the literature. Interfacial energies show large uncertainties due to the conditions at which experiments are performed. Under these circumstances, we hypothesize that accurate molecular models for water and carbon dioxide combined with computer simulation tools can offer an alternative but complementary way to estimate interfacial energies at coexistence conditions from a molecular perspective.

CALCULATIONS

We have evaluated the interfacial free energy of carbon dioxide hydrates at coexistence conditions (three-phase equilibrium or dissociation line) implementing advanced computational methodologies, including the novel Mold Integration methodology. Our calculations are based on the definition of the interfacial free energy, standard statistical thermodynamic techniques, and the use of the most reliable and used molecular models for water (TIP4P/Ice) and carbon dioxide (TraPPE) available in the literature.

FINDINGS

We find that simulations provide an interfacial energy value, at coexistence conditions, consistent with the experiments from its thermodynamic definition. Our calculations are reliable since are based on the use of two molecular models that accurately predict: (1) The ice-water interfacial free energy; and (2) the dissociation line of carbon dioxide hydrates. Computer simulation predictions provide alternative but reliable estimates of the carbon dioxide interfacial energy. Our pioneering work demonstrates that is possible to predict interfacial energies of hydrates from a truly computational molecular perspective and opens a new door to the determination of free energies of hydrates.

A novel hybrid method for the calculation of methane hydrate-water interfacial tension along the three-phase (hydrate-liquid water-vapor) equilibrium line

We use a novel hybrid method to explore the temperature dependence of the solid-liquid interfacial tension of a system that consists of solid methane hydrate and liquid water. The calculated values along the three-phase (hydrate-liquid water-vapor) equilibrium line are obtained through the combination of available experimental measurements and computational results that are based on approaches at the atomistic scale, including molecular dynamics and Monte Carlo. An extensive comparison with available experimental and computational studies is performed, and a critical assessment and re-evaluation of previously reported data is presented.

Exploring CO2 @sI Clathrate Hydrates as CO2 Storage Agents by Computational Density Functional Approaches

The formation of specific clathrate hydrates and their transformation at given thermodynamic conditions depends on the interactions between the guest molecule/s and the host water lattice. Understanding their structural stability is essential to control structure-property relations involved in different technological applications. Thus, the energetic aspects relative to CO₂ @sI clathrate hydrate are investigated through the computation of the underlying interactions, dominated by hydrogen bonds and van der Waals forces, from first-principles electronic structure approaches. The stability of the CO₂ @sI clathrate is evaluated by combining bottom-up and top-down approaches. Guest-free and CO₂ guest-filled aperiodic cages, up to the gradually CO₂ occupation of the entire sI periodic unit cells were considered. Saturation, cohesive and binding energies for the systems are determined by employing a variety of density functionals and their performance is assessed. The dispersion corrections on the non-covalent interactions are found to be important in the stabilization of the CO₂ @sI energies, with the encapsulation of the CO₂ into guest-free/empty cage/lattice being always an energetically favorable process for most of the functionals studied. The PW86PBE functional with XDM or D3(BJ) dispersion corrections predicts a lattice constant in accord to the experimental values available, and simultaneously provides a reliable description for the guest-host interactions in the periodic CO₂ @sI crystal, as well as the energetics of its progressive single cage occupancy process. It has been found that the preferential orientation of the single CO₂ in the large sI crystal cages has a stabilizing effect on the hydrate, concluding that the CO₂ @sI structure is favored either by considering the individual building block cages or the complete sI unit cell crystal. Such benchmark and methodology cross-check studies benefit new data-driven model research by providing high-quality training information, with new insights that indicate the underlying factors governing their structure-driven stability, and triggering further investigations for controlling the stabilization of these promising long-term CO₂ storage materials.

Computational density-functional approaches on finite-size and guest-lattice effects in CO2@sII clathrate hydrate

We performed first-principles computations to investigate guest-host/host-host effects on the encapsulation of the CO₂ molecule in sII clathrate hydrates from finite-size clusters up to periodic 3D crystal lattice systems. Structural and energetic properties were first computed for the individual and first-neighbors clathrate-like sII cages, where highly accurate ab initio quantum chemical methods are available nowadays, allowing in this way the assessment of the density functional (DFT) theoretical approaches employed. The performance of exchange-correlation functionals together with recently developed dispersion-corrected schemes was evaluated in describing interactions in both short-range and long-range regions of the potential. On this basis, structural relaxations of the CO₂-filled and empty sII unit cells yield lattice and compressibility parameters comparable to experimental and previous theoretical values available for sII hydrates. According to these data, the CO₂ enclathration in the sII clathrate cages is a stabilizing process, either by considering both guest-host and host-host interactions in the complete unit cell or only the guest-water energies for the individual clathrate-like sII cages. CO₂@sII clathrates are predicted to be stable whatever the dispersion correction applied and in the case of single cage occupancy are found to be more stable than the CO₂@sI structures. Our results reveal that DFT approaches could provide a good reasonable description of the underlying interactions, enabling the investigation of formation and transformation processes as a function of temperature and pressure.

Molecular modelling techniques for predicting liquid-liquid interfacial properties of methanol plus alkane (n-hexane, n-heptane, n-octane) mixtures

In this work, the liquid-liquid interfacial properties of methanol plus n-alkane (n-hexane, n-heptane, n-octane) mixtures are investigated at atmospheric pressure by two complementary molecular modelling techniques; namely, molecular dynamic simulations (MD) and density gradient theory (DGT) coupled with the PC-SAFT (perturbed-chain statistical associating fluid theory) equation of state. Furthermore, two molecular models of methanol are used, which are based on a non-polarisable three site approach. On the one hand, is the original (flexible) TraPPE-UA model force field. On the other hand, is the rigid approximation denoted as OPLS/2016. In both cases, n-alkanes are modelled using the TraPPE-UA model. Simulations are performed using the direct coexistence technique in the ensemble. Special attention is paid to the comparison between the estimations obtained from different methanol models, the available experimental data and theoretical calculations. In all cases, the rigid model is capable of predicting the experimental phase equilibrium and interfacial properties accurately. Unsurprisingly, the methanol-rich density and interfacial tension are overestimated using the TraPPE model combined with Lorentz-Berthelot mixing rules for predicting the mixture behaviour. Accurate comparison between MD and DGT plus PC-SAFT requires consideration of the cross-interactions between individual influence parameters and fitting the βij values. This latter aspect is particularly important because it allows the exploitation of the link between the EOS model and the direct molecular simulation of the corresponding fluid. At the same time, it was demonstrated that the key property defining the interfacial tension value is the absolute concentration of methanol in the methanol-rich phase. This behaviour indicates that there are more hydrogens bonded with each other, and they interact favourably with an increasing number of carbon atoms in the alkane.

Structural Stability of the CO2 @sI Hydrate: a Bottom-Up Quantum Chemistry Approach on the Guest-Cage and Inter-Cage Interactions

Through reliable first-principles computations, we have demonstrated the impact of CO₂ molecules enclathration on the stability of sI clathrate hydrates. Given the delicate balance between the interaction energy components (van der Waals, hydrogen bonds) present on such systems, we follow a systematic bottom-up approach starting from the individual 5¹² and 5¹² 6² sI cages, up to all existing combinations of two-adjacent sI crystal cages to evaluate how such clathrate-like models perform on the evaluation of the guest-host and first-neighbors inter-cage effects, respectively. Interaction and binding energies of the CO₂ occupation of the sI cages were computed using DF-MP2 and different DFT/DFT-D electronic structure methodologies. The performance of selected DFT functionals, together with various semi-classical dispersion corrections schemes, were validated by comparison with reference ab initio DF-MP2 data, as well as experimental data from x-ray and neutron diffraction studies available. Our investigation confirms that the inclusion of the CO₂ in the cage/s is an energetically favorable process, with the CO₂ molecule preferring to occupy the large 5¹² 6² sI cages compared to the 5¹² ones. Further, the present results conclude on the rigidity of the water cages arrangements, showing the importance of the inter-cage couplings in the cluster models under study. In particular, the guest-cage interaction is the key factor for the preferential orientation of the captured CO₂ molecules in the sI cages, while the inter-cage interactions seems to cause minor distortions with the CO₂ guest neighbors interactions do not extending beyond the large 5¹² 6² sI cages. Such findings on these clathrate-like model systems are in accord with experimental observations, drawing a direct relevance to the structural stability of CO₂ @sI clathrates.

Molecular Dynamics Simulation Study on the Growth of Structure II Nitrogen Hydrate

Crystal growth of N₂ hydrate in a three-phase system consisting of N₂ hydrate, liquid water, and gaseous N₂ was performed by molecular dynamics simulation at 260 K. Pressure influence on hydrate growth was evaluated. The kinetic properties including the growth rates and cage occupancies of the newly formed hydrate and the diffusion coefficient and concentration of N₂ molecules in liquid phase were measured. The results showed that the growth of N₂ hydrate could be divided into two stages where N₂ molecules in gas phase had to dissolve in liquid phase and then form hydrate cages at the liquid-hydrate interface. The diffusion coefficient and concentration of N₂ in liquid phase increased linearly with increasing pressure. As the pressure rose from 50 to 100 MPa, the hydrate growth rate kept increasing from 0.11 to 0.62 cages·ns^-1·Å^-2 and then dropped down to around 0.40 cages·ns^-1·Å^-2 once the pressure surpassed 100 MPa. During the hydrate formation, the initial sII N₂ hydrate phase set in the system served as a template for the subsequent growth of N₂ hydrate so that no new crystal structure was found. Analysis on the cage occupancies revealed that the amount of cages occupied by two N₂ molecules increased evidently when the pressure was above 100 MPa, which slowed down the growth rate of hydrate cages. Additionally, a small fraction of defective cages including two N₂ molecules trapped in 5¹²6⁵ cages and three N₂ molecules trapped 5¹²6⁸ cages was observed during the hydrate growth.

Phase stability of the ice XVII-based CO2 chiral hydrate from molecular dynamics simulations

We computed the phase diagram of CO₂ hydrates at high pressure (HP), from 0.3 to 20 kbar, by means of molecular dynamics simulations. The two CO₂ hydrates known to occur in this pressure range are the cubic structure I (sI) clathrate and the HP hydrate, whose water framework is the recently discovered ice XVII. We investigated the stability of both hydrates upon heating (melting) as well as the phase changes upon compression. The CO₂-filled ice XVII is found to be more stable than the sI clathrate and than the mixture of ice VI and dry ice at pressure values ranging from 6 to 18 kbar and in a wide temperature range, although a phenomenological correction suggests that the stability should more realistically range from 6.5 to 13.5 kbar. Our simulation results support the current hypothesis that the HP hydrate is stable at temperatures above the melting curve of ice VI.

Simulation of Capture and Release Processes of Hydrogen by β-Hydroquinone Clathrate

Using molecular simulation techniques, we investigate the storage capabilities of H₂ gas by the clathrate of hydroquinone (HQ). Quantum mechanics calculations have been used to assess structure and interactions at the atomic scale and molecular dynamics to model the HQ clathrate at successive equilibriums during the processes of capture and release of H₂, as well as the diffusion of H₂ inside the clathrate structure. The thermodynamic conditions of the simulations performed try to reproduce closely the corresponding experimental procedures, with results that are in good agreement with literature observed trends. The results obtained contribute to depict a more complete and better substantiated image of the mechanisms involved in stability and in the processes of capture and release of H₂ by the HQ clathrate.

Grand Canonical Monte Carlo Simulations on Phase Equilibria of Methane, Carbon Dioxide, and Their Mixture Hydrates

The cage occupancy plays a crucial role in the 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 θ_L/θ_S and the abundance ratio of CO₂ to CH₄ vary with the temperature and pressure, which provide the prerequisite information for the 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.

A Systematic Protocol for Benchmarking Guest-Host Interactions by First-Principles Computations: Capturing CO2 in Clathrate Hydrates

Clathrate hydrates of CO₂ have been proposed as potential molecular materials in tackling important environmental problems related to greenhouse gases capture and storage. Despite the increasing interest in such hydrates and their technological applications, a molecular-level understanding of their formation and properties is still far from complete. Modeling interactions is a challenging and computationally demanding task, essential to reliably determine molecular properties. First-principles calculations for the CO₂ guest in all sI, sII, and sH clathrate cages were performed, and the nature of the guest-host interactions, dominated by both hydrogen-bond and van der Waals forces, was systematically investigated. Different families of density functionals, as well as pairwise CO₂ @H₂ O model potentials versus wavefunction-based quantum approaches were studied for CO₂ clathrate-like systems. Benchmark energies for new distance-dependent datasets, consisting of potential energy curves sampling representative configurations of the systems at the repulsive, near-equilibrium, and asymptotic/long-range regions of the full-dimensional surface, were generated, and a general protocol was proposed to assess the accuracy of such conventional and modern approaches at minimum and non-minimum orientations. Our results show that dispersion interactions are important in the guest-host stabilization energies of such clathrate cages, and the encapsulation of the CO₂ into guest-free clathrate cages is always energetically favorable. In addition, the orientation of CO₂ inside each cage was explored, and the ability of current promising approaches to accurately describe non-covalent CO₂ @H₂ O guest-host interactions in sI, sII, and sH clathrates was discussed, providing information for their applicability to future multiscale computer simulations.

Diffusion of gas mixtures in the sI hydrate structure

Replacing methane with carbon dioxide in gas hydrates has been suggested as a way of harvesting methane, while at the same time storing carbon dioxide. Experimental evidence suggests that this process is facilitated if gas mixtures are used instead of pure carbon dioxide. We studied the free energy barriers for diffusion of methane, carbon dioxide, nitrogen, and hydrogen in the sI hydrate structure using molecular simulation techniques. Cage hops between neighboring cages were considered with and without a water vacancy and with a potential inclusion of an additional gas molecule in either the initial or final cage. Our results give little evidence for enhanced methane and carbon dioxide diffusion if nitrogen is present as well. However, the inclusion of hydrogen seems to have a substantial effect as it diffuses rapidly and can easily enter occupied cages, which reduces the barriers of diffusion for the gas molecules that co-occupy a cage with hydrogen.

Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A Molecular Dynamics Study

We investigate the mechanism of a typical kinetic hydrate inhibitor (KHI), polyvinylcaprolactam (PVCap), which has been applied to prevent hydrate plugs from forming in gas pipe lines, using molecular dynamics simulations of crystal growth of ethylene oxide hydrate. Water-soluble ethylene oxide is chosen as a guest species to avoid problems associated with the presence of the gas phase in the simulation cell such as slow crystal growth. A PVCap dodecamer adsorbs irreversibly on the hydrate surface which grows at supercooling of 3 K when the hydrophobic part of two pendent groups are trapped in open cages at the surface. The amide hydrogen bonds make no contribution to the adsorption. PVCap can adsorb on various crystallographic planes of sI hydrate. This is in contrast to antifreeze proteins, each of which prefers a specific plane of ice. The trapped PVCap gives rise to necessarily the concave surface of the hydrate. The crystal growth rate decreases with increasing surface curvature, indicating that the inhibition by PVCap is explained by the Gibbs-Thomson effect.