Monte Carlo simulations of high-pressure phase equilibria of CO2-H2O mixtures

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Atomic-Scale Insights into the Phase Behavior of Carbon Dioxide and Water from 313 to 573 K and 8 to 30 MPa

We performed molecular dynamics (MD) simulations of CO2 + H2O systems by employing widely used force fields (EPM2, TraPPE, and PPL models for CO2; SPC/E and TIP4P/2005 models for H2O). The phase behavior observed in our MD simulations is consistent with the coexistence lines obtained from previous experiments and SAFT-based theoretical models for the equations of state. Our structural analysis reveals a pronounced correlation between phase transitions and the structural orderliness. Specifically, the coordination number of Ow (oxygen in H2O) around other Ow significantly correlates with phase changes. In contrast, coordination numbers pertaining to the CO2 molecules show less sensitivity to the thermodynamic state of the system. Furthermore, our data indicate that a predominant number of H2O molecules exist as monomers without forming hydrogen bonds, particularly in a CO2-rich mixture, signaling a breakdown in the hydrogen bond network's orderliness, as evidenced by a marked decrease in tetrahedrality. These insights are crucial for a deeper atomic-level understanding of phase behaviors, contributing to the well-grounded design of CO2 injection under high-pressure and high-temperature conditions, where an atomic-scale perspective of the phase behavior is still lacking.

Interfacial Tensions, Solubilities, and Transport Properties of the H2/H2O/NaCl System: A Molecular Simulation Study

Data for several key thermodynamic and transport properties needed for technologies using hydrogen (H2), such as underground H2 storage and H2O electrolysis are scarce or completely missing. Force field-based Molecular Dynamics (MD) and Continuous Fractional Component Monte Carlo (CFCMC) simulations are carried out in this work to cover this gap. Extensive new data sets are provided for (a) interfacial tensions of H2 gas in contact with aqueous NaCl solutions for temperatures of (298 to 523) K, pressures of (1 to 600) bar, and molalities of (0 to 6) mol NaCl/kg H2O, (b) self-diffusivities of infinitely diluted H2 in aqueous NaCl solutions for temperatures of (298 to 723) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O, and (c) solubilities of H2 in aqueous NaCl solutions for temperatures of (298 to 363) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O. The force fields used are the TIP4P/2005 for H2O, the Madrid-2019 and the Madrid-Transport for NaCl, and the Vrabec and Marx for H2. Excellent agreement between the simulation results and available experimental data is found with average deviations lower than 10%.

Thermodiffusion of CO2 in Water by Nonequilibrium Molecular Dynamics Simulations

The components of a fluid mixture may segregate due to the Soret effect, a coupling phenomenon in which mass flux can be induced by a thermal gradient. In this work, we evaluate systematically the thermodiffusion of the CO₂-H₂O mixture, and the influence of the geothermal gradient on CO₂ segregation in deep saline aquifers in CO₂ storage. The eHeX method, a nonequilibrium molecular dynamics simulation approach, is judiciously selected to simulate the phenomenon. At 350 K, 400 bar, and CO₂ mole fraction of 0.02 (aquifer conditions), CO₂ accumulates on the cold side, and the thermal diffusion factor is close to 1 in a number of force fields. The lower the temperature, the higher is the separation and the thermal diffusion factor. In colder regions, water self-association is stronger, whereas the CO₂-H₂O cross-association and the CO₂-CO₂ interactions enhance at higher temperatures. Thermodiffusion and gravitational segregation have opposite effects on CO₂ segregation. At typical subsurface conditions, the Soret effect is more pronounced than gravity segregation, and CO₂ concentrates in the top (colder region). Our work sets the stage to model the effect of electrolytes on CO₂ segregation in subsurface aquifers and other areas of interest.

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.

Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations

Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.

Molecular simulation as a computational pharmaceutics tool to predict drug solubility, solubilization processes and partitioning

In this review we will discuss how computational methods, and in particular classical molecular dynamics simulations, can be used to calculate solubility of pharmaceutically relevant molecules and systems. To the extent possible, we focus on the non-technical details of these calculations, and try to show also the added value of a more thorough and detailed understanding of the solubilization process obtained by using computational simulations. Although the main focus is on classical molecular dynamics simulations, we also provide the reader with some insights into other computational techniques, such as the COSMO-method, and also discuss Flory-Huggins theory and solubility parameters. We hope that this review will serve as a valuable starting point for any pharmaceutical researcher, who has not yet fully explored the possibilities offered by computational approaches to solubility calculations.

Molecular Modeling of Thermodynamic and Transport Properties for CO2 and Aqueous Brines

Molecular simulation techniques using classical force-fields occupy the space between ab initio quantum mechanical methods and phenomenological correlations. In particular, Monte Carlo and molecular dynamics algorithms can be used to provide quantitative predictions of thermodynamic and transport properties of fluids relevant for geologic carbon sequestration at conditions for which experimental data are uncertain or not available. These methods can cover time and length scales far exceeding those of quantum chemical methods, while maintaining transferability and predictive power lacking from phenomenological correlations. The accuracy of predictions depends sensitively on the quality of the molecular models used. Many existing fixed-point-charge models for water and aqueous mixtures fail to represent accurately these fluid properties, especially when descriptions covering broad ranges of thermodynamic conditions are needed. Recent work on development of accurate models for water, CO₂, and dissolved salts, as well as their mixtures, is summarized in this Account. Polarizable models that can respond to the different dielectric environments in aqueous versus nonaqueous phases are necessary for predictions of properties over extended ranges of temperatures and pressures. Phase compositions and densities, activity coefficients of the dissolved salts, interfacial tensions, viscosities and diffusivities can be obtained in near-quantitative agreement to available experimental data, using relatively modest computational resources. In some cases, for example, for the composition of the CO₂-rich phase in coexistence with an aqueous phase, recent results from molecular simulations have helped discriminate among conflicting experimental data sets. The sensitivity of properties on the quality of the intermolecular interaction model varies significantly. Properties such as the phase compositions or electrolyte activity coefficients are much more sensitive than phase densities, viscosities, or component diffusivities. Strong confinement effects on physical properties in nanoscale media can also be directly obtained from molecular simulations. Future work on molecular modeling for CO₂ and aqueous brines is likely to be focused on more systematic generation of interaction models by utilizing quantum chemical as well as direct experimental measurements. New ion models need to be developed for use with the current generation of polarizable water models, including ion-ion interactions that will allow for accurate description of dense, mixed brines. Methods will need to be devised that go beyond the use of effective potentials for incorporation of quantum effects known to be important for water, and reactive force fields developed that can handle bond creation and breaking in systems with carbonate and silicate minerals. Another area of potential future work is the integration of molecular simulation methods in multiscale models for the chemical reactions leading to mineral dissolution and flow within the porous media in underground formations.

Molecular Dynamics Simulations of CO2/Water/Quartz Interfacial Properties: Impact of CO2 Dissolution in Water

The safe trapping of carbon dioxide (CO2) in deep saline aquifers is one of the major concerns of CO2 sequestration. The amount of capillary trapping is dominated by the capillary pressure of water and CO2 inside the reservoir, which in turn is controlled by the interfacial tension (IFT) and the contact angle (CA) of CO2/water/rock systems. The measurement of IFT and CA could be very challenging at reservoir conditions, especially in the presence of toxic cocontaminants. Thus, the ability to accurately predict these interfacial properties at reservoir conditions is very advantageous. Although the majority of existing molecular dynamics (MD) studies of CO2/water/mineral systems were able to capture the trends in IFT and CA variations with pressure and temperature, their predictions often deviated from experimental data, possibly due to erroneous models and/or overlooked chemical reactions. The objective of this study was to improve the MD predictions of IFT and CA of CO2/water/quartz systems at various pressure and temperature conditions by (i) considering the chemical reactions between CO2 and water and (ii) using a new molecular model for α-quartz surface. The results showed that the presence of carbonic acid at the CO2/water interface improved the predictions of IFT, especially at low temperature and high pressure where more CO2 dissolution occurs. On the other hand, the effect on CA was minor. The slight decrease in CA observed across the pressure range investigated could be attributed to an increase in the total number of H-bonds between fluid molecules and quartz surface.

Atomistic molecular dynamics simulations of CO₂ diffusivity in H₂O for a wide range of temperatures and pressures

Molecular dynamics simulations were employed for the calculation of diffusion coefficients of CO2 in H2O. Various combinations of existing force fields for H2O (SPC, SPC/E, and TIP4P/2005) and CO2 (EPM2 and TraPPE) were tested over a wide range of temperatures (283.15 K < T < 623.15 K) and pressures (0.1 MPa < P < 100.0 MPa). All force-field combinations qualitatively reproduce the trends of the experimental data; however, two specific combinations were found to be more accurate. In particular, at atmospheric pressure, the TIP4P/2005-EPM2 combination was found to perform better for temperatures lower than 323.15 K, while the SPC/E-TraPPE combination was found to perform better at higher temperatures. The pressure dependence of the diffusion coefficient of CO2 in H2O at constant temperature is shown to be negligible at temperatures lower than 473.15 K, in good agreement with experiments. As temperature increases, the pressure effect becomes substantial. The phenomenon is driven primarily by the higher compressibility of liquid H2O at near-critical conditions. Finally, a simple power-law-type phenomenological equation is proposed to correlate the simulation values; the proposed correlation should be useful for engineering calculations.