One strategy for geological sequestration of carbon dioxide (CO2) is to store it in solid form as a gas hydrate, or as a pool of liquid CO2 below a cap of its hydrate. The economic viability of this strategy can be improved by integrating it with the recovery of methane from its naturally occurring hydrate, such that the methane in the hydrates is replaced with carbon dioxide. Further, CO2 hydrates can also be stored in subsea sediments that are characterized by fine-grained silts, mud and clays, usually with very small mean pore diameters. Engineering any technology along these lines requires a fundamental understanding of both the thermodynamics and kinetics of CO2 hydrate formation in bulk as well as in confined geometries associated with the subsea sediment pores.

The principles of statistical mechanics, along with molecular-based computer simulations, provide a fundamental link between molecular-level structure and interactions and macroscopic properties. The Debenedetti group is using molecular dynamics (MD), Monte Carlo (MC) and path sampling simulations to study CO2 hydrate phase behavior and the kinetics of hydrate formation, both in bulk and in nanoscale confinement. These studies will provide insights into the molecular basis of CO2 hydrate stability and formation kinetics and will thereby provide the knowledge needed for the rational design of hydrate-based CO2 storage systems.


Dissociation curve of CO2 hydrate from MD simulations

Pablo Debenedetti and postdoctoral researcher Sapna Sarupria are developing predictive tools for the calculation of CO2 hydrate equilibrium phase behavior and formation kinetics under conditions relevant to CO2 capture and storage (e.g. in the presence of NaCl, in nano-scale confinement, etc). As a first step in this direction, they are comparing simulation-based predictions of CO2 hydrate dissociation temperatures and pressures with experimental measurements. CO2 hydrate phase boundaries in bulk have been well established experimentally. However, no equivalent curve has been determined in simulations.

Molecular dynamics (MD) is a powerful simulation tool that can provide an understanding of the relationship between atomic-level forces and thermodynamic properties. In this project, they focus on CO2 hydrate formation and stability. They first calibrate the intermolecular potentials used in their simulations of CO2 hydrate by computing the melting (dissociation) curve of CO2 hydrates in the temperature-pressure (T-P) plane. The simulation system consists of CO2 hydrate and water as shown in Figure 12. The system is equilibrated at low temperature, where the CO2 hydrate is stable. The equilibrated structure is used to start simulations at different temperatures chosen using experimental results as a guideline. Simulations are then performed at various pressures to obtain the dissociation temperature of CO2 hydrate at each pressure. These calculations are currently in progress, and will provide the dissociation curve for the given water and CO2 model. The results will be used as a reference for future studies on the effect of various factors, such as confinement, and the presence of salts and alcohols on the stability of CO2 hydrates.

CO2 hydrate has sI hydrate structure, the unit cell of which consists of six large (51262) and two small (512) cages. The cage occupancy corresponds to the number of cages filled by guest molecules. Although some studies have suggested that hydrate stability is affected by cage occupancy, no systematic studies have been performed of this important parameter. The researchers will supplement their studies by exploring the effect of cage occupancy to provide insights into hydrate stability with ocean depth, under conditions relevant to storage of CO2 hydrates in ocean beds.

Figure 12. Snapshot of CO2 hydrate and water system used in their simulations. CO2 molecules are shown in green. Hydrogen bonds between water molecules in the hydrate structure are shown as red dashed lines. Liquid water is shown in blue and water in the hydrate structure is shown in red (oxygen) and white (hydrogens).


Effect of nanoscale confinement on phase equilibrium

The second facet of the Debenedetti group’s work is rooted in fundamental understanding of the effects of nanoscopic confinement on phase behavior. Such knowledge is important for modeling CO2 phase behavior during leaks from geological reservoirs, as well as hydrate phase behavior in the presence of high-surface area silts and clays on ocean floors. Previous studies show that such confinement causes a shift in phase transitions such as vapor-liquid, liquid-liquid and solid-liquid equilibrium. A systematic understanding of the shifts in the coexistence region in confinement does not exist at present.

A fundamental question that arises when studying phase transitions in confinement is their dimensionality. Debenedetti and graduate student Yang Liu focus on the critical behavior in confined systems and determine its dimensionality class. In extremely narrow pores, two-dimensional behavior is expected and for large pores, three-dimensional behavior is approached in the limit where the fluid does not ‘feel’ the presence of the surface. Between these two limits a cross-over from two- to three-dimensional behavior is observed. To investigate this problem systematically, they studied the vapor-liquid (V-L) transition of two different fluids in confinement: (1) Lennard-Jones (LJ) fluid: The Lennard-Jones potential can capture the phase transitions of simple fluids such as argon and krypton. (2) Water (ST2 water model): In ST2 model, each water molecule has a tetrahedral structure with oxygen at the center and four point charges surrounding it. Studying ST2 water enables them to consider the case of fluids that involve both long range electrostatic and short-range directional interactions.

Figure 13. Effective dimensionality of confined Lennard‐Jones (LJ) fluid as a function of wall separation (H) and wall size (Lx=Ly). The units of x‐ and y‐ axis are scaled by the LJ size parameter and H is in units of LJ size parameter. The squares correspond to 2D and triangles represent 3D behavior.. The transition line indicating the crossover from 3D to 2D behavior is also shown (red dashed line).

Figure 13 shows the dependence of the effective dimensionality of the confined Lennard-Jones fluid as a function of the separation between the confining walls (H) and the wall size (Lx=Ly). As expected, for narrow pores, the system displays two-dimensional (2D) behavior for all system sizes and for larger wall separations the behavior is always three-dimensional (3D). The crossover between the two limits can be marked by a “transition line”, as indicated in the figure. To their knowledge, this is the first example of a complete mapping of the evolution of the dimensionality of a first-order transition in a confined system as a function of both degree of confinement and system size. A similar behavior is also observed in the case of vapor-liquid transition in ST2 water, suggesting the generality of these results. These calculations provide a basis for the engineering design of systems involving phase transitions in nanoscopic geometries, such as are relevant for CO2 hydrate formation in clays and fine-grained silts.

Figure 14 shows the difference in the critical temperature at infinite system size, Tc∞(H) ,for a given pore width (H) relative to that in bulk, Tcbulk, as a function of the pore width. The shift in critical temperature, Tc∞(H)−Tcbulk , varies linearly with 1/H at large pore widths. This linear relationship breaks down around H=2, corresponding to two fluid layers between the walls, and no significant change in Tc∞(H)−Tcbulk is observed for smaller pores. Similar behavior is observed for both two- and three- dimensional criticality as well as for ST2 water.

Figure 14. Deviation of the critical temperature, T*c for given wall separation (H), from the bulk value, T*c(bulk) as a function of inverse wall separation for the Lennard‐Jones system.

This study is a significant step in the direction of providing fundamental understanding of phase transitions in nanoscale confinement for the simple LJ fluid, as well as in more complex fluids, like water. The similarity in the critical behavior of Lennard-Jones fluid and water, as well as their consistency with previous studies on the square-well fluid, suggest a broad generality of these findings. A similar approach applied to the study of phase transitions relevant to carbon capture and storage (e.g., CO2 hydrate formation in nanoscopic geometries such as pores, fine-grained silts and clays, CO2-water phase behavior in confinement; see Future Work) will yield knowledge on how the region of phase stability (e.g. temperature, pressure) will shift as a result of nanoscale confinement.