An Accurate Model for Estimating H2 Solubility in Pure Water and Aqueous NaCl Solutions

Directionality of gravitational and thermal diffusive transport in geologic fluid storage

Diffusive transport has implications for the long-term status of underground storage of hydrogen (H_{2}) fuel and carbon dioxide (CO_{2}), technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, CO_{2} and H_{2} will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport ("Ostwald ripening"). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved CO_{2} and H_{2} driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for CO_{2} and H_{2} at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For CO_{2}, even geothermal gradients less than 10^{∘}C/km (far less than typical gradients of 25^{∘}C/km) are sufficient to induce downwards diffusion at depths relevant to storage. Diffusive transport of H_{2} is less affected but still reverses direction under typical gradients, e.g., 30^{∘}C/km, at a depth of 1000 m. This reversal occurs independent of the solute's thermophobicity or thermophilicity in aqueous solutions. The entropic contribution also modifies the magnitude of flux where geothermal gradients are present, with the largest diffusive fluxes estimated for CO_{2} with a 30^{∘}C/km gradient, despite the higher diffusion coefficient of H_{2}. We find a maximum flux on the order of 10^{-13} mol/(cm^{2}s) for CO_{2} in the 30^{∘}C/km scenario; significantly lower than literature estimates for maximum convective fluxes in moderate to high permeability formations. Contrary to previous studies, we find that in diffusion and convection will likely work in concert-both driving CO_{2} downwards, and both driving H_{2} upwards-for conditions representative of their respective storage reservoirs.

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.

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%.

Ab Initio Potential Energy Surface for NaCl-H2 with Correct Long-Range Behavior

We report a full dimensional ab initio potential energy surface for NaCl-H2 based on precise fitting of a large data set of CCSD(T)/aug-cc-pVTZ energies. A major goal of this fit is to describe the very long-range interaction accurately. This is done in this instance via the dipole-quadrupole interaction. The NaCl dipole and the H2 quadrupole are available through previous works over a large range of internuclear distances. We use these to obtain exact effect charges on each atom. Diffusion Monte Carlo calculations are done for the ground vibrational state using the new potential.